LMFDB - Embedded newform 6015.2.a.f.1.4

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:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-2.61575 q^{2} -1.00000 q^{3} +4.84213 q^{4} -1.00000 q^{5} +2.61575 q^{6} +3.80178 q^{7} -7.43431 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.61575 q^{2} -1.00000 q^{3} +4.84213 q^{4} -1.00000 q^{5} +2.61575 q^{6} +3.80178 q^{7} -7.43431 q^{8} +1.00000 q^{9} +2.61575 q^{10} -2.35061 q^{11} -4.84213 q^{12} +1.16032 q^{13} -9.94450 q^{14} +1.00000 q^{15} +9.76200 q^{16} -7.43248 q^{17} -2.61575 q^{18} -7.79377 q^{19} -4.84213 q^{20} -3.80178 q^{21} +6.14859 q^{22} -2.57001 q^{23} +7.43431 q^{24} +1.00000 q^{25} -3.03511 q^{26} -1.00000 q^{27} +18.4087 q^{28} +7.64603 q^{29} -2.61575 q^{30} +9.13454 q^{31} -10.6663 q^{32} +2.35061 q^{33} +19.4415 q^{34} -3.80178 q^{35} +4.84213 q^{36} +7.38946 q^{37} +20.3865 q^{38} -1.16032 q^{39} +7.43431 q^{40} -0.798023 q^{41} +9.94450 q^{42} -6.13950 q^{43} -11.3820 q^{44} -1.00000 q^{45} +6.72249 q^{46} +4.48005 q^{47} -9.76200 q^{48} +7.45353 q^{49} -2.61575 q^{50} +7.43248 q^{51} +5.61843 q^{52} +0.880104 q^{53} +2.61575 q^{54} +2.35061 q^{55} -28.2636 q^{56} +7.79377 q^{57} -20.0001 q^{58} +4.50026 q^{59} +4.84213 q^{60} +4.55807 q^{61} -23.8937 q^{62} +3.80178 q^{63} +8.37638 q^{64} -1.16032 q^{65} -6.14859 q^{66} +1.67345 q^{67} -35.9891 q^{68} +2.57001 q^{69} +9.94450 q^{70} +14.1788 q^{71} -7.43431 q^{72} -12.0104 q^{73} -19.3290 q^{74} -1.00000 q^{75} -37.7385 q^{76} -8.93649 q^{77} +3.03511 q^{78} -15.3068 q^{79} -9.76200 q^{80} +1.00000 q^{81} +2.08743 q^{82} -9.92913 q^{83} -18.4087 q^{84} +7.43248 q^{85} +16.0594 q^{86} -7.64603 q^{87} +17.4751 q^{88} +3.61243 q^{89} +2.61575 q^{90} +4.41128 q^{91} -12.4443 q^{92} -9.13454 q^{93} -11.7187 q^{94} +7.79377 q^{95} +10.6663 q^{96} -19.4066 q^{97} -19.4966 q^{98} -2.35061 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) $ 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9} + 7 q^{10} - q^{11} - 45 q^{12} - 8 q^{13} - 4 q^{14} + 36 q^{15} + 63 q^{16} - 50 q^{17} - 7 q^{18} + 15 q^{19} - 45 q^{20} - 2 q^{21} + 7 q^{22} - 32 q^{23} + 24 q^{24} + 36 q^{25} - 12 q^{26} - 36 q^{27} - 10 q^{28} + 7 q^{29} - 7 q^{30} + 7 q^{31} - 50 q^{32} + q^{33} + 8 q^{34} - 2 q^{35} + 45 q^{36} - 10 q^{37} - 48 q^{38} + 8 q^{39} + 24 q^{40} - 31 q^{41} + 4 q^{42} + 27 q^{43} - 9 q^{44} - 36 q^{45} + 23 q^{46} - 46 q^{47} - 63 q^{48} + 48 q^{49} - 7 q^{50} + 50 q^{51} - 14 q^{52} - 39 q^{53} + 7 q^{54} + q^{55} - 29 q^{56} - 15 q^{57} - 26 q^{58} - 9 q^{59} + 45 q^{60} + 5 q^{61} - 65 q^{62} + 2 q^{63} + 90 q^{64} + 8 q^{65} - 7 q^{66} + 18 q^{67} - 128 q^{68} + 32 q^{69} + 4 q^{70} + 4 q^{71} - 24 q^{72} - 45 q^{73} - 22 q^{74} - 36 q^{75} + 26 q^{76} - 38 q^{77} + 12 q^{78} + 25 q^{79} - 63 q^{80} + 36 q^{81} - 5 q^{82} - 71 q^{83} + 10 q^{84} + 50 q^{85} + 3 q^{86} - 7 q^{87} - 9 q^{88} - 39 q^{89} + 7 q^{90} + 19 q^{91} - 95 q^{92} - 7 q^{93} + 16 q^{94} - 15 q^{95} + 50 q^{96} - 61 q^{97} - 76 q^{98} - q^{99}+O(q^{100}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9 + 7 * q^10 - q^11 - 45 * q^12 - 8 * q^13 - 4 * q^14 + 36 * q^15 + 63 * q^16 - 50 * q^17 - 7 * q^18 + 15 * q^19 - 45 * q^20 - 2 * q^21 + 7 * q^22 - 32 * q^23 + 24 * q^24 + 36 * q^25 - 12 * q^26 - 36 * q^27 - 10 * q^28 + 7 * q^29 - 7 * q^30 + 7 * q^31 - 50 * q^32 + q^33 + 8 * q^34 - 2 * q^35 + 45 * q^36 - 10 * q^37 - 48 * q^38 + 8 * q^39 + 24 * q^40 - 31 * q^41 + 4 * q^42 + 27 * q^43 - 9 * q^44 - 36 * q^45 + 23 * q^46 - 46 * q^47 - 63 * q^48 + 48 * q^49 - 7 * q^50 + 50 * q^51 - 14 * q^52 - 39 * q^53 + 7 * q^54 + q^55 - 29 * q^56 - 15 * q^57 - 26 * q^58 - 9 * q^59 + 45 * q^60 + 5 * q^61 - 65 * q^62 + 2 * q^63 + 90 * q^64 + 8 * q^65 - 7 * q^66 + 18 * q^67 - 128 * q^68 + 32 * q^69 + 4 * q^70 + 4 * q^71 - 24 * q^72 - 45 * q^73 - 22 * q^74 - 36 * q^75 + 26 * q^76 - 38 * q^77 + 12 * q^78 + 25 * q^79 - 63 * q^80 + 36 * q^81 - 5 * q^82 - 71 * q^83 + 10 * q^84 + 50 * q^85 + 3 * q^86 - 7 * q^87 - 9 * q^88 - 39 * q^89 + 7 * q^90 + 19 * q^91 - 95 * q^92 - 7 * q^93 + 16 * q^94 - 15 * q^95 + 50 * q^96 - 61 * q^97 - 76 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.61575	−1.84961	−0.924806	−	0.380438i	$-0.875773\pi$
$2$	−2.61575	−1.84961	−0.924806	+	0.380438i	$0.875773\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.84213	2.42107
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.61575	1.06787
$7$	3.80178	1.43694	0.718469	−	0.695559i	$-0.244843\pi$
$7$	3.80178	1.43694	0.718469	+	0.695559i	$0.244843\pi$
$8$	−7.43431	−2.62842
$9$	1.00000	0.333333
$10$	2.61575	0.827172
$11$	−2.35061	−0.708735	−0.354367	−	0.935106i	$-0.615304\pi$
$11$	−2.35061	−0.708735	−0.354367	+	0.935106i	$0.615304\pi$
$12$	−4.84213	−1.39780
$13$	1.16032	0.321815	0.160908	−	0.986969i	$-0.448558\pi$
$13$	1.16032	0.321815	0.160908	+	0.986969i	$0.448558\pi$
$14$	−9.94450	−2.65778
$15$	1.00000	0.258199
$16$	9.76200	2.44050
$17$	−7.43248	−1.80264	−0.901321	−	0.433153i	$-0.857401\pi$
$17$	−7.43248	−1.80264	−0.901321	+	0.433153i	$0.857401\pi$
$18$	−2.61575	−0.616538
$19$	−7.79377	−1.78801	−0.894007	−	0.448054i	$-0.852117\pi$
$19$	−7.79377	−1.78801	−0.894007	+	0.448054i	$0.852117\pi$
$20$	−4.84213	−1.08273
$21$	−3.80178	−0.829616
$22$	6.14859	1.31088
$23$	−2.57001	−0.535884	−0.267942	−	0.963435i	$-0.586344\pi$
$23$	−2.57001	−0.535884	−0.267942	+	0.963435i	$0.586344\pi$
$24$	7.43431	1.51752
$25$	1.00000	0.200000
$26$	−3.03511	−0.595233
$27$	−1.00000	−0.192450
$28$	18.4087	3.47892
$29$	7.64603	1.41983	0.709916	−	0.704286i	$-0.248733\pi$
$29$	7.64603	1.41983	0.709916	+	0.704286i	$0.248733\pi$
$30$	−2.61575	−0.477568
$31$	9.13454	1.64061	0.820306	−	0.571925i	$-0.193803\pi$
$31$	9.13454	1.64061	0.820306	+	0.571925i	$0.193803\pi$
$32$	−10.6663	−1.88556
$33$	2.35061	0.409188
$34$	19.4415	3.33419
$35$	−3.80178	−0.642618
$36$	4.84213	0.807022
$37$	7.38946	1.21482	0.607410	−	0.794388i	$-0.292209\pi$
$37$	7.38946	1.21482	0.607410	+	0.794388i	$0.292209\pi$
$38$	20.3865	3.30713
$39$	−1.16032	−0.185800
$40$	7.43431	1.17547
$41$	−0.798023	−0.124630	−0.0623151	−	0.998057i	$-0.519848\pi$
$41$	−0.798023	−0.124630	−0.0623151	+	0.998057i	$0.519848\pi$
$42$	9.94450	1.53447
$43$	−6.13950	−0.936264	−0.468132	−	0.883658i	$-0.655073\pi$
$43$	−6.13950	−0.936264	−0.468132	+	0.883658i	$0.655073\pi$
$44$	−11.3820	−1.71589
$45$	−1.00000	−0.149071
$46$	6.72249	0.991178
$47$	4.48005	0.653482	0.326741	−	0.945114i	$-0.394049\pi$
$47$	4.48005	0.653482	0.326741	+	0.945114i	$0.394049\pi$
$48$	−9.76200	−1.40902
$49$	7.45353	1.06479
$50$	−2.61575	−0.369923
$51$	7.43248	1.04076
$52$	5.61843	0.779136
$53$	0.880104	0.120892	0.0604458	−	0.998171i	$-0.480748\pi$
$53$	0.880104	0.120892	0.0604458	+	0.998171i	$0.480748\pi$
$54$	2.61575	0.355958
$55$	2.35061	0.316956
$56$	−28.2636	−3.77688
$57$	7.79377	1.03231
$58$	−20.0001	−2.62614
$59$	4.50026	0.585884	0.292942	−	0.956130i	$-0.405366\pi$
$59$	4.50026	0.585884	0.292942	+	0.956130i	$0.405366\pi$
$60$	4.84213	0.625117
$61$	4.55807	0.583601	0.291801	−	0.956479i	$-0.405746\pi$
$61$	4.55807	0.583601	0.291801	+	0.956479i	$0.405746\pi$
$62$	−23.8937	−3.03450
$63$	3.80178	0.478979
$64$	8.37638	1.04705
$65$	−1.16032	−0.143920
$66$	−6.14859	−0.756840
$67$	1.67345	0.204444	0.102222	−	0.994762i	$-0.467405\pi$
$67$	1.67345	0.204444	0.102222	+	0.994762i	$0.467405\pi$
$68$	−35.9891	−4.36432
$69$	2.57001	0.309393
$70$	9.94450	1.18859
$71$	14.1788	1.68271	0.841357	−	0.540480i	$-0.181757\pi$
$71$	14.1788	1.68271	0.841357	+	0.540480i	$0.181757\pi$
$72$	−7.43431	−0.876141
$73$	−12.0104	−1.40571	−0.702856	−	0.711332i	$-0.748092\pi$
$73$	−12.0104	−1.40571	−0.702856	+	0.711332i	$0.748092\pi$
$74$	−19.3290	−2.24695
$75$	−1.00000	−0.115470
$76$	−37.7385	−4.32890
$77$	−8.93649	−1.01841
$78$	3.03511	0.343658
$79$	−15.3068	−1.72215	−0.861074	−	0.508480i	$-0.830208\pi$
$79$	−15.3068	−1.72215	−0.861074	+	0.508480i	$0.830208\pi$
$80$	−9.76200	−1.09142
$81$	1.00000	0.111111
$82$	2.08743	0.230518
$83$	−9.92913	−1.08986	−0.544932	−	0.838480i	$-0.683444\pi$
$83$	−9.92913	−1.08986	−0.544932	+	0.838480i	$0.683444\pi$
$84$	−18.4087	−2.00856
$85$	7.43248	0.806166
$86$	16.0594	1.73173
$87$	−7.64603	−0.819741
$88$	17.4751	1.86286
$89$	3.61243	0.382917	0.191458	−	0.981501i	$-0.438678\pi$
$89$	3.61243	0.382917	0.191458	+	0.981501i	$0.438678\pi$
$90$	2.61575	0.275724
$91$	4.41128	0.462428
$92$	−12.4443	−1.29741
$93$	−9.13454	−0.947208
$94$	−11.7187	−1.20869
$95$	7.79377	0.799624
$96$	10.6663	1.08863
$97$	−19.4066	−1.97044	−0.985222	−	0.171280i	$-0.945210\pi$
$97$	−19.4066	−1.97044	−0.985222	+	0.171280i	$0.945210\pi$
$98$	−19.4966	−1.96945
$99$	−2.35061	−0.236245
$100$	4.84213	0.484213
$101$	−7.06594	−0.703088	−0.351544	−	0.936171i	$-0.614343\pi$
$101$	−7.06594	−0.703088	−0.351544	+	0.936171i	$0.614343\pi$
$102$	−19.4415	−1.92499
$103$	12.6112	1.24262	0.621308	−	0.783567i	$-0.286602\pi$
$103$	12.6112	1.24262	0.621308	+	0.783567i	$0.286602\pi$
$104$	−8.62618	−0.845867
$105$	3.80178	0.371016
$106$	−2.30213	−0.223603
$107$	15.8042	1.52785	0.763926	−	0.645303i	$-0.223269\pi$
$107$	15.8042	1.52785	0.763926	+	0.645303i	$0.223269\pi$
$108$	−4.84213	−0.465935
$109$	7.71374	0.738842	0.369421	−	0.929262i	$-0.379556\pi$
$109$	7.71374	0.738842	0.369421	+	0.929262i	$0.379556\pi$
$110$	−6.14859	−0.586245
$111$	−7.38946	−0.701377
$112$	37.1130	3.50685
$113$	15.5372	1.46162	0.730809	−	0.682582i	$-0.239143\pi$
$113$	15.5372	1.46162	0.730809	+	0.682582i	$0.239143\pi$
$114$	−20.3865	−1.90937
$115$	2.57001	0.239655
$116$	37.0231	3.43751
$117$	1.16032	0.107272
$118$	−11.7716	−1.08366
$119$	−28.2567	−2.59028
$120$	−7.43431	−0.678656
$121$	−5.47465	−0.497695
$122$	−11.9228	−1.07944
$123$	0.798023	0.0719553
$124$	44.2307	3.97203
$125$	−1.00000	−0.0894427
$126$	−9.94450	−0.885926
$127$	−10.5975	−0.940376	−0.470188	−	0.882566i	$-0.655814\pi$
$127$	−10.5975	−0.940376	−0.470188	+	0.882566i	$0.655814\pi$
$128$	−0.577866	−0.0510766
$129$	6.13950	0.540552
$130$	3.03511	0.266196
$131$	9.83993	0.859718	0.429859	−	0.902896i	$-0.358563\pi$
$131$	9.83993	0.859718	0.429859	+	0.902896i	$0.358563\pi$
$132$	11.3820	0.990672
$133$	−29.6302	−2.56926
$134$	−4.37731	−0.378142
$135$	1.00000	0.0860663
$136$	55.2553	4.73811
$137$	−16.3998	−1.40113	−0.700563	−	0.713590i	$-0.747068\pi$
$137$	−16.3998	−1.40113	−0.700563	+	0.713590i	$0.747068\pi$
$138$	−6.72249	−0.572257
$139$	22.5388	1.91172	0.955858	−	0.293828i	$-0.0949293\pi$
$139$	22.5388	1.91172	0.955858	+	0.293828i	$0.0949293\pi$
$140$	−18.4087	−1.55582
$141$	−4.48005	−0.377288
$142$	−37.0882	−3.11237
$143$	−2.72746	−0.228081
$144$	9.76200	0.813500
$145$	−7.64603	−0.634968
$146$	31.4162	2.60002
$147$	−7.45353	−0.614757
$148$	35.7808	2.94116
$149$	13.1930	1.08081	0.540405	−	0.841405i	$-0.318271\pi$
$149$	13.1930	1.08081	0.540405	+	0.841405i	$0.318271\pi$
$150$	2.61575	0.213575
$151$	−0.00253793	−0.000206534 0	−0.000103267	−	1.00000i	$-0.500033\pi$
$151$	−0.00253793	−0.000206534 0	−0.000103267		1.00000i	$0.500033\pi$
$152$	57.9413	4.69966
$153$	−7.43248	−0.600880
$154$	23.3756	1.88366
$155$	−9.13454	−0.733704
$156$	−5.61843	−0.449834
$157$	−9.92804	−0.792344	−0.396172	−	0.918176i	$-0.629662\pi$
$157$	−9.92804	−0.792344	−0.396172	+	0.918176i	$0.629662\pi$
$158$	40.0387	3.18531
$159$	−0.880104	−0.0697968
$160$	10.6663	0.843246
$161$	−9.77061	−0.770032
$162$	−2.61575	−0.205513
$163$	9.11591	0.714013	0.357006	−	0.934102i	$-0.383797\pi$
$163$	9.11591	0.714013	0.357006	+	0.934102i	$0.383797\pi$
$164$	−3.86413	−0.301738
$165$	−2.35061	−0.182994
$166$	25.9721	2.01583
$167$	−20.3193	−1.57235	−0.786176	−	0.618002i	$-0.787942\pi$
$167$	−20.3193	−1.57235	−0.786176	+	0.618002i	$0.787942\pi$
$168$	28.2636	2.18058
$169$	−11.6537	−0.896435
$170$	−19.4415	−1.49109
$171$	−7.79377	−0.596004
$172$	−29.7283	−2.26676
$173$	−13.9026	−1.05699	−0.528497	−	0.848935i	$-0.677244\pi$
$173$	−13.9026	−1.05699	−0.528497	+	0.848935i	$0.677244\pi$
$174$	20.0001	1.51620
$175$	3.80178	0.287388
$176$	−22.9466	−1.72967
$177$	−4.50026	−0.338261
$178$	−9.44920	−0.708248
$179$	−18.0809	−1.35143	−0.675714	−	0.737164i	$-0.736165\pi$
$179$	−18.0809	−1.35143	−0.675714	+	0.737164i	$0.736165\pi$
$180$	−4.84213	−0.360911
$181$	17.7671	1.32062	0.660310	−	0.750993i	$-0.270425\pi$
$181$	17.7671	1.32062	0.660310	+	0.750993i	$0.270425\pi$
$182$	−11.5388	−0.855313
$183$	−4.55807	−0.336942
$184$	19.1062	1.40853
$185$	−7.38946	−0.543284
$186$	23.8937	1.75197
$187$	17.4708	1.27759
$188$	21.6930	1.58212
$189$	−3.80178	−0.276539
$190$	−20.3865	−1.47899
$191$	16.3969	1.18644	0.593219	−	0.805041i	$-0.297857\pi$
$191$	16.3969	1.18644	0.593219	+	0.805041i	$0.297857\pi$
$192$	−8.37638	−0.604513
$193$	−7.20262	−0.518456	−0.259228	−	0.965816i	$-0.583468\pi$
$193$	−7.20262	−0.518456	−0.259228	+	0.965816i	$0.583468\pi$
$194$	50.7628	3.64456
$195$	1.16032	0.0830923
$196$	36.0910	2.57793
$197$	−13.5298	−0.963962	−0.481981	−	0.876182i	$-0.660082\pi$
$197$	−13.5298	−0.963962	−0.481981	+	0.876182i	$0.660082\pi$
$198$	6.14859	0.436962
$199$	−1.92721	−0.136616	−0.0683081	−	0.997664i	$-0.521760\pi$
$199$	−1.92721	−0.136616	−0.0683081	+	0.997664i	$0.521760\pi$
$200$	−7.43431	−0.525685
$201$	−1.67345	−0.118036
$202$	18.4827	1.30044
$203$	29.0685	2.04021
$204$	35.9891	2.51974
$205$	0.798023	0.0557363
$206$	−32.9876	−2.29836
$207$	−2.57001	−0.178628
$208$	11.3271	0.785390
$209$	18.3201	1.26723
$210$	−9.94450	−0.686235
$211$	−24.8692	−1.71207	−0.856034	−	0.516919i	$-0.827079\pi$
$211$	−24.8692	−1.71207	−0.856034	+	0.516919i	$0.827079\pi$
$212$	4.26158	0.292687
$213$	−14.1788	−0.971515
$214$	−41.3399	−2.82594
$215$	6.13950	0.418710
$216$	7.43431	0.505840
$217$	34.7275	2.35746
$218$	−20.1772	−1.36657
$219$	12.0104	0.811589
$220$	11.3820	0.767371
$221$	−8.62406	−0.580117
$222$	19.3290	1.29728
$223$	12.7981	0.857022	0.428511	−	0.903537i	$-0.359038\pi$
$223$	12.7981	0.857022	0.428511	+	0.903537i	$0.359038\pi$
$224$	−40.5510	−2.70943
$225$	1.00000	0.0666667
$226$	−40.6414	−2.70343
$227$	−7.25239	−0.481358	−0.240679	−	0.970605i	$-0.577370\pi$
$227$	−7.25239	−0.481358	−0.240679	+	0.970605i	$0.577370\pi$
$228$	37.7385	2.49929
$229$	−0.638914	−0.0422206	−0.0211103	−	0.999777i	$-0.506720\pi$
$229$	−0.638914	−0.0422206	−0.0211103	+	0.999777i	$0.506720\pi$
$230$	−6.72249	−0.443268
$231$	8.93649	0.587978
$232$	−56.8429	−3.73192
$233$	−10.6992	−0.700928	−0.350464	−	0.936576i	$-0.613976\pi$
$233$	−10.6992	−0.700928	−0.350464	+	0.936576i	$0.613976\pi$
$234$	−3.03511	−0.198411
$235$	−4.48005	−0.292246
$236$	21.7909	1.41847
$237$	15.3068	0.994283
$238$	73.9123	4.79102
$239$	−12.2367	−0.791527	−0.395764	−	0.918352i	$-0.629520\pi$
$239$	−12.2367	−0.791527	−0.395764	+	0.918352i	$0.629520\pi$
$240$	9.76200	0.630134
$241$	−9.78583	−0.630361	−0.315180	−	0.949032i	$-0.602065\pi$
$241$	−9.78583	−0.630361	−0.315180	+	0.949032i	$0.602065\pi$
$242$	14.3203	0.920544
$243$	−1.00000	−0.0641500
$244$	22.0708	1.41294
$245$	−7.45353	−0.476189
$246$	−2.08743	−0.133089
$247$	−9.04327	−0.575410
$248$	−67.9090	−4.31223
$249$	9.92913	0.629233
$250$	2.61575	0.165434
$251$	−10.9343	−0.690168	−0.345084	−	0.938572i	$-0.612149\pi$
$251$	−10.9343	−0.690168	−0.345084	+	0.938572i	$0.612149\pi$
$252$	18.4087	1.15964
$253$	6.04108	0.379799
$254$	27.7204	1.73933
$255$	−7.43248	−0.465440
$256$	−15.2412	−0.952575
$257$	25.8099	1.60998	0.804988	−	0.593290i	$-0.202171\pi$
$257$	25.8099	1.60998	0.804988	+	0.593290i	$0.202171\pi$
$258$	−16.0594	−0.999813
$259$	28.0931	1.74562
$260$	−5.61843	−0.348440
$261$	7.64603	0.473278
$262$	−25.7388	−1.59015
$263$	−11.9439	−0.736494	−0.368247	−	0.929728i	$-0.620042\pi$
$263$	−11.9439	−0.736494	−0.368247	+	0.929728i	$0.620042\pi$
$264$	−17.4751	−1.07552
$265$	−0.880104	−0.0540644
$266$	77.5051	4.75214
$267$	−3.61243	−0.221077
$268$	8.10305	0.494973
$269$	10.2715	0.626267	0.313133	−	0.949709i	$-0.398621\pi$
$269$	10.2715	0.626267	0.313133	+	0.949709i	$0.398621\pi$
$270$	−2.61575	−0.159189
$271$	−0.942577	−0.0572575	−0.0286287	−	0.999590i	$-0.509114\pi$
$271$	−0.942577	−0.0572575	−0.0286287	+	0.999590i	$0.509114\pi$
$272$	−72.5559	−4.39935
$273$	−4.41128	−0.266983
$274$	42.8976	2.59154
$275$	−2.35061	−0.141747
$276$	12.4443	0.749060
$277$	0.928675	0.0557987	0.0278993	−	0.999611i	$-0.491118\pi$
$277$	0.928675	0.0557987	0.0278993	+	0.999611i	$0.491118\pi$
$278$	−58.9558	−3.53594
$279$	9.13454	0.546871
$280$	28.2636	1.68907
$281$	−2.15984	−0.128845	−0.0644227	−	0.997923i	$-0.520521\pi$
$281$	−2.15984	−0.128845	−0.0644227	+	0.997923i	$0.520521\pi$
$282$	11.7187	0.697837
$283$	−27.2926	−1.62237	−0.811187	−	0.584787i	$-0.801178\pi$
$283$	−27.2926	−1.62237	−0.811187	+	0.584787i	$0.801178\pi$
$284$	68.6557	4.07396
$285$	−7.79377	−0.461663
$286$	7.13434	0.421862
$287$	−3.03391	−0.179086
$288$	−10.6663	−0.628518
$289$	38.2418	2.24952
$290$	20.0001	1.17445
$291$	19.4066	1.13764
$292$	−58.1560	−3.40333
$293$	8.07739	0.471886	0.235943	−	0.971767i	$-0.424182\pi$
$293$	8.07739	0.471886	0.235943	+	0.971767i	$0.424182\pi$
$294$	19.4966	1.13706
$295$	−4.50026	−0.262015
$296$	−54.9355	−3.19306
$297$	2.35061	0.136396
$298$	−34.5094	−1.99908
$299$	−2.98203	−0.172456
$300$	−4.84213	−0.279561
$301$	−23.3410	−1.34535
$302$	0.00663858	0.000382007 0
$303$	7.06594	0.405928
$304$	−76.0828	−4.36365
$305$	−4.55807	−0.260995
$306$	19.4415	1.11140
$307$	−28.0346	−1.60002	−0.800010	−	0.599986i	$-0.795173\pi$
$307$	−28.0346	−1.60002	−0.800010	+	0.599986i	$0.795173\pi$
$308$	−43.2717	−2.46563
$309$	−12.6112	−0.717424
$310$	23.8937	1.35707
$311$	11.7167	0.664396	0.332198	−	0.943210i	$-0.392210\pi$
$311$	11.7167	0.664396	0.332198	+	0.943210i	$0.392210\pi$
$312$	8.62618	0.488361
$313$	−28.1238	−1.58965	−0.794824	−	0.606840i	$-0.792437\pi$
$313$	−28.1238	−1.58965	−0.794824	+	0.606840i	$0.792437\pi$
$314$	25.9692	1.46553
$315$	−3.80178	−0.214206
$316$	−74.1175	−4.16944
$317$	−19.5808	−1.09977	−0.549884	−	0.835241i	$-0.685328\pi$
$317$	−19.5808	−1.09977	−0.549884	+	0.835241i	$0.685328\pi$
$318$	2.30213	0.129097
$319$	−17.9728	−1.00628
$320$	−8.37638	−0.468254
$321$	−15.8042	−0.882106
$322$	25.5574	1.42426
$323$	57.9270	3.22315
$324$	4.84213	0.269007
$325$	1.16032	0.0643630
$326$	−23.8449	−1.32065
$327$	−7.71374	−0.426571
$328$	5.93274	0.327581
$329$	17.0322	0.939014
$330$	6.14859	0.338469
$331$	17.3333	0.952726	0.476363	−	0.879249i	$-0.341955\pi$
$331$	17.3333	0.952726	0.476363	+	0.879249i	$0.341955\pi$
$332$	−48.0782	−2.63863
$333$	7.38946	0.404940
$334$	53.1501	2.90824
$335$	−1.67345	−0.0914302
$336$	−37.1130	−2.02468
$337$	8.93953	0.486967	0.243484	−	0.969905i	$-0.421710\pi$
$337$	8.93953	0.486967	0.243484	+	0.969905i	$0.421710\pi$
$338$	30.4830	1.65806
$339$	−15.5372	−0.843866
$340$	35.9891	1.95178
$341$	−21.4717	−1.16276
$342$	20.3865	1.10238
$343$	1.72423	0.0930994
$344$	45.6429	2.46090
$345$	−2.57001	−0.138365
$346$	36.3657	1.95503
$347$	1.06157	0.0569882	0.0284941	−	0.999594i	$-0.490929\pi$
$347$	1.06157	0.0569882	0.0284941	+	0.999594i	$0.490929\pi$
$348$	−37.0231	−1.98465
$349$	−23.5127	−1.25861	−0.629304	−	0.777159i	$-0.716660\pi$
$349$	−23.5127	−1.25861	−0.629304	+	0.777159i	$0.716660\pi$
$350$	−9.94450	−0.531556
$351$	−1.16032	−0.0619333
$352$	25.0723	1.33636
$353$	9.38236	0.499373	0.249686	−	0.968327i	$-0.419672\pi$
$353$	9.38236	0.499373	0.249686	+	0.968327i	$0.419672\pi$
$354$	11.7716	0.625651
$355$	−14.1788	−0.752533
$356$	17.4919	0.927067
$357$	28.2567	1.49550
$358$	47.2950	2.49962
$359$	−16.8048	−0.886925	−0.443463	−	0.896293i	$-0.646250\pi$
$359$	−16.8048	−0.886925	−0.443463	+	0.896293i	$0.646250\pi$
$360$	7.43431	0.391822
$361$	41.7428	2.19699
$362$	−46.4743	−2.44263
$363$	5.47465	0.287345
$364$	21.3600	1.11957
$365$	12.0104	0.628654
$366$	11.9228	0.623213
$367$	36.3015	1.89492	0.947462	−	0.319868i	$-0.103639\pi$
$367$	36.3015	1.89492	0.947462	+	0.319868i	$0.103639\pi$
$368$	−25.0884	−1.30782
$369$	−0.798023	−0.0415434
$370$	19.3290	1.00487
$371$	3.34596	0.173714
$372$	−44.2307	−2.29325
$373$	5.94865	0.308009	0.154005	−	0.988070i	$-0.450783\pi$
$373$	5.94865	0.308009	0.154005	+	0.988070i	$0.450783\pi$
$374$	−45.6993	−2.36305
$375$	1.00000	0.0516398
$376$	−33.3061	−1.71763
$377$	8.87185	0.456924
$378$	9.94450	0.511490
$379$	−13.4924	−0.693056	−0.346528	−	0.938040i	$-0.612639\pi$
$379$	−13.4924	−0.693056	−0.346528	+	0.938040i	$0.612639\pi$
$380$	37.7385	1.93594
$381$	10.5975	0.542927
$382$	−42.8901	−2.19445
$383$	−2.75817	−0.140936	−0.0704680	−	0.997514i	$-0.522449\pi$
$383$	−2.75817	−0.140936	−0.0704680	+	0.997514i	$0.522449\pi$
$384$	0.577866	0.0294891
$385$	8.93649	0.455446
$386$	18.8402	0.958943
$387$	−6.13950	−0.312088
$388$	−93.9695	−4.77058
$389$	20.9972	1.06460	0.532300	−	0.846556i	$-0.321328\pi$
$389$	20.9972	1.06460	0.532300	+	0.846556i	$0.321328\pi$
$390$	−3.03511	−0.153689
$391$	19.1015	0.966006
$392$	−55.4118	−2.79872
$393$	−9.83993	−0.496359
$394$	35.3907	1.78296
$395$	15.3068	0.770168
$396$	−11.3820	−0.571965
$397$	−10.4838	−0.526166	−0.263083	−	0.964773i	$-0.584739\pi$
$397$	−10.4838	−0.526166	−0.263083	+	0.964773i	$0.584739\pi$
$398$	5.04109	0.252687
$399$	29.6302	1.48337
$400$	9.76200	0.488100
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	4.37731	0.218321
$403$	10.5990	0.527974
$404$	−34.2143	−1.70222
$405$	−1.00000	−0.0496904
$406$	−76.0359	−3.77360
$407$	−17.3697	−0.860985
$408$	−55.2553	−2.73555
$409$	−9.17537	−0.453693	−0.226846	−	0.973931i	$-0.572842\pi$
$409$	−9.17537	−0.453693	−0.226846	+	0.973931i	$0.572842\pi$
$410$	−2.08743	−0.103091
$411$	16.3998	0.808941
$412$	61.0650	3.00846
$413$	17.1090	0.841879
$414$	6.72249	0.330393
$415$	9.92913	0.487402
$416$	−12.3763	−0.606800
$417$	−22.5388	−1.10373
$418$	−47.9207	−2.34388
$419$	−2.05880	−0.100579	−0.0502895	−	0.998735i	$-0.516014\pi$
$419$	−2.05880	−0.100579	−0.0502895	+	0.998735i	$0.516014\pi$
$420$	18.4087	0.898254
$421$	29.2474	1.42543	0.712716	−	0.701453i	$-0.247465\pi$
$421$	29.2474	1.42543	0.712716	+	0.701453i	$0.247465\pi$
$422$	65.0516	3.16666
$423$	4.48005	0.217827
$424$	−6.54296	−0.317754
$425$	−7.43248	−0.360528
$426$	37.0882	1.79693
$427$	17.3288	0.838599
$428$	76.5262	3.69903
$429$	2.72746	0.131683
$430$	−16.0594	−0.774452
$431$	−35.6737	−1.71834	−0.859170	−	0.511689i	$-0.829020\pi$
$431$	−35.6737	−1.71834	−0.859170	+	0.511689i	$0.829020\pi$
$432$	−9.76200	−0.469674
$433$	−38.8927	−1.86906	−0.934532	−	0.355879i	$-0.884182\pi$
$433$	−38.8927	−1.86906	−0.934532	+	0.355879i	$0.884182\pi$
$434$	−90.8384	−4.36038
$435$	7.64603	0.366599
$436$	37.3510	1.78879
$437$	20.0301	0.958167
$438$	−31.4162	−1.50112
$439$	−23.5214	−1.12261	−0.561306	−	0.827608i	$-0.689701\pi$
$439$	−23.5214	−1.12261	−0.561306	+	0.827608i	$0.689701\pi$
$440$	−17.4751	−0.833094
$441$	7.45353	0.354930
$442$	22.5584	1.07299
$443$	−24.5391	−1.16589	−0.582945	−	0.812512i	$-0.698100\pi$
$443$	−24.5391	−1.16589	−0.582945	+	0.812512i	$0.698100\pi$
$444$	−35.7808	−1.69808
$445$	−3.61243	−0.171246
$446$	−33.4765	−1.58516
$447$	−13.1930	−0.624006
$448$	31.8451	1.50454
$449$	11.7786	0.555869	0.277934	−	0.960600i	$-0.410350\pi$
$449$	11.7786	0.555869	0.277934	+	0.960600i	$0.410350\pi$
$450$	−2.61575	−0.123308
$451$	1.87584	0.0883297
$452$	75.2333	3.53868
$453$	0.00253793	0.000119242 0
$454$	18.9704	0.890326
$455$	−4.41128	−0.206804
$456$	−57.9413	−2.71335
$457$	27.1795	1.27140	0.635701	−	0.771935i	$-0.280711\pi$
$457$	27.1795	1.27140	0.635701	+	0.771935i	$0.280711\pi$
$458$	1.67124	0.0780918
$459$	7.43248	0.346918
$460$	12.4443	0.580220
$461$	1.99472	0.0929034	0.0464517	−	0.998921i	$-0.485209\pi$
$461$	1.99472	0.0929034	0.0464517	+	0.998921i	$0.485209\pi$
$462$	−23.3756	−1.08753
$463$	−25.6282	−1.19105	−0.595523	−	0.803339i	$-0.703055\pi$
$463$	−25.6282	−1.19105	−0.595523	+	0.803339i	$0.703055\pi$
$464$	74.6406	3.46510
$465$	9.13454	0.423604
$466$	27.9864	1.29645
$467$	11.1630	0.516561	0.258280	−	0.966070i	$-0.416844\pi$
$467$	11.1630	0.516561	0.258280	+	0.966070i	$0.416844\pi$
$468$	5.61843	0.259712
$469$	6.36208	0.293773
$470$	11.7187	0.540542
$471$	9.92804	0.457460
$472$	−33.4563	−1.53995
$473$	14.4315	0.663563
$474$	−40.0387	−1.83904
$475$	−7.79377	−0.357603
$476$	−136.823	−6.27125
$477$	0.880104	0.0402972
$478$	32.0082	1.46402
$479$	−35.2718	−1.61161	−0.805805	−	0.592180i	$-0.798267\pi$
$479$	−35.2718	−1.61161	−0.805805	+	0.592180i	$0.798267\pi$
$480$	−10.6663	−0.486848
$481$	8.57415	0.390947
$482$	25.5973	1.16592
$483$	9.77061	0.444578
$484$	−26.5090	−1.20495
$485$	19.4066	0.881210
$486$	2.61575	0.118653
$487$	−0.891326	−0.0403899	−0.0201949	−	0.999796i	$-0.506429\pi$
$487$	−0.891326	−0.0403899	−0.0201949	+	0.999796i	$0.506429\pi$
$488$	−33.8861	−1.53395
$489$	−9.11591	−0.412236
$490$	19.4966	0.880765
$491$	−12.4400	−0.561410	−0.280705	−	0.959794i	$-0.590568\pi$
$491$	−12.4400	−0.561410	−0.280705	+	0.959794i	$0.590568\pi$
$492$	3.86413	0.174209
$493$	−56.8290	−2.55945
$494$	23.6549	1.06429
$495$	2.35061	0.105652
$496$	89.1714	4.00391
$497$	53.9047	2.41796
$498$	−25.9721	−1.16384
$499$	26.4523	1.18417	0.592084	−	0.805876i	$-0.298305\pi$
$499$	26.4523	1.18417	0.592084	+	0.805876i	$0.298305\pi$
$500$	−4.84213	−0.216547
$501$	20.3193	0.907798
$502$	28.6014	1.27654
$503$	6.49440	0.289571	0.144786	−	0.989463i	$-0.453751\pi$
$503$	6.49440	0.289571	0.144786	+	0.989463i	$0.453751\pi$
$504$	−28.2636	−1.25896
$505$	7.06594	0.314430
$506$	−15.8019	−0.702482
$507$	11.6537	0.517557
$508$	−51.3145	−2.27671
$509$	−25.2685	−1.12001	−0.560004	−	0.828490i	$-0.689200\pi$
$509$	−25.2685	−1.12001	−0.560004	+	0.828490i	$0.689200\pi$
$510$	19.4415	0.860884
$511$	−45.6610	−2.01992
$512$	41.0229	1.81297
$513$	7.79377	0.344103
$514$	−67.5122	−2.97783
$515$	−12.6112	−0.555715
$516$	29.7283	1.30871
$517$	−10.5308	−0.463146
$518$	−73.4845	−3.22872
$519$	13.9026	0.610256
$520$	8.62618	0.378283
$521$	−16.8005	−0.736045	−0.368022	−	0.929817i	$-0.619965\pi$
$521$	−16.8005	−0.736045	−0.368022	+	0.929817i	$0.619965\pi$
$522$	−20.0001	−0.875380
$523$	13.6605	0.597334	0.298667	−	0.954357i	$-0.403458\pi$
$523$	13.6605	0.597334	0.298667	+	0.954357i	$0.403458\pi$
$524$	47.6462	2.08144
$525$	−3.80178	−0.165923
$526$	31.2423	1.36223
$527$	−67.8923	−2.95744
$528$	22.9466	0.998623
$529$	−16.3951	−0.712829
$530$	2.30213	0.0999981
$531$	4.50026	0.195295
$532$	−143.473	−6.22036
$533$	−0.925962	−0.0401079
$534$	9.44920	0.408907
$535$	−15.8042	−0.683277
$536$	−12.4409	−0.537366
$537$	18.0809	0.780248
$538$	−26.8678	−1.15835
$539$	−17.5203	−0.754654
$540$	4.84213	0.208372
$541$	22.9807	0.988018	0.494009	−	0.869457i	$-0.335531\pi$
$541$	22.9807	0.988018	0.494009	+	0.869457i	$0.335531\pi$
$542$	2.46554	0.105904
$543$	−17.7671	−0.762460
$544$	79.2771	3.39898
$545$	−7.71374	−0.330420
$546$	11.5388	0.493815
$547$	17.2504	0.737574	0.368787	−	0.929514i	$-0.379773\pi$
$547$	17.2504	0.737574	0.368787	+	0.929514i	$0.379773\pi$
$548$	−79.4099	−3.39222
$549$	4.55807	0.194534
$550$	6.14859	0.262177
$551$	−59.5914	−2.53868
$552$	−19.1062	−0.813215
$553$	−58.1930	−2.47462
$554$	−2.42918	−0.103206
$555$	7.38946	0.313665
$556$	109.136	4.62839
$557$	−2.86749	−0.121500	−0.0607498	−	0.998153i	$-0.519349\pi$
$557$	−2.86749	−0.121500	−0.0607498	+	0.998153i	$0.519349\pi$
$558$	−23.8937	−1.01150
$559$	−7.12378	−0.301304
$560$	−37.1130	−1.56831
$561$	−17.4708	−0.737619
$562$	5.64960	0.238314
$563$	27.9732	1.17893	0.589465	−	0.807794i	$-0.299338\pi$
$563$	27.9732	1.17893	0.589465	+	0.807794i	$0.299338\pi$
$564$	−21.6930	−0.913440
$565$	−15.5372	−0.653656
$566$	71.3904	3.00076
$567$	3.80178	0.159660
$568$	−105.410	−4.42289
$569$	−3.12463	−0.130991	−0.0654956	−	0.997853i	$-0.520863\pi$
$569$	−3.12463	−0.130991	−0.0654956	+	0.997853i	$0.520863\pi$
$570$	20.3865	0.853898
$571$	9.24024	0.386692	0.193346	−	0.981131i	$-0.438066\pi$
$571$	9.24024	0.386692	0.193346	+	0.981131i	$0.438066\pi$
$572$	−13.2067	−0.552201
$573$	−16.3969	−0.684990
$574$	7.93593	0.331239
$575$	−2.57001	−0.107177
$576$	8.37638	0.349016
$577$	−13.4026	−0.557957	−0.278978	−	0.960297i	$-0.589996\pi$
$577$	−13.4026	−0.557957	−0.278978	+	0.960297i	$0.589996\pi$
$578$	−100.031	−4.16073
$579$	7.20262	0.299331
$580$	−37.0231	−1.53730
$581$	−37.7484	−1.56607
$582$	−50.7628	−2.10419
$583$	−2.06878	−0.0856801
$584$	89.2891	3.69481
$585$	−1.16032	−0.0479734
$586$	−21.1284	−0.872807
$587$	5.56160	0.229552	0.114776	−	0.993391i	$-0.463385\pi$
$587$	5.56160	0.229552	0.114776	+	0.993391i	$0.463385\pi$
$588$	−36.0910	−1.48837
$589$	−71.1925	−2.93344
$590$	11.7716	0.484627
$591$	13.5298	0.556543
$592$	72.1359	2.96477
$593$	19.9292	0.818395	0.409197	−	0.912446i	$-0.365809\pi$
$593$	19.9292	0.818395	0.409197	+	0.912446i	$0.365809\pi$
$594$	−6.14859	−0.252280
$595$	28.2567	1.15841
$596$	63.8821	2.61671
$597$	1.92721	0.0788754
$598$	7.80025	0.318976
$599$	−7.18366	−0.293516	−0.146758	−	0.989172i	$-0.546884\pi$
$599$	−7.18366	−0.293516	−0.146758	+	0.989172i	$0.546884\pi$
$600$	7.43431	0.303504
$601$	−31.0266	−1.26560	−0.632800	−	0.774315i	$-0.718095\pi$
$601$	−31.0266	−1.26560	−0.632800	+	0.774315i	$0.718095\pi$
$602$	61.0542	2.48838
$603$	1.67345	0.0681480
$604$	−0.0122890	−0.000500032 0
$605$	5.47465	0.222576
$606$	−18.4827	−0.750809
$607$	−0.0669795	−0.00271861	−0.00135931	−	0.999999i	$-0.500433\pi$
$607$	−0.0669795	−0.00271861	−0.00135931	+	0.999999i	$0.500433\pi$
$608$	83.1308	3.37140
$609$	−29.0685	−1.17792
$610$	11.9228	0.482739
$611$	5.19830	0.210301
$612$	−35.9891	−1.45477
$613$	15.9822	0.645515	0.322758	−	0.946482i	$-0.395390\pi$
$613$	15.9822	0.645515	0.322758	+	0.946482i	$0.395390\pi$
$614$	73.3315	2.95942
$615$	−0.798023	−0.0321794
$616$	66.4366	2.67681
$617$	−33.0946	−1.33234	−0.666168	−	0.745801i	$-0.732067\pi$
$617$	−33.0946	−1.33234	−0.666168	+	0.745801i	$0.732067\pi$
$618$	32.9876	1.32696
$619$	−16.3878	−0.658682	−0.329341	−	0.944211i	$-0.606827\pi$
$619$	−16.3878	−0.658682	−0.329341	+	0.944211i	$0.606827\pi$
$620$	−44.2307	−1.77635
$621$	2.57001	0.103131
$622$	−30.6480	−1.22887
$623$	13.7337	0.550228
$624$	−11.3271	−0.453445
$625$	1.00000	0.0400000
$626$	73.5646	2.94023
$627$	−18.3201	−0.731634
$628$	−48.0729	−1.91832
$629$	−54.9220	−2.18988
$630$	9.94450	0.396198
$631$	10.7112	0.426407	0.213204	−	0.977008i	$-0.431610\pi$
$631$	10.7112	0.426407	0.213204	+	0.977008i	$0.431610\pi$
$632$	113.795	4.52654
$633$	24.8692	0.988463
$634$	51.2184	2.03414
$635$	10.5975	0.420549
$636$	−4.26158	−0.168983
$637$	8.64849	0.342666
$638$	47.0123	1.86124
$639$	14.1788	0.560905
$640$	0.577866	0.0228421
$641$	−21.9409	−0.866614	−0.433307	−	0.901246i	$-0.642653\pi$
$641$	−21.9409	−0.866614	−0.433307	+	0.901246i	$0.642653\pi$
$642$	41.3399	1.63155
$643$	−4.55624	−0.179681	−0.0898404	−	0.995956i	$-0.528636\pi$
$643$	−4.55624	−0.179681	−0.0898404	+	0.995956i	$0.528636\pi$
$644$	−47.3106	−1.86430
$645$	−6.13950	−0.241742
$646$	−151.522	−5.96157
$647$	13.8882	0.546001	0.273000	−	0.962014i	$-0.411984\pi$
$647$	13.8882	0.546001	0.273000	+	0.962014i	$0.411984\pi$
$648$	−7.43431	−0.292047
$649$	−10.5783	−0.415237
$650$	−3.03511	−0.119047
$651$	−34.7275	−1.36108
$652$	44.1405	1.72867
$653$	6.25873	0.244923	0.122461	−	0.992473i	$-0.460921\pi$
$653$	6.25873	0.244923	0.122461	+	0.992473i	$0.460921\pi$
$654$	20.1772	0.788991
$655$	−9.83993	−0.384478
$656$	−7.79030	−0.304160
$657$	−12.0104	−0.468571
$658$	−44.5518	−1.73681
$659$	−17.5287	−0.682820	−0.341410	−	0.939914i	$-0.610904\pi$
$659$	−17.5287	−0.682820	−0.341410	+	0.939914i	$0.610904\pi$
$660$	−11.3820	−0.443042
$661$	−44.8221	−1.74338	−0.871689	−	0.490060i	$-0.836975\pi$
$661$	−44.8221	−1.74338	−0.871689	+	0.490060i	$0.836975\pi$
$662$	−45.3396	−1.76218
$663$	8.62406	0.334931
$664$	73.8162	2.86462
$665$	29.6302	1.14901
$666$	−19.3290	−0.748982
$667$	−19.6504	−0.760865
$668$	−98.3886	−3.80677
$669$	−12.7981	−0.494802
$670$	4.37731	0.169110
$671$	−10.7142	−0.413619
$672$	40.5510	1.56429
$673$	−20.2827	−0.781842	−0.390921	−	0.920424i	$-0.627843\pi$
$673$	−20.2827	−0.781842	−0.390921	+	0.920424i	$0.627843\pi$
$674$	−23.3836	−0.900701
$675$	−1.00000	−0.0384900
$676$	−56.4286	−2.17033
$677$	−5.49772	−0.211294	−0.105647	−	0.994404i	$-0.533691\pi$
$677$	−5.49772	−0.211294	−0.105647	+	0.994404i	$0.533691\pi$
$678$	40.6414	1.56083
$679$	−73.7797	−2.83141
$680$	−55.2553	−2.11895
$681$	7.25239	0.277912
$682$	56.1646	2.15065
$683$	9.47662	0.362613	0.181306	−	0.983427i	$-0.441967\pi$
$683$	9.47662	0.362613	0.181306	+	0.983427i	$0.441967\pi$
$684$	−37.7385	−1.44297
$685$	16.3998	0.626603
$686$	−4.51014	−0.172198
$687$	0.638914	0.0243761
$688$	−59.9337	−2.28495
$689$	1.02120	0.0389047
$690$	6.72249	0.255921
$691$	10.7893	0.410443	0.205222	−	0.978716i	$-0.434208\pi$
$691$	10.7893	0.410443	0.205222	+	0.978716i	$0.434208\pi$
$692$	−67.3182	−2.55905
$693$	−8.93649	−0.339469
$694$	−2.77680	−0.105406
$695$	−22.5388	−0.854946
$696$	56.8429	2.15463
$697$	5.93129	0.224664
$698$	61.5034	2.32794
$699$	10.6992	0.404681
$700$	18.4087	0.695785
$701$	−23.5055	−0.887791	−0.443895	−	0.896079i	$-0.646404\pi$
$701$	−23.5055	−0.887791	−0.443895	+	0.896079i	$0.646404\pi$
$702$	3.03511	0.114553
$703$	−57.5918	−2.17211
$704$	−19.6896	−0.742079
$705$	4.48005	0.168728
$706$	−24.5419	−0.923646
$707$	−26.8632	−1.01029
$708$	−21.7909	−0.818951
$709$	40.4733	1.52001	0.760004	−	0.649919i	$-0.225197\pi$
$709$	40.4733	1.52001	0.760004	+	0.649919i	$0.225197\pi$
$710$	37.0882	1.39189
$711$	−15.3068	−0.574049
$712$	−26.8559	−1.00647
$713$	−23.4759	−0.879178
$714$	−73.9123	−2.76610
$715$	2.72746	0.102001
$716$	−87.5501	−3.27190
$717$	12.2367	0.456989
$718$	43.9572	1.64047
$719$	−42.0795	−1.56930	−0.784651	−	0.619938i	$-0.787158\pi$
$719$	−42.0795	−1.56930	−0.784651	+	0.619938i	$0.787158\pi$
$720$	−9.76200	−0.363808
$721$	47.9449	1.78556
$722$	−109.189	−4.06358
$723$	9.78583	0.363939
$724$	86.0308	3.19731
$725$	7.64603	0.283967
$726$	−14.3203	−0.531476
$727$	−47.6425	−1.76696	−0.883482	−	0.468465i	$-0.844807\pi$
$727$	−47.6425	−1.76696	−0.883482	+	0.468465i	$0.844807\pi$
$728$	−32.7948	−1.21546
$729$	1.00000	0.0370370
$730$	−31.4162	−1.16277
$731$	45.6317	1.68775
$732$	−22.0708	−0.815760
$733$	−1.04782	−0.0387020	−0.0193510	−	0.999813i	$-0.506160\pi$
$733$	−1.04782	−0.0387020	−0.0193510	+	0.999813i	$0.506160\pi$
$734$	−94.9556	−3.50488
$735$	7.45353	0.274928
$736$	27.4125	1.01044
$737$	−3.93361	−0.144897
$738$	2.08743	0.0768392
$739$	40.7385	1.49859	0.749295	−	0.662236i	$-0.230392\pi$
$739$	40.7385	1.49859	0.749295	+	0.662236i	$0.230392\pi$
$740$	−35.7808	−1.31533
$741$	9.04327	0.332213
$742$	−8.75219	−0.321303
$743$	−28.1610	−1.03313	−0.516563	−	0.856249i	$-0.672789\pi$
$743$	−28.1610	−1.03313	−0.516563	+	0.856249i	$0.672789\pi$
$744$	67.9090	2.48966
$745$	−13.1930	−0.483353
$746$	−15.5602	−0.569698
$747$	−9.92913	−0.363288
$748$	84.5961	3.09314
$749$	60.0842	2.19543
$750$	−2.61575	−0.0955136
$751$	20.0080	0.730103	0.365051	−	0.930987i	$-0.381051\pi$
$751$	20.0080	0.730103	0.365051	+	0.930987i	$0.381051\pi$
$752$	43.7342	1.59482
$753$	10.9343	0.398468
$754$	−23.2065	−0.845132
$755$	0.00253793	9.23647e−5 0
$756$	−18.4087	−0.669519
$757$	32.3568	1.17603	0.588014	−	0.808851i	$-0.299910\pi$
$757$	32.3568	1.17603	0.588014	+	0.808851i	$0.299910\pi$
$758$	35.2926	1.28189
$759$	−6.04108	−0.219277
$760$	−57.9413	−2.10175
$761$	11.6504	0.422328	0.211164	−	0.977451i	$-0.432275\pi$
$761$	11.6504	0.422328	0.211164	+	0.977451i	$0.432275\pi$
$762$	−27.7204	−1.00420
$763$	29.3259	1.06167
$764$	79.3960	2.87245
$765$	7.43248	0.268722
$766$	7.21468	0.260677
$767$	5.22175	0.188546
$768$	15.2412	0.549970
$769$	24.0704	0.868001	0.434000	−	0.900913i	$-0.357102\pi$
$769$	24.0704	0.868001	0.434000	+	0.900913i	$0.357102\pi$
$770$	−23.3756	−0.842398
$771$	−25.8099	−0.929521
$772$	−34.8761	−1.25522
$773$	−23.2883	−0.837622	−0.418811	−	0.908073i	$-0.637553\pi$
$773$	−23.2883	−0.837622	−0.418811	+	0.908073i	$0.637553\pi$
$774$	16.0594	0.577242
$775$	9.13454	0.328122
$776$	144.275	5.17916
$777$	−28.0931	−1.00783
$778$	−54.9234	−1.96910
$779$	6.21960	0.222840
$780$	5.61843	0.201172
$781$	−33.3288	−1.19260
$782$	−49.9648	−1.78674
$783$	−7.64603	−0.273247
$784$	72.7614	2.59862
$785$	9.92804	0.354347
$786$	25.7388	0.918071
$787$	−2.53894	−0.0905033	−0.0452516	−	0.998976i	$-0.514409\pi$
$787$	−2.53894	−0.0905033	−0.0452516	+	0.998976i	$0.514409\pi$
$788$	−65.5133	−2.33382
$789$	11.9439	0.425215
$790$	−40.0387	−1.42451
$791$	59.0691	2.10025
$792$	17.4751	0.620952
$793$	5.28883	0.187812
$794$	27.4229	0.973203
$795$	0.880104	0.0312141
$796$	−9.33181	−0.330757
$797$	−13.1588	−0.466108	−0.233054	−	0.972464i	$-0.574872\pi$
$797$	−13.1588	−0.466108	−0.233054	+	0.972464i	$0.574872\pi$
$798$	−77.5051	−2.74365
$799$	−33.2979	−1.17799
$800$	−10.6663	−0.377111
$801$	3.61243	0.127639
$802$	2.61575	0.0923653
$803$	28.2318	0.996277
$804$	−8.10305	−0.285773
$805$	9.77061	0.344369
$806$	−27.7243	−0.976547
$807$	−10.2715	−0.361575
$808$	52.5304	1.84801
$809$	−4.65526	−0.163670	−0.0818351	−	0.996646i	$-0.526078\pi$
$809$	−4.65526	−0.163670	−0.0818351	+	0.996646i	$0.526078\pi$
$810$	2.61575	0.0919080
$811$	35.7099	1.25395	0.626973	−	0.779041i	$-0.284294\pi$
$811$	35.7099	1.25395	0.626973	+	0.779041i	$0.284294\pi$
$812$	140.754	4.93949
$813$	0.942577	0.0330576
$814$	45.4348	1.59249
$815$	−9.11591	−0.319316
$816$	72.5559	2.53996
$817$	47.8498	1.67405
$818$	24.0004	0.839156
$819$	4.41128	0.154143
$820$	3.86413	0.134941
$821$	0.225643	0.00787500	0.00393750	−	0.999992i	$-0.498747\pi$
$821$	0.225643	0.00787500	0.00393750	+	0.999992i	$0.498747\pi$
$822$	−42.8976	−1.49623
$823$	−10.0758	−0.351222	−0.175611	−	0.984460i	$-0.556190\pi$
$823$	−10.0758	−0.351222	−0.175611	+	0.984460i	$0.556190\pi$
$824$	−93.7553	−3.26612
$825$	2.35061	0.0818376
$826$	−44.7529	−1.55715
$827$	−38.8561	−1.35116	−0.675580	−	0.737286i	$-0.736107\pi$
$827$	−38.8561	−1.35116	−0.675580	+	0.737286i	$0.736107\pi$
$828$	−12.4443	−0.432470
$829$	−8.46397	−0.293966	−0.146983	−	0.989139i	$-0.546956\pi$
$829$	−8.46397	−0.293966	−0.146983	+	0.989139i	$0.546956\pi$
$830$	−25.9721	−0.901504
$831$	−0.928675	−0.0322154
$832$	9.71929	0.336956
$833$	−55.3982	−1.91943
$834$	58.9558	2.04147
$835$	20.3193	0.703177
$836$	88.7083	3.06804
$837$	−9.13454	−0.315736
$838$	5.38531	0.186032
$839$	−49.1426	−1.69659	−0.848296	−	0.529522i	$-0.822371\pi$
$839$	−49.1426	−1.69659	−0.848296	+	0.529522i	$0.822371\pi$
$840$	−28.2636	−0.975187
$841$	29.4618	1.01592
$842$	−76.5039	−2.63650
$843$	2.15984	0.0743889
$844$	−120.420	−4.14503
$845$	11.6537	0.400898
$846$	−11.7187	−0.402896
$847$	−20.8134	−0.715157
$848$	8.59158	0.295036
$849$	27.2926	0.936678
$850$	19.4415	0.666838
$851$	−18.9910	−0.651002
$852$	−68.6557	−2.35210
$853$	53.6157	1.83577	0.917883	−	0.396852i	$-0.129897\pi$
$853$	53.6157	1.83577	0.917883	+	0.396852i	$0.129897\pi$
$854$	−45.3277	−1.55108
$855$	7.79377	0.266541
$856$	−117.494	−4.01585
$857$	45.7792	1.56379	0.781893	−	0.623413i	$-0.214254\pi$
$857$	45.7792	1.56379	0.781893	+	0.623413i	$0.214254\pi$
$858$	−7.13434	−0.243562
$859$	−3.34528	−0.114139	−0.0570697	−	0.998370i	$-0.518176\pi$
$859$	−3.34528	−0.114139	−0.0570697	+	0.998370i	$0.518176\pi$
$860$	29.7283	1.01373
$861$	3.03391	0.103395
$862$	93.3133	3.17827
$863$	−48.6515	−1.65612	−0.828058	−	0.560643i	$-0.810554\pi$
$863$	−48.6515	−1.65612	−0.828058	+	0.560643i	$0.810554\pi$
$864$	10.6663	0.362875
$865$	13.9026	0.472702
$866$	101.734	3.45705
$867$	−38.2418	−1.29876
$868$	168.155	5.70756
$869$	35.9802	1.22055
$870$	−20.0001	−0.678067
$871$	1.94173	0.0657932
$872$	−57.3463	−1.94199
$873$	−19.4066	−0.656815
$874$	−52.3936	−1.77224
$875$	−3.80178	−0.128524
$876$	58.1560	1.96491
$877$	3.35546	0.113306	0.0566529	−	0.998394i	$-0.481957\pi$
$877$	3.35546	0.113306	0.0566529	+	0.998394i	$0.481957\pi$
$878$	61.5259	2.07640
$879$	−8.07739	−0.272444
$880$	22.9466	0.773530
$881$	−57.6306	−1.94162	−0.970812	−	0.239843i	$-0.922904\pi$
$881$	−57.6306	−1.94162	−0.970812	+	0.239843i	$0.922904\pi$
$882$	−19.4966	−0.656483
$883$	−18.0952	−0.608953	−0.304477	−	0.952520i	$-0.598482\pi$
$883$	−18.0952	−0.608953	−0.304477	+	0.952520i	$0.598482\pi$
$884$	−41.7589	−1.40450
$885$	4.50026	0.151275
$886$	64.1882	2.15644
$887$	32.8145	1.10180	0.550901	−	0.834571i	$-0.314284\pi$
$887$	32.8145	1.10180	0.550901	+	0.834571i	$0.314284\pi$
$888$	54.9355	1.84352
$889$	−40.2894	−1.35126
$890$	9.44920	0.316738
$891$	−2.35061	−0.0787483
$892$	61.9699	2.07491
$893$	−34.9165	−1.16844
$894$	34.5094	1.15417
$895$	18.0809	0.604377
$896$	−2.19692	−0.0733939
$897$	2.98203	0.0995672
$898$	−30.8100	−1.02814
$899$	69.8430	2.32939
$900$	4.84213	0.161404
$901$	−6.54136	−0.217924
$902$	−4.90672	−0.163376
$903$	23.3410	0.776740
$904$	−115.508	−3.84175
$905$	−17.7671	−0.590599
$906$	−0.00663858	−0.000220552 0
$907$	53.1182	1.76376	0.881881	−	0.471473i	$-0.156277\pi$
$907$	53.1182	1.76376	0.881881	+	0.471473i	$0.156277\pi$
$908$	−35.1171	−1.16540
$909$	−7.06594	−0.234363
$910$	11.5388	0.382508
$911$	20.7637	0.687933	0.343966	−	0.938982i	$-0.388229\pi$
$911$	20.7637	0.687933	0.343966	+	0.938982i	$0.388229\pi$
$912$	76.0828	2.51935
$913$	23.3395	0.772424
$914$	−71.0946	−2.35160
$915$	4.55807	0.150685
$916$	−3.09371	−0.102219
$917$	37.4092	1.23536
$918$	−19.4415	−0.641665
$919$	−32.5861	−1.07492	−0.537458	−	0.843290i	$-0.680615\pi$
$919$	−32.5861	−1.07492	−0.537458	+	0.843290i	$0.680615\pi$
$920$	−19.1062	−0.629914
$921$	28.0346	0.923772
$922$	−5.21769	−0.171835
$923$	16.4520	0.541523
$924$	43.2717	1.42353
$925$	7.38946	0.242964
$926$	67.0370	2.20297
$927$	12.6112	0.414205
$928$	−81.5550	−2.67717
$929$	−54.4679	−1.78703	−0.893517	−	0.449030i	$-0.851770\pi$
$929$	−54.4679	−1.78703	−0.893517	+	0.449030i	$0.851770\pi$
$930$	−23.8937	−0.783504
$931$	−58.0911	−1.90386
$932$	−51.8070	−1.69699
$933$	−11.7167	−0.383589
$934$	−29.1995	−0.955438
$935$	−17.4708	−0.571357
$936$	−8.62618	−0.281956
$937$	−11.4015	−0.372470	−0.186235	−	0.982505i	$-0.559629\pi$
$937$	−11.4015	−0.372470	−0.186235	+	0.982505i	$0.559629\pi$
$938$	−16.6416	−0.543367
$939$	28.1238	0.917784
$940$	−21.6930	−0.707548
$941$	−21.5910	−0.703846	−0.351923	−	0.936029i	$-0.614472\pi$
$941$	−21.5910	−0.703846	−0.351923	+	0.936029i	$0.614472\pi$
$942$	−25.9692	−0.846124
$943$	2.05092	0.0667873
$944$	43.9316	1.42985
$945$	3.80178	0.123672
$946$	−37.7493	−1.22733
$947$	53.4832	1.73797	0.868985	−	0.494838i	$-0.164772\pi$
$947$	53.4832	1.73797	0.868985	+	0.494838i	$0.164772\pi$
$948$	74.1175	2.40723
$949$	−13.9359	−0.452380
$950$	20.3865	0.661426
$951$	19.5808	0.634951
$952$	210.069	6.80836
$953$	−51.8572	−1.67982	−0.839910	−	0.542726i	$-0.817392\pi$
$953$	−51.8572	−1.67982	−0.839910	+	0.542726i	$0.817392\pi$
$954$	−2.30213	−0.0745342
$955$	−16.3969	−0.530591
$956$	−59.2518	−1.91634
$957$	17.9728	0.580979
$958$	92.2622	2.98086
$959$	−62.3483	−2.01333
$960$	8.37638	0.270346
$961$	52.4399	1.69161
$962$	−22.4278	−0.723101
$963$	15.8042	0.509284
$964$	−47.3843	−1.52615
$965$	7.20262	0.231861
$966$	−25.5574	−0.822297
$967$	5.26547	0.169326	0.0846631	−	0.996410i	$-0.473019\pi$
$967$	5.26547	0.169326	0.0846631	+	0.996410i	$0.473019\pi$
$968$	40.7002	1.30815
$969$	−57.9270	−1.86088
$970$	−50.7628	−1.62990
$971$	−25.6270	−0.822408	−0.411204	−	0.911543i	$-0.634892\pi$
$971$	−25.6270	−0.822408	−0.411204	+	0.911543i	$0.634892\pi$
$972$	−4.84213	−0.155312
$973$	85.6876	2.74702
$974$	2.33148	0.0747056
$975$	−1.16032	−0.0371600
$976$	44.4959	1.42428
$977$	12.0933	0.386898	0.193449	−	0.981110i	$-0.438033\pi$
$977$	12.0933	0.386898	0.193449	+	0.981110i	$0.438033\pi$
$978$	23.8449	0.762476
$979$	−8.49140	−0.271386
$980$	−36.0910	−1.15288
$981$	7.71374	0.246281
$982$	32.5400	1.03839
$983$	31.5367	1.00586	0.502932	−	0.864326i	$-0.332255\pi$
$983$	31.5367	1.00586	0.502932	+	0.864326i	$0.332255\pi$
$984$	−5.93274	−0.189129
$985$	13.5298	0.431097
$986$	148.650	4.73399
$987$	−17.0322	−0.542140
$988$	−43.7887	−1.39311
$989$	15.7786	0.501729
$990$	−6.14859	−0.195415
$991$	41.7338	1.32572	0.662860	−	0.748744i	$-0.269343\pi$
$991$	41.7338	1.32572	0.662860	+	0.748744i	$0.269343\pi$
$992$	−97.4319	−3.09347
$993$	−17.3333	−0.550057
$994$	−141.001	−4.47228
$995$	1.92721	0.0610967
$996$	48.0782	1.52342
$997$	5.71297	0.180932	0.0904658	−	0.995900i	$-0.471164\pi$
$997$	5.71297	0.180932	0.0904658	+	0.995900i	$0.471164\pi$
$998$	−69.1926	−2.19025
$999$	−7.38946	−0.233792

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.f.1.4	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.f.1.4	✓	36	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)

\(f(q)\)	\(=\)	\(q-2.61575 q^{2} -1.00000 q^{3} +4.84213 q^{4} -1.00000 q^{5} +2.61575 q^{6} +3.80178 q^{7} -7.43431 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.61575 q^{2} -1.00000 q^{3} +4.84213 q^{4} -1.00000 q^{5} +2.61575 q^{6} +3.80178 q^{7} -7.43431 q^{8} +1.00000 q^{9} +2.61575 q^{10} -2.35061 q^{11} -4.84213 q^{12} +1.16032 q^{13} -9.94450 q^{14} +1.00000 q^{15} +9.76200 q^{16} -7.43248 q^{17} -2.61575 q^{18} -7.79377 q^{19} -4.84213 q^{20} -3.80178 q^{21} +6.14859 q^{22} -2.57001 q^{23} +7.43431 q^{24} +1.00000 q^{25} -3.03511 q^{26} -1.00000 q^{27} +18.4087 q^{28} +7.64603 q^{29} -2.61575 q^{30} +9.13454 q^{31} -10.6663 q^{32} +2.35061 q^{33} +19.4415 q^{34} -3.80178 q^{35} +4.84213 q^{36} +7.38946 q^{37} +20.3865 q^{38} -1.16032 q^{39} +7.43431 q^{40} -0.798023 q^{41} +9.94450 q^{42} -6.13950 q^{43} -11.3820 q^{44} -1.00000 q^{45} +6.72249 q^{46} +4.48005 q^{47} -9.76200 q^{48} +7.45353 q^{49} -2.61575 q^{50} +7.43248 q^{51} +5.61843 q^{52} +0.880104 q^{53} +2.61575 q^{54} +2.35061 q^{55} -28.2636 q^{56} +7.79377 q^{57} -20.0001 q^{58} +4.50026 q^{59} +4.84213 q^{60} +4.55807 q^{61} -23.8937 q^{62} +3.80178 q^{63} +8.37638 q^{64} -1.16032 q^{65} -6.14859 q^{66} +1.67345 q^{67} -35.9891 q^{68} +2.57001 q^{69} +9.94450 q^{70} +14.1788 q^{71} -7.43431 q^{72} -12.0104 q^{73} -19.3290 q^{74} -1.00000 q^{75} -37.7385 q^{76} -8.93649 q^{77} +3.03511 q^{78} -15.3068 q^{79} -9.76200 q^{80} +1.00000 q^{81} +2.08743 q^{82} -9.92913 q^{83} -18.4087 q^{84} +7.43248 q^{85} +16.0594 q^{86} -7.64603 q^{87} +17.4751 q^{88} +3.61243 q^{89} +2.61575 q^{90} +4.41128 q^{91} -12.4443 q^{92} -9.13454 q^{93} -11.7187 q^{94} +7.79377 q^{95} +10.6663 q^{96} -19.4066 q^{97} -19.4966 q^{98} -2.35061 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9} + 7 q^{10} - q^{11} - 45 q^{12} - 8 q^{13} - 4 q^{14} + 36 q^{15} + 63 q^{16} - 50 q^{17} - 7 q^{18} + 15 q^{19} - 45 q^{20} - 2 q^{21} + 7 q^{22} - 32 q^{23} + 24 q^{24} + 36 q^{25} - 12 q^{26} - 36 q^{27} - 10 q^{28} + 7 q^{29} - 7 q^{30} + 7 q^{31} - 50 q^{32} + q^{33} + 8 q^{34} - 2 q^{35} + 45 q^{36} - 10 q^{37} - 48 q^{38} + 8 q^{39} + 24 q^{40} - 31 q^{41} + 4 q^{42} + 27 q^{43} - 9 q^{44} - 36 q^{45} + 23 q^{46} - 46 q^{47} - 63 q^{48} + 48 q^{49} - 7 q^{50} + 50 q^{51} - 14 q^{52} - 39 q^{53} + 7 q^{54} + q^{55} - 29 q^{56} - 15 q^{57} - 26 q^{58} - 9 q^{59} + 45 q^{60} + 5 q^{61} - 65 q^{62} + 2 q^{63} + 90 q^{64} + 8 q^{65} - 7 q^{66} + 18 q^{67} - 128 q^{68} + 32 q^{69} + 4 q^{70} + 4 q^{71} - 24 q^{72} - 45 q^{73} - 22 q^{74} - 36 q^{75} + 26 q^{76} - 38 q^{77} + 12 q^{78} + 25 q^{79} - 63 q^{80} + 36 q^{81} - 5 q^{82} - 71 q^{83} + 10 q^{84} + 50 q^{85} + 3 q^{86} - 7 q^{87} - 9 q^{88} - 39 q^{89} + 7 q^{90} + 19 q^{91} - 95 q^{92} - 7 q^{93} + 16 q^{94} - 15 q^{95} + 50 q^{96} - 61 q^{97} - 76 q^{98} - q^{99}+O(q^{100}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9 + 7 * q^10 - q^11 - 45 * q^12 - 8 * q^13 - 4 * q^14 + 36 * q^15 + 63 * q^16 - 50 * q^17 - 7 * q^18 + 15 * q^19 - 45 * q^20 - 2 * q^21 + 7 * q^22 - 32 * q^23 + 24 * q^24 + 36 * q^25 - 12 * q^26 - 36 * q^27 - 10 * q^28 + 7 * q^29 - 7 * q^30 + 7 * q^31 - 50 * q^32 + q^33 + 8 * q^34 - 2 * q^35 + 45 * q^36 - 10 * q^37 - 48 * q^38 + 8 * q^39 + 24 * q^40 - 31 * q^41 + 4 * q^42 + 27 * q^43 - 9 * q^44 - 36 * q^45 + 23 * q^46 - 46 * q^47 - 63 * q^48 + 48 * q^49 - 7 * q^50 + 50 * q^51 - 14 * q^52 - 39 * q^53 + 7 * q^54 + q^55 - 29 * q^56 - 15 * q^57 - 26 * q^58 - 9 * q^59 + 45 * q^60 + 5 * q^61 - 65 * q^62 + 2 * q^63 + 90 * q^64 + 8 * q^65 - 7 * q^66 + 18 * q^67 - 128 * q^68 + 32 * q^69 + 4 * q^70 + 4 * q^71 - 24 * q^72 - 45 * q^73 - 22 * q^74 - 36 * q^75 + 26 * q^76 - 38 * q^77 + 12 * q^78 + 25 * q^79 - 63 * q^80 + 36 * q^81 - 5 * q^82 - 71 * q^83 + 10 * q^84 + 50 * q^85 + 3 * q^86 - 7 * q^87 - 9 * q^88 - 39 * q^89 + 7 * q^90 + 19 * q^91 - 95 * q^92 - 7 * q^93 + 16 * q^94 - 15 * q^95 + 50 * q^96 - 61 * q^97 - 76 * q^98 - q^99

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