LMFDB - Embedded newform 4015.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76022 q^{2} +1.97999 q^{3} +5.61884 q^{4} -1.00000 q^{5} -5.46521 q^{6} -3.73820 q^{7} -9.98882 q^{8} +0.920356 q^{9} +O(q^{10})$	\(q-2.76022 q^{2} +1.97999 q^{3} +5.61884 q^{4} -1.00000 q^{5} -5.46521 q^{6} -3.73820 q^{7} -9.98882 q^{8} +0.920356 q^{9} +2.76022 q^{10} +1.00000 q^{11} +11.1252 q^{12} -2.49281 q^{13} +10.3183 q^{14} -1.97999 q^{15} +16.3337 q^{16} +4.28886 q^{17} -2.54039 q^{18} -0.168312 q^{19} -5.61884 q^{20} -7.40160 q^{21} -2.76022 q^{22} +8.49572 q^{23} -19.7777 q^{24} +1.00000 q^{25} +6.88070 q^{26} -4.11767 q^{27} -21.0044 q^{28} -1.68870 q^{29} +5.46521 q^{30} +3.82176 q^{31} -25.1070 q^{32} +1.97999 q^{33} -11.8382 q^{34} +3.73820 q^{35} +5.17133 q^{36} +2.48474 q^{37} +0.464579 q^{38} -4.93573 q^{39} +9.98882 q^{40} -11.3228 q^{41} +20.4301 q^{42} +5.53496 q^{43} +5.61884 q^{44} -0.920356 q^{45} -23.4501 q^{46} -11.5059 q^{47} +32.3405 q^{48} +6.97416 q^{49} -2.76022 q^{50} +8.49189 q^{51} -14.0067 q^{52} -8.28829 q^{53} +11.3657 q^{54} -1.00000 q^{55} +37.3402 q^{56} -0.333256 q^{57} +4.66118 q^{58} +6.84600 q^{59} -11.1252 q^{60} +15.1844 q^{61} -10.5489 q^{62} -3.44048 q^{63} +36.6337 q^{64} +2.49281 q^{65} -5.46521 q^{66} -10.9701 q^{67} +24.0984 q^{68} +16.8214 q^{69} -10.3183 q^{70} +0.974056 q^{71} -9.19326 q^{72} +1.00000 q^{73} -6.85844 q^{74} +1.97999 q^{75} -0.945719 q^{76} -3.73820 q^{77} +13.6237 q^{78} +12.3928 q^{79} -16.3337 q^{80} -10.9140 q^{81} +31.2536 q^{82} -2.95398 q^{83} -41.5884 q^{84} -4.28886 q^{85} -15.2777 q^{86} -3.34360 q^{87} -9.98882 q^{88} +13.6496 q^{89} +2.54039 q^{90} +9.31861 q^{91} +47.7361 q^{92} +7.56703 q^{93} +31.7588 q^{94} +0.168312 q^{95} -49.7116 q^{96} -2.58830 q^{97} -19.2502 q^{98} +0.920356 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9} + 7 q^{10} + 31 q^{11} - 4 q^{12} - 24 q^{13} - 9 q^{14} + 4 q^{15} + 43 q^{16} - 49 q^{17} - 35 q^{18} - 22 q^{19} - 39 q^{20} - 8 q^{21} - 7 q^{22} - q^{23} - 13 q^{24} + 31 q^{25} - 9 q^{26} - 22 q^{27} - 34 q^{28} - 12 q^{29} + 5 q^{30} + 4 q^{31} - 45 q^{32} - 4 q^{33} + 2 q^{34} + 11 q^{35} + 34 q^{36} - 18 q^{37} - 7 q^{38} - q^{39} + 24 q^{40} - 58 q^{41} - 21 q^{42} - 41 q^{43} + 39 q^{44} - 31 q^{45} + 23 q^{46} - 31 q^{47} - 29 q^{48} + 44 q^{49} - 7 q^{50} + 8 q^{51} - 89 q^{52} - 46 q^{53} - 47 q^{54} - 31 q^{55} + 10 q^{56} - 47 q^{57} - 34 q^{58} - 9 q^{59} + 4 q^{60} - 5 q^{61} - 50 q^{62} - 61 q^{63} + 78 q^{64} + 24 q^{65} - 5 q^{66} + q^{67} - 115 q^{68} - 19 q^{69} + 9 q^{70} - 8 q^{71} - 93 q^{72} + 31 q^{73} - 19 q^{74} - 4 q^{75} - 7 q^{76} - 11 q^{77} + 57 q^{78} - 43 q^{80} + 43 q^{81} + 20 q^{82} - 29 q^{83} - 32 q^{84} + 49 q^{85} + 25 q^{86} - 62 q^{87} - 24 q^{88} - 77 q^{89} + 35 q^{90} - 11 q^{91} - 25 q^{92} - 38 q^{94} + 22 q^{95} - 23 q^{96} - 39 q^{97} - 65 q^{98} + 31 q^{99}+O(q^{100}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9 + 7 * q^10 + 31 * q^11 - 4 * q^12 - 24 * q^13 - 9 * q^14 + 4 * q^15 + 43 * q^16 - 49 * q^17 - 35 * q^18 - 22 * q^19 - 39 * q^20 - 8 * q^21 - 7 * q^22 - q^23 - 13 * q^24 + 31 * q^25 - 9 * q^26 - 22 * q^27 - 34 * q^28 - 12 * q^29 + 5 * q^30 + 4 * q^31 - 45 * q^32 - 4 * q^33 + 2 * q^34 + 11 * q^35 + 34 * q^36 - 18 * q^37 - 7 * q^38 - q^39 + 24 * q^40 - 58 * q^41 - 21 * q^42 - 41 * q^43 + 39 * q^44 - 31 * q^45 + 23 * q^46 - 31 * q^47 - 29 * q^48 + 44 * q^49 - 7 * q^50 + 8 * q^51 - 89 * q^52 - 46 * q^53 - 47 * q^54 - 31 * q^55 + 10 * q^56 - 47 * q^57 - 34 * q^58 - 9 * q^59 + 4 * q^60 - 5 * q^61 - 50 * q^62 - 61 * q^63 + 78 * q^64 + 24 * q^65 - 5 * q^66 + q^67 - 115 * q^68 - 19 * q^69 + 9 * q^70 - 8 * q^71 - 93 * q^72 + 31 * q^73 - 19 * q^74 - 4 * q^75 - 7 * q^76 - 11 * q^77 + 57 * q^78 - 43 * q^80 + 43 * q^81 + 20 * q^82 - 29 * q^83 - 32 * q^84 + 49 * q^85 + 25 * q^86 - 62 * q^87 - 24 * q^88 - 77 * q^89 + 35 * q^90 - 11 * q^91 - 25 * q^92 - 38 * q^94 + 22 * q^95 - 23 * q^96 - 39 * q^97 - 65 * q^98 + 31 * 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 $

$2$	−2.76022	−1.95177	−0.975887	−	0.218277i	$-0.929956\pi$
$2$	−2.76022	−1.95177	−0.975887	+	0.218277i	$0.929956\pi$
$3$	1.97999	1.14315	0.571574	−	0.820551i	$-0.306333\pi$
$3$	1.97999	1.14315	0.571574	+	0.820551i	$0.306333\pi$
$4$	5.61884	2.80942
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−5.46521	−2.23116
$7$	−3.73820	−1.41291	−0.706454	−	0.707759i	$-0.749706\pi$
$7$	−3.73820	−1.41291	−0.706454	+	0.707759i	$0.749706\pi$
$8$	−9.98882	−3.53158
$9$	0.920356	0.306785
$10$	2.76022	0.872860
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	11.1252	3.21158
$13$	−2.49281	−0.691380	−0.345690	−	0.938349i	$-0.612355\pi$
$13$	−2.49281	−0.691380	−0.345690	+	0.938349i	$0.612355\pi$
$14$	10.3183	2.75768
$15$	−1.97999	−0.511231
$16$	16.3337	4.08342
$17$	4.28886	1.04020	0.520100	−	0.854105i	$-0.325895\pi$
$17$	4.28886	1.04020	0.520100	+	0.854105i	$0.325895\pi$
$18$	−2.54039	−0.598775
$19$	−0.168312	−0.0386134	−0.0193067	−	0.999814i	$-0.506146\pi$
$19$	−0.168312	−0.0386134	−0.0193067	+	0.999814i	$0.506146\pi$
$20$	−5.61884	−1.25641
$21$	−7.40160	−1.61516
$22$	−2.76022	−0.588482
$23$	8.49572	1.77148	0.885740	−	0.464181i	$-0.153651\pi$
$23$	8.49572	1.77148	0.885740	+	0.464181i	$0.153651\pi$
$24$	−19.7777	−4.03711
$25$	1.00000	0.200000
$26$	6.88070	1.34942
$27$	−4.11767	−0.792446
$28$	−21.0044	−3.96945
$29$	−1.68870	−0.313583	−0.156792	−	0.987632i	$-0.550115\pi$
$29$	−1.68870	−0.313583	−0.156792	+	0.987632i	$0.550115\pi$
$30$	5.46521	0.997807
$31$	3.82176	0.686408	0.343204	−	0.939261i	$-0.388488\pi$
$31$	3.82176	0.686408	0.343204	+	0.939261i	$0.388488\pi$
$32$	−25.1070	−4.43834
$33$	1.97999	0.344672
$34$	−11.8382	−2.03024
$35$	3.73820	0.631872
$36$	5.17133	0.861889
$37$	2.48474	0.408489	0.204244	−	0.978920i	$-0.434526\pi$
$37$	2.48474	0.408489	0.204244	+	0.978920i	$0.434526\pi$
$38$	0.464579	0.0753647
$39$	−4.93573	−0.790349
$40$	9.98882	1.57937
$41$	−11.3228	−1.76833	−0.884166	−	0.467173i	$-0.845273\pi$
$41$	−11.3228	−1.76833	−0.884166	+	0.467173i	$0.845273\pi$
$42$	20.4301	3.15243
$43$	5.53496	0.844074	0.422037	−	0.906579i	$-0.361315\pi$
$43$	5.53496	0.844074	0.422037	+	0.906579i	$0.361315\pi$
$44$	5.61884	0.847072
$45$	−0.920356	−0.137199
$46$	−23.4501	−3.45753
$47$	−11.5059	−1.67830	−0.839151	−	0.543899i	$-0.816948\pi$
$47$	−11.5059	−1.67830	−0.839151	+	0.543899i	$0.816948\pi$
$48$	32.3405	4.66795
$49$	6.97416	0.996309
$50$	−2.76022	−0.390355
$51$	8.49189	1.18910
$52$	−14.0067	−1.94238
$53$	−8.28829	−1.13848	−0.569242	−	0.822170i	$-0.692763\pi$
$53$	−8.28829	−1.13848	−0.569242	+	0.822170i	$0.692763\pi$
$54$	11.3657	1.54668
$55$	−1.00000	−0.134840
$56$	37.3402	4.98980
$57$	−0.333256	−0.0441408
$58$	4.66118	0.612043
$59$	6.84600	0.891273	0.445636	−	0.895214i	$-0.352977\pi$
$59$	6.84600	0.891273	0.445636	+	0.895214i	$0.352977\pi$
$60$	−11.1252	−1.43626
$61$	15.1844	1.94417	0.972084	−	0.234633i	$-0.0753887\pi$
$61$	15.1844	1.94417	0.972084	+	0.234633i	$0.0753887\pi$
$62$	−10.5489	−1.33971
$63$	−3.44048	−0.433459
$64$	36.6337	4.57921
$65$	2.49281	0.309194
$66$	−5.46521	−0.672721
$67$	−10.9701	−1.34021	−0.670106	−	0.742265i	$-0.733752\pi$
$67$	−10.9701	−1.34021	−0.670106	+	0.742265i	$0.733752\pi$
$68$	24.0984	2.92236
$69$	16.8214	2.02506
$70$	−10.3183	−1.23327
$71$	0.974056	0.115599	0.0577996	−	0.998328i	$-0.481592\pi$
$71$	0.974056	0.115599	0.0577996	+	0.998328i	$0.481592\pi$
$72$	−9.19326	−1.08344
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−6.85844	−0.797278
$75$	1.97999	0.228629
$76$	−0.945719	−0.108481
$77$	−3.73820	−0.426008
$78$	13.6237	1.54258
$79$	12.3928	1.39429	0.697147	−	0.716928i	$-0.254453\pi$
$79$	12.3928	1.39429	0.697147	+	0.716928i	$0.254453\pi$
$80$	−16.3337	−1.82616
$81$	−10.9140	−1.21267
$82$	31.2536	3.45138
$83$	−2.95398	−0.324241	−0.162121	−	0.986771i	$-0.551833\pi$
$83$	−2.95398	−0.324241	−0.162121	+	0.986771i	$0.551833\pi$
$84$	−41.5884	−4.53767
$85$	−4.28886	−0.465192
$86$	−15.2777	−1.64744
$87$	−3.34360	−0.358472
$88$	−9.98882	−1.06481
$89$	13.6496	1.44685	0.723426	−	0.690402i	$-0.242566\pi$
$89$	13.6496	1.44685	0.723426	+	0.690402i	$0.242566\pi$
$90$	2.54039	0.267780
$91$	9.31861	0.976856
$92$	47.7361	4.97683
$93$	7.56703	0.784665
$94$	31.7588	3.27567
$95$	0.168312	0.0172685
$96$	−49.7116	−5.07367
$97$	−2.58830	−0.262802	−0.131401	−	0.991329i	$-0.541947\pi$
$97$	−2.58830	−0.262802	−0.131401	+	0.991329i	$0.541947\pi$
$98$	−19.2502	−1.94457
$99$	0.920356	0.0924992
$100$	5.61884	0.561884
$101$	−10.3129	−1.02618	−0.513088	−	0.858336i	$-0.671499\pi$
$101$	−10.3129	−1.02618	−0.513088	+	0.858336i	$0.671499\pi$
$102$	−23.4395	−2.32086
$103$	−1.31268	−0.129342	−0.0646709	−	0.997907i	$-0.520600\pi$
$103$	−1.31268	−0.129342	−0.0646709	+	0.997907i	$0.520600\pi$
$104$	24.9002	2.44166
$105$	7.40160	0.722322
$106$	22.8775	2.22206
$107$	−16.1054	−1.55697	−0.778483	−	0.627666i	$-0.784010\pi$
$107$	−16.1054	−1.55697	−0.778483	+	0.627666i	$0.784010\pi$
$108$	−23.1365	−2.22632
$109$	−3.88844	−0.372445	−0.186222	−	0.982508i	$-0.559625\pi$
$109$	−3.88844	−0.372445	−0.186222	+	0.982508i	$0.559625\pi$
$110$	2.76022	0.263177
$111$	4.91976	0.466963
$112$	−61.0587	−5.76950
$113$	−3.58203	−0.336969	−0.168485	−	0.985704i	$-0.553887\pi$
$113$	−3.58203	−0.336969	−0.168485	+	0.985704i	$0.553887\pi$
$114$	0.919862	0.0861529
$115$	−8.49572	−0.792230
$116$	−9.48852	−0.880987
$117$	−2.29427	−0.212105
$118$	−18.8965	−1.73956
$119$	−16.0326	−1.46971
$120$	19.7777	1.80545
$121$	1.00000	0.0909091
$122$	−41.9125	−3.79458
$123$	−22.4191	−2.02146
$124$	21.4738	1.92841
$125$	−1.00000	−0.0894427
$126$	9.49649	0.846014
$127$	−14.9941	−1.33051	−0.665256	−	0.746615i	$-0.731678\pi$
$127$	−14.9941	−1.33051	−0.665256	+	0.746615i	$0.731678\pi$
$128$	−50.9031	−4.49924
$129$	10.9592	0.964901
$130$	−6.88070	−0.603478
$131$	−18.7637	−1.63940	−0.819698	−	0.572796i	$-0.805859\pi$
$131$	−18.7637	−1.63940	−0.819698	+	0.572796i	$0.805859\pi$
$132$	11.1252	0.968328
$133$	0.629185	0.0545572
$134$	30.2800	2.61579
$135$	4.11767	0.354393
$136$	−42.8406	−3.67355
$137$	−13.8448	−1.18284	−0.591420	−	0.806364i	$-0.701432\pi$
$137$	−13.8448	−1.18284	−0.591420	+	0.806364i	$0.701432\pi$
$138$	−46.4309	−3.95246
$139$	−8.01774	−0.680056	−0.340028	−	0.940415i	$-0.610437\pi$
$139$	−8.01774	−0.680056	−0.340028	+	0.940415i	$0.610437\pi$
$140$	21.0044	1.77519
$141$	−22.7815	−1.91855
$142$	−2.68861	−0.225623
$143$	−2.49281	−0.208459
$144$	15.0328	1.25273
$145$	1.68870	0.140239
$146$	−2.76022	−0.228438
$147$	13.8088	1.13893
$148$	13.9614	1.14762
$149$	−0.230012	−0.0188433	−0.00942164	−	0.999956i	$-0.502999\pi$
$149$	−0.230012	−0.0188433	−0.00942164	+	0.999956i	$0.502999\pi$
$150$	−5.46521	−0.446233
$151$	14.8344	1.20720	0.603601	−	0.797286i	$-0.293732\pi$
$151$	14.8344	1.20720	0.603601	+	0.797286i	$0.293732\pi$
$152$	1.68124	0.136366
$153$	3.94727	0.319118
$154$	10.3183	0.831471
$155$	−3.82176	−0.306971
$156$	−27.7331	−2.22042
$157$	15.8331	1.26362	0.631809	−	0.775124i	$-0.282313\pi$
$157$	15.8331	1.26362	0.631809	+	0.775124i	$0.282313\pi$
$158$	−34.2068	−2.72135
$159$	−16.4107	−1.30145
$160$	25.1070	1.98489
$161$	−31.7587	−2.50294
$162$	30.1251	2.36685
$163$	−20.9993	−1.64480	−0.822398	−	0.568913i	$-0.807364\pi$
$163$	−20.9993	−1.64480	−0.822398	+	0.568913i	$0.807364\pi$
$164$	−63.6213	−4.96799
$165$	−1.97999	−0.154142
$166$	8.15364	0.632845
$167$	6.92554	0.535915	0.267957	−	0.963431i	$-0.413651\pi$
$167$	6.92554	0.535915	0.267957	+	0.963431i	$0.413651\pi$
$168$	73.9332	5.70407
$169$	−6.78592	−0.521994
$170$	11.8382	0.907949
$171$	−0.154907	−0.0118460
$172$	31.1001	2.37136
$173$	13.1850	1.00244	0.501219	−	0.865320i	$-0.332885\pi$
$173$	13.1850	1.00244	0.501219	+	0.865320i	$0.332885\pi$
$174$	9.22909	0.699656
$175$	−3.73820	−0.282582
$176$	16.3337	1.23120
$177$	13.5550	1.01886
$178$	−37.6759	−2.82393
$179$	−9.83911	−0.735410	−0.367705	−	0.929943i	$-0.619856\pi$
$179$	−9.83911	−0.735410	−0.367705	+	0.929943i	$0.619856\pi$
$180$	−5.17133	−0.385448
$181$	7.26513	0.540013	0.270006	−	0.962859i	$-0.412974\pi$
$181$	7.26513	0.540013	0.270006	+	0.962859i	$0.412974\pi$
$182$	−25.7215	−1.90660
$183$	30.0650	2.22247
$184$	−84.8622	−6.25613
$185$	−2.48474	−0.182682
$186$	−20.8867	−1.53149
$187$	4.28886	0.313632
$188$	−64.6496	−4.71506
$189$	15.3927	1.11965
$190$	−0.464579	−0.0337041
$191$	−0.111254	−0.00805009	−0.00402504	−	0.999992i	$-0.501281\pi$
$191$	−0.111254	−0.00805009	−0.00402504	+	0.999992i	$0.501281\pi$
$192$	72.5343	5.23471
$193$	−1.21166	−0.0872172	−0.0436086	−	0.999049i	$-0.513885\pi$
$193$	−1.21166	−0.0872172	−0.0436086	+	0.999049i	$0.513885\pi$
$194$	7.14428	0.512929
$195$	4.93573	0.353455
$196$	39.1867	2.79905
$197$	−9.06072	−0.645549	−0.322775	−	0.946476i	$-0.604616\pi$
$197$	−9.06072	−0.645549	−0.322775	+	0.946476i	$0.604616\pi$
$198$	−2.54039	−0.180538
$199$	6.96635	0.493832	0.246916	−	0.969037i	$-0.420583\pi$
$199$	6.96635	0.493832	0.246916	+	0.969037i	$0.420583\pi$
$200$	−9.98882	−0.706316
$201$	−21.7207	−1.53206
$202$	28.4660	2.00286
$203$	6.31269	0.443064
$204$	47.7146	3.34069
$205$	11.3228	0.790822
$206$	3.62328	0.252446
$207$	7.81909	0.543464
$208$	−40.7167	−2.82320
$209$	−0.168312	−0.0116424
$210$	−20.4301	−1.40981
$211$	−12.1402	−0.835764	−0.417882	−	0.908501i	$-0.637227\pi$
$211$	−12.1402	−0.835764	−0.417882	+	0.908501i	$0.637227\pi$
$212$	−46.5706	−3.19848
$213$	1.92862	0.132147
$214$	44.4545	3.03884
$215$	−5.53496	−0.377481
$216$	41.1307	2.79859
$217$	−14.2865	−0.969831
$218$	10.7330	0.726928
$219$	1.97999	0.133795
$220$	−5.61884	−0.378822
$221$	−10.6913	−0.719174
$222$	−13.5796	−0.911405
$223$	−20.9061	−1.39997	−0.699987	−	0.714156i	$-0.746811\pi$
$223$	−20.9061	−1.39997	−0.699987	+	0.714156i	$0.746811\pi$
$224$	93.8552	6.27096
$225$	0.920356	0.0613570
$226$	9.88721	0.657688
$227$	28.3631	1.88253	0.941263	−	0.337675i	$-0.109640\pi$
$227$	28.3631	1.88253	0.941263	+	0.337675i	$0.109640\pi$
$228$	−1.87251	−0.124010
$229$	9.84593	0.650637	0.325319	−	0.945604i	$-0.394528\pi$
$229$	9.84593	0.650637	0.325319	+	0.945604i	$0.394528\pi$
$230$	23.4501	1.54625
$231$	−7.40160	−0.486990
$232$	16.8681	1.10744
$233$	−9.06085	−0.593596	−0.296798	−	0.954940i	$-0.595919\pi$
$233$	−9.06085	−0.593596	−0.296798	+	0.954940i	$0.595919\pi$
$234$	6.33270	0.413981
$235$	11.5059	0.750559
$236$	38.4666	2.50396
$237$	24.5375	1.59388
$238$	44.2536	2.86854
$239$	−5.13149	−0.331929	−0.165964	−	0.986132i	$-0.553074\pi$
$239$	−5.13149	−0.331929	−0.165964	+	0.986132i	$0.553074\pi$
$240$	−32.3405	−2.08757
$241$	−4.18269	−0.269431	−0.134715	−	0.990884i	$-0.543012\pi$
$241$	−4.18269	−0.269431	−0.134715	+	0.990884i	$0.543012\pi$
$242$	−2.76022	−0.177434
$243$	−9.25661	−0.593812
$244$	85.3190	5.46199
$245$	−6.97416	−0.445563
$246$	61.8818	3.94544
$247$	0.419569	0.0266966
$248$	−38.1748	−2.42410
$249$	−5.84884	−0.370655
$250$	2.76022	0.174572
$251$	−21.7387	−1.37213	−0.686067	−	0.727538i	$-0.740664\pi$
$251$	−21.7387	−1.37213	−0.686067	+	0.727538i	$0.740664\pi$
$252$	−19.3315	−1.21777
$253$	8.49572	0.534122
$254$	41.3871	2.59686
$255$	−8.49189	−0.531783
$256$	67.2367	4.20229
$257$	−26.9057	−1.67833	−0.839165	−	0.543877i	$-0.816956\pi$
$257$	−26.9057	−1.67833	−0.839165	+	0.543877i	$0.816956\pi$
$258$	−30.2498	−1.88327
$259$	−9.28846	−0.577157
$260$	14.0067	0.868657
$261$	−1.55420	−0.0962027
$262$	51.7922	3.19973
$263$	−17.9101	−1.10438	−0.552192	−	0.833717i	$-0.686209\pi$
$263$	−17.9101	−1.10438	−0.552192	+	0.833717i	$0.686209\pi$
$264$	−19.7777	−1.21724
$265$	8.28829	0.509146
$266$	−1.73669	−0.106483
$267$	27.0260	1.65396
$268$	−61.6393	−3.76522
$269$	−13.3354	−0.813076	−0.406538	−	0.913634i	$-0.633264\pi$
$269$	−13.3354	−0.813076	−0.406538	+	0.913634i	$0.633264\pi$
$270$	−11.3657	−0.691695
$271$	16.3265	0.991764	0.495882	−	0.868390i	$-0.334845\pi$
$271$	16.3265	0.991764	0.495882	+	0.868390i	$0.334845\pi$
$272$	70.0529	4.24758
$273$	18.4507	1.11669
$274$	38.2147	2.30863
$275$	1.00000	0.0603023
$276$	94.5170	5.68925
$277$	−14.7857	−0.888388	−0.444194	−	0.895931i	$-0.646510\pi$
$277$	−14.7857	−0.888388	−0.444194	+	0.895931i	$0.646510\pi$
$278$	22.1308	1.32732
$279$	3.51738	0.210580
$280$	−37.3402	−2.23150
$281$	−24.8624	−1.48317	−0.741584	−	0.670860i	$-0.765925\pi$
$281$	−24.8624	−1.48317	−0.741584	+	0.670860i	$0.765925\pi$
$282$	62.8820	3.74457
$283$	−12.4905	−0.742486	−0.371243	−	0.928536i	$-0.621068\pi$
$283$	−12.4905	−0.742486	−0.371243	+	0.928536i	$0.621068\pi$
$284$	5.47307	0.324767
$285$	0.333256	0.0197404
$286$	6.88070	0.406865
$287$	42.3271	2.49849
$288$	−23.1074	−1.36162
$289$	1.39429	0.0820168
$290$	−4.66118	−0.273714
$291$	−5.12480	−0.300421
$292$	5.61884	0.328818
$293$	29.3701	1.71582	0.857911	−	0.513799i	$-0.171762\pi$
$293$	29.3701	1.71582	0.857911	+	0.513799i	$0.171762\pi$
$294$	−38.1153	−2.22293
$295$	−6.84600	−0.398589
$296$	−24.8196	−1.44261
$297$	−4.11767	−0.238932
$298$	0.634884	0.0367778
$299$	−21.1782	−1.22477
$300$	11.1252	0.642316
$301$	−20.6908	−1.19260
$302$	−40.9462	−2.35619
$303$	−20.4195	−1.17307
$304$	−2.74916	−0.157675
$305$	−15.1844	−0.869458
$306$	−10.8954	−0.622846
$307$	−6.15065	−0.351036	−0.175518	−	0.984476i	$-0.556160\pi$
$307$	−6.15065	−0.351036	−0.175518	+	0.984476i	$0.556160\pi$
$308$	−21.0044	−1.19683
$309$	−2.59908	−0.147857
$310$	10.5489	0.599138
$311$	−29.9814	−1.70009	−0.850044	−	0.526712i	$-0.823425\pi$
$311$	−29.9814	−1.70009	−0.850044	+	0.526712i	$0.823425\pi$
$312$	49.3021	2.79118
$313$	17.5994	0.994776	0.497388	−	0.867528i	$-0.334292\pi$
$313$	17.5994	0.994776	0.497388	+	0.867528i	$0.334292\pi$
$314$	−43.7029	−2.46630
$315$	3.44048	0.193849
$316$	69.6329	3.91716
$317$	−18.0718	−1.01501	−0.507507	−	0.861648i	$-0.669433\pi$
$317$	−18.0718	−1.01501	−0.507507	+	0.861648i	$0.669433\pi$
$318$	45.2973	2.54015
$319$	−1.68870	−0.0945489
$320$	−36.6337	−2.04788
$321$	−31.8885	−1.77984
$322$	87.6613	4.88517
$323$	−0.721866	−0.0401657
$324$	−61.3241	−3.40689
$325$	−2.49281	−0.138276
$326$	57.9629	3.21027
$327$	−7.69907	−0.425759
$328$	113.102	6.24500
$329$	43.0112	2.37129
$330$	5.46521	0.300850
$331$	3.08498	0.169566	0.0847829	−	0.996399i	$-0.472980\pi$
$331$	3.08498	0.169566	0.0847829	+	0.996399i	$0.472980\pi$
$332$	−16.5979	−0.910930
$333$	2.28684	0.125318
$334$	−19.1161	−1.04598
$335$	10.9701	0.599361
$336$	−120.895	−6.59539
$337$	2.12693	0.115861	0.0579306	−	0.998321i	$-0.481550\pi$
$337$	2.12693	0.115861	0.0579306	+	0.998321i	$0.481550\pi$
$338$	18.7307	1.01881
$339$	−7.09238	−0.385205
$340$	−24.0984	−1.30692
$341$	3.82176	0.206960
$342$	0.427578	0.0231208
$343$	0.0965948	0.00521563
$344$	−55.2877	−2.98091
$345$	−16.8214	−0.905636
$346$	−36.3936	−1.95653
$347$	−13.4096	−0.719863	−0.359931	−	0.932979i	$-0.617200\pi$
$347$	−13.4096	−0.719863	−0.359931	+	0.932979i	$0.617200\pi$
$348$	−18.7872	−1.00710
$349$	−15.5867	−0.834338	−0.417169	−	0.908829i	$-0.636978\pi$
$349$	−15.5867	−0.834338	−0.417169	+	0.908829i	$0.636978\pi$
$350$	10.3183	0.551535
$351$	10.2646	0.547882
$352$	−25.1070	−1.33821
$353$	0.465530	0.0247777	0.0123888	−	0.999923i	$-0.496056\pi$
$353$	0.465530	0.0247777	0.0123888	+	0.999923i	$0.496056\pi$
$354$	−37.4148	−1.98858
$355$	−0.974056	−0.0516975
$356$	76.6948	4.06482
$357$	−31.7444	−1.68009
$358$	27.1582	1.43535
$359$	−5.77163	−0.304615	−0.152307	−	0.988333i	$-0.548670\pi$
$359$	−5.77163	−0.304615	−0.152307	+	0.988333i	$0.548670\pi$
$360$	9.19326	0.484528
$361$	−18.9717	−0.998509
$362$	−20.0534	−1.05398
$363$	1.97999	0.103922
$364$	52.3598	2.74440
$365$	−1.00000	−0.0523424
$366$	−82.9862	−4.33776
$367$	33.1574	1.73080	0.865402	−	0.501078i	$-0.167063\pi$
$367$	33.1574	1.73080	0.865402	+	0.501078i	$0.167063\pi$
$368$	138.767	7.23371
$369$	−10.4210	−0.542498
$370$	6.85844	0.356553
$371$	30.9833	1.60857
$372$	42.5180	2.20445
$373$	18.3972	0.952569	0.476285	−	0.879291i	$-0.341983\pi$
$373$	18.3972	0.952569	0.476285	+	0.879291i	$0.341983\pi$
$374$	−11.8382	−0.612139
$375$	−1.97999	−0.102246
$376$	114.930	5.92706
$377$	4.20959	0.216805
$378$	−42.4873	−2.18531
$379$	−6.41008	−0.329264	−0.164632	−	0.986355i	$-0.552644\pi$
$379$	−6.41008	−0.329264	−0.164632	+	0.986355i	$0.552644\pi$
$380$	0.945719	0.0485144
$381$	−29.6882	−1.52097
$382$	0.307087	0.0157119
$383$	−23.3360	−1.19242	−0.596208	−	0.802830i	$-0.703326\pi$
$383$	−23.3360	−1.19242	−0.596208	+	0.802830i	$0.703326\pi$
$384$	−100.788	−5.14330
$385$	3.73820	0.190516
$386$	3.34445	0.170228
$387$	5.09414	0.258949
$388$	−14.5432	−0.738320
$389$	−14.1552	−0.717697	−0.358848	−	0.933396i	$-0.616831\pi$
$389$	−14.1552	−0.717697	−0.358848	+	0.933396i	$0.616831\pi$
$390$	−13.6237	−0.689864
$391$	36.4369	1.84270
$392$	−69.6636	−3.51854
$393$	−37.1520	−1.87407
$394$	25.0096	1.25997
$395$	−12.3928	−0.623547
$396$	5.17133	0.259869
$397$	24.1733	1.21322	0.606611	−	0.794999i	$-0.292529\pi$
$397$	24.1733	1.21322	0.606611	+	0.794999i	$0.292529\pi$
$398$	−19.2287	−0.963848
$399$	1.24578	0.0623669
$400$	16.3337	0.816685
$401$	−5.37213	−0.268271	−0.134136	−	0.990963i	$-0.542826\pi$
$401$	−5.37213	−0.268271	−0.134136	+	0.990963i	$0.542826\pi$
$402$	59.9540	2.99024
$403$	−9.52690	−0.474568
$404$	−57.9468	−2.88296
$405$	10.9140	0.542322
$406$	−17.4244	−0.864761
$407$	2.48474	0.123164
$408$	−84.8239	−4.19941
$409$	−29.8701	−1.47698	−0.738490	−	0.674264i	$-0.764461\pi$
$409$	−29.8701	−1.47698	−0.738490	+	0.674264i	$0.764461\pi$
$410$	−31.2536	−1.54351
$411$	−27.4125	−1.35216
$412$	−7.37571	−0.363375
$413$	−25.5917	−1.25929
$414$	−21.5824	−1.06072
$415$	2.95398	0.145005
$416$	62.5870	3.06858
$417$	−15.8750	−0.777404
$418$	0.464579	0.0227233
$419$	22.0755	1.07846	0.539228	−	0.842160i	$-0.318716\pi$
$419$	22.0755	1.07846	0.539228	+	0.842160i	$0.318716\pi$
$420$	41.5884	2.02931
$421$	−36.0026	−1.75466	−0.877329	−	0.479889i	$-0.840677\pi$
$421$	−36.0026	−1.75466	−0.877329	+	0.479889i	$0.840677\pi$
$422$	33.5096	1.63122
$423$	−10.5895	−0.514878
$424$	82.7902	4.02065
$425$	4.28886	0.208040
$426$	−5.32342	−0.257921
$427$	−56.7625	−2.74693
$428$	−90.4935	−4.37417
$429$	−4.93573	−0.238299
$430$	15.2777	0.736758
$431$	10.2062	0.491614	0.245807	−	0.969319i	$-0.420947\pi$
$431$	10.2062	0.491614	0.245807	+	0.969319i	$0.420947\pi$
$432$	−67.2568	−3.23589
$433$	−35.2183	−1.69249	−0.846243	−	0.532798i	$-0.821141\pi$
$433$	−35.2183	−1.69249	−0.846243	+	0.532798i	$0.821141\pi$
$434$	39.4340	1.89289
$435$	3.34360	0.160313
$436$	−21.8485	−1.04635
$437$	−1.42993	−0.0684030
$438$	−5.46521	−0.261138
$439$	−8.84645	−0.422218	−0.211109	−	0.977463i	$-0.567707\pi$
$439$	−8.84645	−0.422218	−0.211109	+	0.977463i	$0.567707\pi$
$440$	9.98882	0.476198
$441$	6.41871	0.305653
$442$	29.5103	1.40366
$443$	14.2548	0.677268	0.338634	−	0.940918i	$-0.390035\pi$
$443$	14.2548	0.677268	0.338634	+	0.940918i	$0.390035\pi$
$444$	27.6433	1.31189
$445$	−13.6496	−0.647052
$446$	57.7054	2.73243
$447$	−0.455420	−0.0215406
$448$	−136.944	−6.47000
$449$	−6.48797	−0.306186	−0.153093	−	0.988212i	$-0.548923\pi$
$449$	−6.48797	−0.306186	−0.153093	+	0.988212i	$0.548923\pi$
$450$	−2.54039	−0.119755
$451$	−11.3228	−0.533172
$452$	−20.1269	−0.946688
$453$	29.3719	1.38001
$454$	−78.2886	−3.67426
$455$	−9.31861	−0.436863
$456$	3.32883	0.155887
$457$	32.2093	1.50669	0.753343	−	0.657628i	$-0.228440\pi$
$457$	32.2093	1.50669	0.753343	+	0.657628i	$0.228440\pi$
$458$	−27.1770	−1.26990
$459$	−17.6601	−0.824303
$460$	−47.7361	−2.22571
$461$	41.9149	1.95217	0.976085	−	0.217389i	$-0.0697539\pi$
$461$	41.9149	1.95217	0.976085	+	0.217389i	$0.0697539\pi$
$462$	20.4301	0.950493
$463$	−38.6823	−1.79772	−0.898860	−	0.438236i	$-0.855603\pi$
$463$	−38.6823	−1.79772	−0.898860	+	0.438236i	$0.855603\pi$
$464$	−27.5827	−1.28049
$465$	−7.56703	−0.350913
$466$	25.0100	1.15856
$467$	−10.1849	−0.471300	−0.235650	−	0.971838i	$-0.575722\pi$
$467$	−10.1849	−0.471300	−0.235650	+	0.971838i	$0.575722\pi$
$468$	−12.8911	−0.595893
$469$	41.0085	1.89360
$470$	−31.7588	−1.46492
$471$	31.3493	1.44450
$472$	−68.3834	−3.14760
$473$	5.53496	0.254498
$474$	−67.7290	−3.11090
$475$	−0.168312	−0.00772269
$476$	−90.0847	−4.12903
$477$	−7.62817	−0.349270
$478$	14.1641	0.647850
$479$	1.42771	0.0652336	0.0326168	−	0.999468i	$-0.489616\pi$
$479$	1.42771	0.0652336	0.0326168	+	0.999468i	$0.489616\pi$
$480$	49.7116	2.26902
$481$	−6.19397	−0.282421
$482$	11.5452	0.525867
$483$	−62.8819	−2.86123
$484$	5.61884	0.255402
$485$	2.58830	0.117528
$486$	25.5503	1.15899
$487$	25.7237	1.16565	0.582826	−	0.812597i	$-0.301947\pi$
$487$	25.7237	1.16565	0.582826	+	0.812597i	$0.301947\pi$
$488$	−151.675	−6.86598
$489$	−41.5785	−1.88024
$490$	19.2502	0.869638
$491$	2.14738	0.0969097	0.0484549	−	0.998825i	$-0.484570\pi$
$491$	2.14738	0.0969097	0.0484549	+	0.998825i	$0.484570\pi$
$492$	−125.969	−5.67914
$493$	−7.24258	−0.326189
$494$	−1.15811	−0.0521056
$495$	−0.920356	−0.0413669
$496$	62.4234	2.80289
$497$	−3.64122	−0.163331
$498$	16.1441	0.723435
$499$	0.725361	0.0324716	0.0162358	−	0.999868i	$-0.494832\pi$
$499$	0.725361	0.0324716	0.0162358	+	0.999868i	$0.494832\pi$
$500$	−5.61884	−0.251282
$501$	13.7125	0.612629
$502$	60.0037	2.67810
$503$	8.08145	0.360334	0.180167	−	0.983636i	$-0.442336\pi$
$503$	8.08145	0.360334	0.180167	+	0.983636i	$0.442336\pi$
$504$	34.3663	1.53080
$505$	10.3129	0.458920
$506$	−23.4501	−1.04248
$507$	−13.4360	−0.596716
$508$	−84.2495	−3.73797
$509$	17.3007	0.766838	0.383419	−	0.923574i	$-0.374746\pi$
$509$	17.3007	0.766838	0.383419	+	0.923574i	$0.374746\pi$
$510$	23.4395	1.03792
$511$	−3.73820	−0.165368
$512$	−83.7821	−3.70268
$513$	0.693054	0.0305991
$514$	74.2657	3.27572
$515$	1.31268	0.0578434
$516$	61.5778	2.71081
$517$	−11.5059	−0.506027
$518$	25.6382	1.12648
$519$	26.1062	1.14593
$520$	−24.9002	−1.09194
$521$	−14.0875	−0.617183	−0.308591	−	0.951195i	$-0.599858\pi$
$521$	−14.0875	−0.617183	−0.308591	+	0.951195i	$0.599858\pi$
$522$	4.28995	0.187766
$523$	1.89101	0.0826882	0.0413441	−	0.999145i	$-0.486836\pi$
$523$	1.89101	0.0826882	0.0413441	+	0.999145i	$0.486836\pi$
$524$	−105.431	−4.60575
$525$	−7.40160	−0.323032
$526$	49.4359	2.15551
$527$	16.3910	0.714002
$528$	32.3405	1.40744
$529$	49.1773	2.13814
$530$	−22.8775	−0.993737
$531$	6.30075	0.273429
$532$	3.53529	0.153274
$533$	28.2257	1.22259
$534$	−74.5978	−3.22816
$535$	16.1054	0.696296
$536$	109.578	4.73307
$537$	−19.4813	−0.840681
$538$	36.8088	1.58694
$539$	6.97416	0.300398
$540$	23.1365	0.995638
$541$	29.2054	1.25564	0.627819	−	0.778359i	$-0.283948\pi$
$541$	29.2054	1.25564	0.627819	+	0.778359i	$0.283948\pi$
$542$	−45.0648	−1.93570
$543$	14.3849	0.617314
$544$	−107.680	−4.61676
$545$	3.88844	0.166562
$546$	−50.9282	−2.17953
$547$	−17.8010	−0.761117	−0.380559	−	0.924757i	$-0.624268\pi$
$547$	−17.8010	−0.761117	−0.380559	+	0.924757i	$0.624268\pi$
$548$	−77.7916	−3.32309
$549$	13.9751	0.596442
$550$	−2.76022	−0.117696
$551$	0.284228	0.0121085
$552$	−168.026	−7.15167
$553$	−46.3266	−1.97001
$554$	40.8119	1.73393
$555$	−4.91976	−0.208832
$556$	−45.0504	−1.91056
$557$	−5.34791	−0.226598	−0.113299	−	0.993561i	$-0.536142\pi$
$557$	−5.34791	−0.226598	−0.113299	+	0.993561i	$0.536142\pi$
$558$	−9.70875	−0.411004
$559$	−13.7976	−0.583576
$560$	61.0587	2.58020
$561$	8.49189	0.358528
$562$	68.6259	2.89481
$563$	3.60191	0.151802	0.0759012	−	0.997115i	$-0.475817\pi$
$563$	3.60191	0.151802	0.0759012	+	0.997115i	$0.475817\pi$
$564$	−128.005	−5.39000
$565$	3.58203	0.150697
$566$	34.4767	1.44916
$567$	40.7988	1.71339
$568$	−9.72967	−0.408248
$569$	−10.9610	−0.459508	−0.229754	−	0.973249i	$-0.573792\pi$
$569$	−10.9610	−0.459508	−0.229754	+	0.973249i	$0.573792\pi$
$570$	−0.919862	−0.0385288
$571$	−16.1426	−0.675548	−0.337774	−	0.941227i	$-0.609674\pi$
$571$	−16.1426	−0.675548	−0.337774	+	0.941227i	$0.609674\pi$
$572$	−14.0067	−0.585649
$573$	−0.220282	−0.00920243
$574$	−116.832	−4.87649
$575$	8.49572	0.354296
$576$	33.7160	1.40483
$577$	32.4740	1.35191	0.675955	−	0.736943i	$-0.263731\pi$
$577$	32.4740	1.35191	0.675955	+	0.736943i	$0.263731\pi$
$578$	−3.84854	−0.160078
$579$	−2.39907	−0.0997021
$580$	9.48852	0.393989
$581$	11.0426	0.458123
$582$	14.1456	0.586354
$583$	−8.28829	−0.343266
$584$	−9.98882	−0.413340
$585$	2.29427	0.0948563
$586$	−81.0682	−3.34889
$587$	6.74667	0.278465	0.139232	−	0.990260i	$-0.455536\pi$
$587$	6.74667	0.278465	0.139232	+	0.990260i	$0.455536\pi$
$588$	77.5892	3.19973
$589$	−0.643248	−0.0265046
$590$	18.8965	0.777956
$591$	−17.9401	−0.737958
$592$	40.5850	1.66803
$593$	−21.1842	−0.869930	−0.434965	−	0.900447i	$-0.643239\pi$
$593$	−21.1842	−0.869930	−0.434965	+	0.900447i	$0.643239\pi$
$594$	11.3657	0.466340
$595$	16.0326	0.657273
$596$	−1.29240	−0.0529387
$597$	13.7933	0.564522
$598$	58.4566	2.39047
$599$	10.8431	0.443038	0.221519	−	0.975156i	$-0.428898\pi$
$599$	10.8431	0.443038	0.221519	+	0.975156i	$0.428898\pi$
$600$	−19.7777	−0.807423
$601$	−47.4261	−1.93455	−0.967275	−	0.253729i	$-0.918343\pi$
$601$	−47.4261	−1.93455	−0.967275	+	0.253729i	$0.918343\pi$
$602$	57.1113	2.32768
$603$	−10.0964	−0.411158
$604$	83.3519	3.39154
$605$	−1.00000	−0.0406558
$606$	56.3624	2.28957
$607$	−21.5599	−0.875088	−0.437544	−	0.899197i	$-0.644152\pi$
$607$	−21.5599	−0.875088	−0.437544	+	0.899197i	$0.644152\pi$
$608$	4.22582	0.171380
$609$	12.4991	0.506487
$610$	41.9125	1.69699
$611$	28.6819	1.16034
$612$	22.1791	0.896537
$613$	−14.8259	−0.598811	−0.299405	−	0.954126i	$-0.596788\pi$
$613$	−14.8259	−0.598811	−0.299405	+	0.954126i	$0.596788\pi$
$614$	16.9772	0.685144
$615$	22.4191	0.904026
$616$	37.3402	1.50448
$617$	1.97911	0.0796758	0.0398379	−	0.999206i	$-0.487316\pi$
$617$	1.97911	0.0796758	0.0398379	+	0.999206i	$0.487316\pi$
$618$	7.17405	0.288583
$619$	20.2176	0.812613	0.406307	−	0.913737i	$-0.366816\pi$
$619$	20.2176	0.812613	0.406307	+	0.913737i	$0.366816\pi$
$620$	−21.4738	−0.862410
$621$	−34.9826	−1.40380
$622$	82.7553	3.31819
$623$	−51.0249	−2.04427
$624$	−80.6187	−3.22733
$625$	1.00000	0.0400000
$626$	−48.5783	−1.94158
$627$	−0.333256	−0.0133090
$628$	88.9636	3.55004
$629$	10.6567	0.424910
$630$	−9.49649	−0.378349
$631$	3.33151	0.132625	0.0663127	−	0.997799i	$-0.478877\pi$
$631$	3.33151	0.132625	0.0663127	+	0.997799i	$0.478877\pi$
$632$	−123.789	−4.92406
$633$	−24.0374	−0.955401
$634$	49.8822	1.98108
$635$	14.9941	0.595023
$636$	−92.2092	−3.65633
$637$	−17.3852	−0.688828
$638$	4.66118	0.184538
$639$	0.896478	0.0354641
$640$	50.9031	2.01212
$641$	23.1848	0.915743	0.457871	−	0.889018i	$-0.348612\pi$
$641$	23.1848	0.915743	0.457871	+	0.889018i	$0.348612\pi$
$642$	88.0193	3.47385
$643$	23.1320	0.912237	0.456119	−	0.889919i	$-0.349239\pi$
$643$	23.1320	0.912237	0.456119	+	0.889919i	$0.349239\pi$
$644$	−178.447	−7.03181
$645$	−10.9592	−0.431517
$646$	1.99251	0.0783944
$647$	46.9272	1.84490	0.922449	−	0.386118i	$-0.126184\pi$
$647$	46.9272	1.84490	0.922449	+	0.386118i	$0.126184\pi$
$648$	109.018	4.28263
$649$	6.84600	0.268729
$650$	6.88070	0.269883
$651$	−28.2871	−1.10866
$652$	−117.992	−4.62092
$653$	−18.5743	−0.726870	−0.363435	−	0.931620i	$-0.618396\pi$
$653$	−18.5743	−0.726870	−0.363435	+	0.931620i	$0.618396\pi$
$654$	21.2512	0.830986
$655$	18.7637	0.733160
$656$	−184.944	−7.22085
$657$	0.920356	0.0359065
$658$	−118.721	−4.62821
$659$	32.7004	1.27383	0.636913	−	0.770935i	$-0.280211\pi$
$659$	32.7004	1.27383	0.636913	+	0.770935i	$0.280211\pi$
$660$	−11.1252	−0.433049
$661$	−11.4602	−0.445750	−0.222875	−	0.974847i	$-0.571544\pi$
$661$	−11.4602	−0.445750	−0.222875	+	0.974847i	$0.571544\pi$
$662$	−8.51524	−0.330954
$663$	−21.1686	−0.822121
$664$	29.5067	1.14508
$665$	−0.629185	−0.0243987
$666$	−6.31221	−0.244593
$667$	−14.3467	−0.555507
$668$	38.9135	1.50561
$669$	−41.3938	−1.60038
$670$	−30.2800	−1.16982
$671$	15.1844	0.586189
$672$	185.832	7.16863
$673$	−4.57981	−0.176539	−0.0882694	−	0.996097i	$-0.528134\pi$
$673$	−4.57981	−0.176539	−0.0882694	+	0.996097i	$0.528134\pi$
$674$	−5.87080	−0.226135
$675$	−4.11767	−0.158489
$676$	−38.1290	−1.46650
$677$	−40.1952	−1.54483	−0.772413	−	0.635120i	$-0.780951\pi$
$677$	−40.1952	−1.54483	−0.772413	+	0.635120i	$0.780951\pi$
$678$	19.5766	0.751834
$679$	9.67558	0.371315
$680$	42.8406	1.64286
$681$	56.1586	2.15200
$682$	−10.5489	−0.403939
$683$	28.6544	1.09643	0.548215	−	0.836337i	$-0.315307\pi$
$683$	28.6544	1.09643	0.548215	+	0.836337i	$0.315307\pi$
$684$	−0.870398	−0.0332805
$685$	13.8448	0.528982
$686$	−0.266623	−0.0101797
$687$	19.4948	0.743774
$688$	90.4064	3.44671
$689$	20.6611	0.787125
$690$	46.4309	1.76760
$691$	−0.424923	−0.0161648	−0.00808242	−	0.999967i	$-0.502573\pi$
$691$	−0.424923	−0.0161648	−0.00808242	+	0.999967i	$0.502573\pi$
$692$	74.0845	2.81627
$693$	−3.44048	−0.130693
$694$	37.0134	1.40501
$695$	8.01774	0.304130
$696$	33.3986	1.26597
$697$	−48.5621	−1.83942
$698$	43.0228	1.62844
$699$	−17.9404	−0.678567
$700$	−21.0044	−0.793890
$701$	−1.26901	−0.0479297	−0.0239648	−	0.999713i	$-0.507629\pi$
$701$	−1.26901	−0.0479297	−0.0239648	+	0.999713i	$0.507629\pi$
$702$	−28.3325	−1.06934
$703$	−0.418212	−0.0157732
$704$	36.6337	1.38068
$705$	22.7815	0.858000
$706$	−1.28497	−0.0483604
$707$	38.5519	1.44989
$708$	76.1634	2.86239
$709$	28.0461	1.05330	0.526648	−	0.850084i	$-0.323449\pi$
$709$	28.0461	1.05330	0.526648	+	0.850084i	$0.323449\pi$
$710$	2.68861	0.100902
$711$	11.4057	0.427749
$712$	−136.343	−5.10967
$713$	32.4686	1.21596
$714$	87.6217	3.27916
$715$	2.49281	0.0932256
$716$	−55.2844	−2.06607
$717$	−10.1603	−0.379443
$718$	15.9310	0.594540
$719$	−44.1796	−1.64762	−0.823810	−	0.566867i	$-0.808155\pi$
$719$	−44.1796	−1.64762	−0.823810	+	0.566867i	$0.808155\pi$
$720$	−15.0328	−0.560240
$721$	4.90705	0.182748
$722$	52.3661	1.94886
$723$	−8.28167	−0.307999
$724$	40.8216	1.51712
$725$	−1.68870	−0.0627166
$726$	−5.46521	−0.202833
$727$	−8.69050	−0.322313	−0.161156	−	0.986929i	$-0.551522\pi$
$727$	−8.69050	−0.322313	−0.161156	+	0.986929i	$0.551522\pi$
$728$	−93.0819	−3.44984
$729$	14.4141	0.533854
$730$	2.76022	0.102161
$731$	23.7387	0.878006
$732$	168.931	6.24385
$733$	10.0039	0.369504	0.184752	−	0.982785i	$-0.440852\pi$
$733$	10.0039	0.369504	0.184752	+	0.982785i	$0.440852\pi$
$734$	−91.5220	−3.37814
$735$	−13.8088	−0.509344
$736$	−213.302	−7.86243
$737$	−10.9701	−0.404089
$738$	28.7644	1.05883
$739$	19.5857	0.720473	0.360237	−	0.932861i	$-0.382696\pi$
$739$	19.5857	0.720473	0.360237	+	0.932861i	$0.382696\pi$
$740$	−13.9614	−0.513230
$741$	0.830742	0.0305181
$742$	−85.5209	−3.13957
$743$	−2.36884	−0.0869044	−0.0434522	−	0.999056i	$-0.513836\pi$
$743$	−2.36884	−0.0869044	−0.0434522	+	0.999056i	$0.513836\pi$
$744$	−75.5857	−2.77111
$745$	0.230012	0.00842697
$746$	−50.7803	−1.85920
$747$	−2.71871	−0.0994724
$748$	24.0984	0.881125
$749$	60.2052	2.19985
$750$	5.46521	0.199561
$751$	−26.1073	−0.952669	−0.476335	−	0.879264i	$-0.658035\pi$
$751$	−26.1073	−0.952669	−0.476335	+	0.879264i	$0.658035\pi$
$752$	−187.933	−6.85322
$753$	−43.0424	−1.56855
$754$	−11.6194	−0.423154
$755$	−14.8344	−0.539878
$756$	86.4891	3.14558
$757$	−29.8214	−1.08388	−0.541938	−	0.840418i	$-0.682309\pi$
$757$	−29.8214	−1.08388	−0.541938	+	0.840418i	$0.682309\pi$
$758$	17.6933	0.642648
$759$	16.8214	0.610580
$760$	−1.68124	−0.0609849
$761$	−14.6771	−0.532046	−0.266023	−	0.963967i	$-0.585710\pi$
$761$	−14.6771	−0.532046	−0.266023	+	0.963967i	$0.585710\pi$
$762$	81.9460	2.96859
$763$	14.5358	0.526230
$764$	−0.625121	−0.0226161
$765$	−3.94727	−0.142714
$766$	64.4127	2.32732
$767$	−17.0657	−0.616208
$768$	133.128	4.80384
$769$	−3.31357	−0.119490	−0.0597452	−	0.998214i	$-0.519029\pi$
$769$	−3.31357	−0.119490	−0.0597452	+	0.998214i	$0.519029\pi$
$770$	−10.3183	−0.371845
$771$	−53.2729	−1.91858
$772$	−6.80813	−0.245030
$773$	−14.4485	−0.519678	−0.259839	−	0.965652i	$-0.583669\pi$
$773$	−14.4485	−0.519678	−0.259839	+	0.965652i	$0.583669\pi$
$774$	−14.0610	−0.505411
$775$	3.82176	0.137282
$776$	25.8540	0.928105
$777$	−18.3910	−0.659775
$778$	39.0715	1.40078
$779$	1.90577	0.0682814
$780$	27.7331	0.993003
$781$	0.974056	0.0348545
$782$	−100.574	−3.59652
$783$	6.95350	0.248498
$784$	113.914	4.06835
$785$	−15.8331	−0.565107
$786$	102.548	3.65776
$787$	−28.8416	−1.02809	−0.514046	−	0.857762i	$-0.671854\pi$
$787$	−28.8416	−1.02809	−0.514046	+	0.857762i	$0.671854\pi$
$788$	−50.9107	−1.81362
$789$	−35.4618	−1.26247
$790$	34.2068	1.21702
$791$	13.3904	0.476106
$792$	−9.19326	−0.326668
$793$	−37.8519	−1.34416
$794$	−66.7236	−2.36793
$795$	16.4107	0.582028
$796$	39.1428	1.38738
$797$	36.8081	1.30381	0.651905	−	0.758300i	$-0.273970\pi$
$797$	36.8081	1.30381	0.651905	+	0.758300i	$0.273970\pi$
$798$	−3.43863	−0.121726
$799$	−49.3470	−1.74577
$800$	−25.1070	−0.887668
$801$	12.5625	0.443873
$802$	14.8283	0.523605
$803$	1.00000	0.0352892
$804$	−122.045	−4.30420
$805$	31.7587	1.11935
$806$	26.2964	0.926250
$807$	−26.4040	−0.929465
$808$	103.014	3.62402
$809$	30.9746	1.08901	0.544504	−	0.838758i	$-0.316718\pi$
$809$	30.9746	1.08901	0.544504	+	0.838758i	$0.316718\pi$
$810$	−30.1251	−1.05849
$811$	5.71282	0.200604	0.100302	−	0.994957i	$-0.468019\pi$
$811$	5.71282	0.200604	0.100302	+	0.994957i	$0.468019\pi$
$812$	35.4700	1.24475
$813$	32.3263	1.13373
$814$	−6.85844	−0.240388
$815$	20.9993	0.735575
$816$	138.704	4.85561
$817$	−0.931601	−0.0325926
$818$	82.4482	2.88273
$819$	8.57644	0.299685
$820$	63.6213	2.22175
$821$	−34.9377	−1.21933	−0.609666	−	0.792658i	$-0.708697\pi$
$821$	−34.9377	−1.21933	−0.609666	+	0.792658i	$0.708697\pi$
$822$	75.6647	2.63911
$823$	−7.38959	−0.257585	−0.128792	−	0.991672i	$-0.541110\pi$
$823$	−7.38959	−0.257585	−0.128792	+	0.991672i	$0.541110\pi$
$824$	13.1121	0.456781
$825$	1.97999	0.0689344
$826$	70.6389	2.45784
$827$	44.9570	1.56331	0.781654	−	0.623712i	$-0.214376\pi$
$827$	44.9570	1.56331	0.781654	+	0.623712i	$0.214376\pi$
$828$	43.9342	1.52682
$829$	9.64091	0.334843	0.167421	−	0.985885i	$-0.446456\pi$
$829$	9.64091	0.334843	0.167421	+	0.985885i	$0.446456\pi$
$830$	−8.15364	−0.283017
$831$	−29.2756	−1.01556
$832$	−91.3206	−3.16597
$833$	29.9112	1.03636
$834$	43.8187	1.51732
$835$	−6.92554	−0.239668
$836$	−0.945719	−0.0327084
$837$	−15.7367	−0.543941
$838$	−60.9332	−2.10490
$839$	−33.5175	−1.15715	−0.578577	−	0.815628i	$-0.696392\pi$
$839$	−33.5175	−1.15715	−0.578577	+	0.815628i	$0.696392\pi$
$840$	−73.9332	−2.55094
$841$	−26.1483	−0.901666
$842$	99.3752	3.42470
$843$	−49.2273	−1.69548
$844$	−68.2137	−2.34801
$845$	6.78592	0.233443
$846$	29.2293	1.00493
$847$	−3.73820	−0.128446
$848$	−135.378	−4.64891
$849$	−24.7311	−0.848770
$850$	−11.8382	−0.406047
$851$	21.1097	0.723630
$852$	10.8366	0.371256
$853$	12.4771	0.427208	0.213604	−	0.976920i	$-0.431480\pi$
$853$	12.4771	0.427208	0.213604	+	0.976920i	$0.431480\pi$
$854$	156.677	5.36139
$855$	0.154907	0.00529771
$856$	160.874	5.49855
$857$	43.6882	1.49236	0.746181	−	0.665743i	$-0.231885\pi$
$857$	43.6882	1.49236	0.746181	+	0.665743i	$0.231885\pi$
$858$	13.6237	0.465106
$859$	10.3840	0.354298	0.177149	−	0.984184i	$-0.443313\pi$
$859$	10.3840	0.354298	0.177149	+	0.984184i	$0.443313\pi$
$860$	−31.1001	−1.06050
$861$	83.8072	2.85614
$862$	−28.1713	−0.959520
$863$	51.7414	1.76130	0.880649	−	0.473770i	$-0.157107\pi$
$863$	51.7414	1.76130	0.880649	+	0.473770i	$0.157107\pi$
$864$	103.383	3.51715
$865$	−13.1850	−0.448304
$866$	97.2105	3.30335
$867$	2.76067	0.0937573
$868$	−80.2736	−2.72466
$869$	12.3928	0.420395
$870$	−9.22909	−0.312895
$871$	27.3464	0.926596
$872$	38.8409	1.31532
$873$	−2.38215	−0.0806237
$874$	3.94694	0.133507
$875$	3.73820	0.126374
$876$	11.1252	0.375887
$877$	8.64644	0.291970	0.145985	−	0.989287i	$-0.453365\pi$
$877$	8.64644	0.291970	0.145985	+	0.989287i	$0.453365\pi$
$878$	24.4182	0.824074
$879$	58.1525	1.96144
$880$	−16.3337	−0.550609
$881$	20.6642	0.696195	0.348097	−	0.937458i	$-0.386828\pi$
$881$	20.6642	0.696195	0.348097	+	0.937458i	$0.386828\pi$
$882$	−17.7171	−0.596565
$883$	9.83788	0.331071	0.165536	−	0.986204i	$-0.447065\pi$
$883$	9.83788	0.331071	0.165536	+	0.986204i	$0.447065\pi$
$884$	−60.0726	−2.02046
$885$	−13.5550	−0.455646
$886$	−39.3466	−1.32187
$887$	−0.725419	−0.0243572	−0.0121786	−	0.999926i	$-0.503877\pi$
$887$	−0.725419	−0.0243572	−0.0121786	+	0.999926i	$0.503877\pi$
$888$	−49.1425	−1.64912
$889$	56.0510	1.87989
$890$	37.6759	1.26290
$891$	−10.9140	−0.365633
$892$	−117.468	−3.93311
$893$	1.93657	0.0648050
$894$	1.25706	0.0420425
$895$	9.83911	0.328885
$896$	190.286	6.35701
$897$	−41.9326	−1.40009
$898$	17.9083	0.597606
$899$	−6.45379	−0.215246
$900$	5.17133	0.172378
$901$	−35.5473	−1.18425
$902$	31.2536	1.04063
$903$	−40.9676	−1.36332
$904$	35.7803	1.19003
$905$	−7.26513	−0.241501
$906$	−81.0729	−2.69347
$907$	33.8004	1.12232	0.561161	−	0.827706i	$-0.310355\pi$
$907$	33.8004	1.12232	0.561161	+	0.827706i	$0.310355\pi$
$908$	159.368	5.28881
$909$	−9.49157	−0.314816
$910$	25.7215	0.852658
$911$	17.7464	0.587965	0.293982	−	0.955811i	$-0.405019\pi$
$911$	17.7464	0.587965	0.293982	+	0.955811i	$0.405019\pi$
$912$	−5.44330	−0.180246
$913$	−2.95398	−0.0977624
$914$	−88.9048	−2.94071
$915$	−30.0650	−0.993919
$916$	55.3227	1.82791
$917$	70.1427	2.31632
$918$	48.7459	1.60885
$919$	−18.6905	−0.616544	−0.308272	−	0.951298i	$-0.599751\pi$
$919$	−18.6905	−0.616544	−0.308272	+	0.951298i	$0.599751\pi$
$920$	84.8622	2.79782
$921$	−12.1782	−0.401286
$922$	−115.694	−3.81019
$923$	−2.42813	−0.0799229
$924$	−41.5884	−1.36816
$925$	2.48474	0.0816977
$926$	106.772	3.50874
$927$	−1.20813	−0.0396801
$928$	42.3982	1.39179
$929$	−49.6585	−1.62924	−0.814622	−	0.579993i	$-0.803055\pi$
$929$	−49.6585	−1.62924	−0.814622	+	0.579993i	$0.803055\pi$
$930$	20.8867	0.684902
$931$	−1.17384	−0.0384709
$932$	−50.9115	−1.66766
$933$	−59.3628	−1.94345
$934$	28.1126	0.919871
$935$	−4.28886	−0.140261
$936$	22.9170	0.749066
$937$	0.436337	0.0142545	0.00712725	−	0.999975i	$-0.497731\pi$
$937$	0.436337	0.0142545	0.00712725	+	0.999975i	$0.497731\pi$
$938$	−113.193	−3.69587
$939$	34.8466	1.13718
$940$	64.6496	2.10864
$941$	−24.5180	−0.799265	−0.399633	−	0.916675i	$-0.630862\pi$
$941$	−24.5180	−0.799265	−0.399633	+	0.916675i	$0.630862\pi$
$942$	−86.5312	−2.81934
$943$	−96.1958	−3.13257
$944$	111.820	3.63944
$945$	−15.3927	−0.500724
$946$	−15.2777	−0.496722
$947$	16.0125	0.520336	0.260168	−	0.965563i	$-0.416222\pi$
$947$	16.0125	0.520336	0.260168	+	0.965563i	$0.416222\pi$
$948$	137.872	4.47789
$949$	−2.49281	−0.0809199
$950$	0.464579	0.0150729
$951$	−35.7820	−1.16031
$952$	160.147	5.19039
$953$	9.37541	0.303699	0.151850	−	0.988404i	$-0.451477\pi$
$953$	9.37541	0.303699	0.151850	+	0.988404i	$0.451477\pi$
$954$	21.0555	0.681696
$955$	0.111254	0.00360011
$956$	−28.8331	−0.932528
$957$	−3.34360	−0.108083
$958$	−3.94079	−0.127321
$959$	51.7546	1.67124
$960$	−72.5343	−2.34103
$961$	−16.3942	−0.528844
$962$	17.0968	0.551222
$963$	−14.8227	−0.477654
$964$	−23.5018	−0.756944
$965$	1.21166	0.0390047
$966$	173.568	5.58447
$967$	−34.7845	−1.11860	−0.559298	−	0.828967i	$-0.688929\pi$
$967$	−34.7845	−1.11860	−0.559298	+	0.828967i	$0.688929\pi$
$968$	−9.98882	−0.321053
$969$	−1.42929	−0.0459153
$970$	−7.14428	−0.229389
$971$	−50.5068	−1.62084	−0.810420	−	0.585849i	$-0.800761\pi$
$971$	−50.5068	−1.62084	−0.810420	+	0.585849i	$0.800761\pi$
$972$	−52.0114	−1.66827
$973$	29.9719	0.960856
$974$	−71.0031	−2.27509
$975$	−4.93573	−0.158070
$976$	248.018	7.93886
$977$	14.3980	0.460632	0.230316	−	0.973116i	$-0.426024\pi$
$977$	14.3980	0.460632	0.230316	+	0.973116i	$0.426024\pi$
$978$	114.766	3.66981
$979$	13.6496	0.436242
$980$	−39.1867	−1.25177
$981$	−3.57875	−0.114261
$982$	−5.92724	−0.189146
$983$	30.2773	0.965696	0.482848	−	0.875704i	$-0.339602\pi$
$983$	30.2773	0.965696	0.482848	+	0.875704i	$0.339602\pi$
$984$	223.940	7.13896
$985$	9.06072	0.288698
$986$	19.9911	0.636648
$987$	85.1617	2.71073
$988$	2.35749	0.0750018
$989$	47.0235	1.49526
$990$	2.54039	0.0807389
$991$	17.2983	0.549499	0.274749	−	0.961516i	$-0.411405\pi$
$991$	17.2983	0.549499	0.274749	+	0.961516i	$0.411405\pi$
$992$	−95.9530	−3.04651
$993$	6.10822	0.193839
$994$	10.0506	0.318785
$995$	−6.96635	−0.220848
$996$	−32.8637	−1.04133
$997$	7.07637	0.224111	0.112055	−	0.993702i	$-0.464257\pi$
$997$	7.07637	0.224111	0.112055	+	0.993702i	$0.464257\pi$
$998$	−2.00216	−0.0633772
$999$	−10.2313	−0.323705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.f.1.2	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.f.1.2	✓	31	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.76022 q^{2} +1.97999 q^{3} +5.61884 q^{4} -1.00000 q^{5} -5.46521 q^{6} -3.73820 q^{7} -9.98882 q^{8} +0.920356 q^{9} +O(q^{10})\)	\(q-2.76022 q^{2} +1.97999 q^{3} +5.61884 q^{4} -1.00000 q^{5} -5.46521 q^{6} -3.73820 q^{7} -9.98882 q^{8} +0.920356 q^{9} +2.76022 q^{10} +1.00000 q^{11} +11.1252 q^{12} -2.49281 q^{13} +10.3183 q^{14} -1.97999 q^{15} +16.3337 q^{16} +4.28886 q^{17} -2.54039 q^{18} -0.168312 q^{19} -5.61884 q^{20} -7.40160 q^{21} -2.76022 q^{22} +8.49572 q^{23} -19.7777 q^{24} +1.00000 q^{25} +6.88070 q^{26} -4.11767 q^{27} -21.0044 q^{28} -1.68870 q^{29} +5.46521 q^{30} +3.82176 q^{31} -25.1070 q^{32} +1.97999 q^{33} -11.8382 q^{34} +3.73820 q^{35} +5.17133 q^{36} +2.48474 q^{37} +0.464579 q^{38} -4.93573 q^{39} +9.98882 q^{40} -11.3228 q^{41} +20.4301 q^{42} +5.53496 q^{43} +5.61884 q^{44} -0.920356 q^{45} -23.4501 q^{46} -11.5059 q^{47} +32.3405 q^{48} +6.97416 q^{49} -2.76022 q^{50} +8.49189 q^{51} -14.0067 q^{52} -8.28829 q^{53} +11.3657 q^{54} -1.00000 q^{55} +37.3402 q^{56} -0.333256 q^{57} +4.66118 q^{58} +6.84600 q^{59} -11.1252 q^{60} +15.1844 q^{61} -10.5489 q^{62} -3.44048 q^{63} +36.6337 q^{64} +2.49281 q^{65} -5.46521 q^{66} -10.9701 q^{67} +24.0984 q^{68} +16.8214 q^{69} -10.3183 q^{70} +0.974056 q^{71} -9.19326 q^{72} +1.00000 q^{73} -6.85844 q^{74} +1.97999 q^{75} -0.945719 q^{76} -3.73820 q^{77} +13.6237 q^{78} +12.3928 q^{79} -16.3337 q^{80} -10.9140 q^{81} +31.2536 q^{82} -2.95398 q^{83} -41.5884 q^{84} -4.28886 q^{85} -15.2777 q^{86} -3.34360 q^{87} -9.98882 q^{88} +13.6496 q^{89} +2.54039 q^{90} +9.31861 q^{91} +47.7361 q^{92} +7.56703 q^{93} +31.7588 q^{94} +0.168312 q^{95} -49.7116 q^{96} -2.58830 q^{97} -19.2502 q^{98} +0.920356 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9} + 7 q^{10} + 31 q^{11} - 4 q^{12} - 24 q^{13} - 9 q^{14} + 4 q^{15} + 43 q^{16} - 49 q^{17} - 35 q^{18} - 22 q^{19} - 39 q^{20} - 8 q^{21} - 7 q^{22} - q^{23} - 13 q^{24} + 31 q^{25} - 9 q^{26} - 22 q^{27} - 34 q^{28} - 12 q^{29} + 5 q^{30} + 4 q^{31} - 45 q^{32} - 4 q^{33} + 2 q^{34} + 11 q^{35} + 34 q^{36} - 18 q^{37} - 7 q^{38} - q^{39} + 24 q^{40} - 58 q^{41} - 21 q^{42} - 41 q^{43} + 39 q^{44} - 31 q^{45} + 23 q^{46} - 31 q^{47} - 29 q^{48} + 44 q^{49} - 7 q^{50} + 8 q^{51} - 89 q^{52} - 46 q^{53} - 47 q^{54} - 31 q^{55} + 10 q^{56} - 47 q^{57} - 34 q^{58} - 9 q^{59} + 4 q^{60} - 5 q^{61} - 50 q^{62} - 61 q^{63} + 78 q^{64} + 24 q^{65} - 5 q^{66} + q^{67} - 115 q^{68} - 19 q^{69} + 9 q^{70} - 8 q^{71} - 93 q^{72} + 31 q^{73} - 19 q^{74} - 4 q^{75} - 7 q^{76} - 11 q^{77} + 57 q^{78} - 43 q^{80} + 43 q^{81} + 20 q^{82} - 29 q^{83} - 32 q^{84} + 49 q^{85} + 25 q^{86} - 62 q^{87} - 24 q^{88} - 77 q^{89} + 35 q^{90} - 11 q^{91} - 25 q^{92} - 38 q^{94} + 22 q^{95} - 23 q^{96} - 39 q^{97} - 65 q^{98} + 31 q^{99}+O(q^{100}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9 + 7 * q^10 + 31 * q^11 - 4 * q^12 - 24 * q^13 - 9 * q^14 + 4 * q^15 + 43 * q^16 - 49 * q^17 - 35 * q^18 - 22 * q^19 - 39 * q^20 - 8 * q^21 - 7 * q^22 - q^23 - 13 * q^24 + 31 * q^25 - 9 * q^26 - 22 * q^27 - 34 * q^28 - 12 * q^29 + 5 * q^30 + 4 * q^31 - 45 * q^32 - 4 * q^33 + 2 * q^34 + 11 * q^35 + 34 * q^36 - 18 * q^37 - 7 * q^38 - q^39 + 24 * q^40 - 58 * q^41 - 21 * q^42 - 41 * q^43 + 39 * q^44 - 31 * q^45 + 23 * q^46 - 31 * q^47 - 29 * q^48 + 44 * q^49 - 7 * q^50 + 8 * q^51 - 89 * q^52 - 46 * q^53 - 47 * q^54 - 31 * q^55 + 10 * q^56 - 47 * q^57 - 34 * q^58 - 9 * q^59 + 4 * q^60 - 5 * q^61 - 50 * q^62 - 61 * q^63 + 78 * q^64 + 24 * q^65 - 5 * q^66 + q^67 - 115 * q^68 - 19 * q^69 + 9 * q^70 - 8 * q^71 - 93 * q^72 + 31 * q^73 - 19 * q^74 - 4 * q^75 - 7 * q^76 - 11 * q^77 + 57 * q^78 - 43 * q^80 + 43 * q^81 + 20 * q^82 - 29 * q^83 - 32 * q^84 + 49 * q^85 + 25 * q^86 - 62 * q^87 - 24 * q^88 - 77 * q^89 + 35 * q^90 - 11 * q^91 - 25 * q^92 - 38 * q^94 + 22 * q^95 - 23 * q^96 - 39 * q^97 - 65 * q^98 + 31 * q^99

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