LMFDB - Embedded newform 8015.2.a.i.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$1$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.65863 q^{2} +1.21505 q^{3} +0.751045 q^{4} +1.00000 q^{5} -2.01532 q^{6} -1.00000 q^{7} +2.07155 q^{8} -1.52365 q^{9} +O(q^{10})$	\(q-1.65863 q^{2} +1.21505 q^{3} +0.751045 q^{4} +1.00000 q^{5} -2.01532 q^{6} -1.00000 q^{7} +2.07155 q^{8} -1.52365 q^{9} -1.65863 q^{10} -5.02519 q^{11} +0.912560 q^{12} -1.70016 q^{13} +1.65863 q^{14} +1.21505 q^{15} -4.93802 q^{16} +4.99037 q^{17} +2.52716 q^{18} -0.872568 q^{19} +0.751045 q^{20} -1.21505 q^{21} +8.33493 q^{22} -2.73016 q^{23} +2.51705 q^{24} +1.00000 q^{25} +2.81993 q^{26} -5.49647 q^{27} -0.751045 q^{28} +0.150614 q^{29} -2.01532 q^{30} +7.20088 q^{31} +4.04724 q^{32} -6.10588 q^{33} -8.27717 q^{34} -1.00000 q^{35} -1.14433 q^{36} +4.43604 q^{37} +1.44727 q^{38} -2.06578 q^{39} +2.07155 q^{40} +6.95313 q^{41} +2.01532 q^{42} +3.64530 q^{43} -3.77415 q^{44} -1.52365 q^{45} +4.52833 q^{46} -4.69774 q^{47} -5.99996 q^{48} +1.00000 q^{49} -1.65863 q^{50} +6.06357 q^{51} -1.27689 q^{52} +5.70549 q^{53} +9.11660 q^{54} -5.02519 q^{55} -2.07155 q^{56} -1.06022 q^{57} -0.249812 q^{58} +12.3536 q^{59} +0.912560 q^{60} -0.319003 q^{61} -11.9436 q^{62} +1.52365 q^{63} +3.16319 q^{64} -1.70016 q^{65} +10.1274 q^{66} +1.80573 q^{67} +3.74800 q^{68} -3.31730 q^{69} +1.65863 q^{70} -3.63277 q^{71} -3.15631 q^{72} -6.37006 q^{73} -7.35773 q^{74} +1.21505 q^{75} -0.655338 q^{76} +5.02519 q^{77} +3.42636 q^{78} +6.92372 q^{79} -4.93802 q^{80} -2.10757 q^{81} -11.5327 q^{82} -2.79360 q^{83} -0.912560 q^{84} +4.99037 q^{85} -6.04620 q^{86} +0.183003 q^{87} -10.4099 q^{88} -7.82447 q^{89} +2.52716 q^{90} +1.70016 q^{91} -2.05048 q^{92} +8.74946 q^{93} +7.79180 q^{94} -0.872568 q^{95} +4.91761 q^{96} -7.30500 q^{97} -1.65863 q^{98} +7.65661 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) $ 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9 - 2 * q^10 - 15 * q^11 - 3 * q^12 - 17 * q^13 + 2 * q^14 + 10 * q^16 - 7 * q^17 - 16 * q^18 - 32 * q^19 + 30 * q^20 - 14 * q^22 + 8 * q^23 - 35 * q^24 + 44 * q^25 - 27 * q^26 + 6 * q^27 - 30 * q^28 - 42 * q^29 - 7 * q^30 - 43 * q^31 - 8 * q^32 - 33 * q^33 - 33 * q^34 - 44 * q^35 - 11 * q^36 - 44 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 - 62 * q^41 + 7 * q^42 - 7 * q^43 - 45 * q^44 + 16 * q^45 - 15 * q^46 + 2 * q^47 - 26 * q^48 + 44 * q^49 - 2 * q^50 - 25 * q^51 - 35 * q^52 - 25 * q^53 - 76 * q^54 - 15 * q^55 + 3 * q^56 - 7 * q^57 - 2 * q^58 - 35 * q^59 - 3 * q^60 - 86 * q^61 - 23 * q^62 - 16 * q^63 - 5 * q^64 - 17 * q^65 - 6 * q^66 + 2 * q^67 - q^68 - 75 * q^69 + 2 * q^70 - 54 * q^71 - 3 * q^72 - 52 * q^73 - 22 * q^74 - 77 * q^76 + 15 * q^77 + 2 * q^78 + 46 * q^79 + 10 * q^80 - 72 * q^81 - 16 * q^82 + 26 * q^83 + 3 * q^84 - 7 * q^85 - 33 * q^86 - 8 * q^87 - 23 * q^88 - 105 * q^89 - 16 * q^90 + 17 * q^91 - 41 * q^92 - 11 * q^93 - 47 * q^94 - 32 * q^95 - 39 * q^96 - 80 * q^97 - 2 * q^98 - 53 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.65863	−1.17283	−0.586413	−	0.810012i	$-0.699461\pi$
$2$	−1.65863	−1.17283	−0.586413	+	0.810012i	$0.699461\pi$
$3$	1.21505	0.701511	0.350756	−	0.936467i	$-0.385925\pi$
$3$	1.21505	0.701511	0.350756	+	0.936467i	$0.385925\pi$
$4$	0.751045	0.375523
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.01532	−0.822751
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.07155	0.732404
$9$	−1.52365	−0.507882
$10$	−1.65863	−0.524504
$11$	−5.02519	−1.51515	−0.757577	−	0.652746i	$-0.773617\pi$
$11$	−5.02519	−1.51515	−0.757577	+	0.652746i	$0.773617\pi$
$12$	0.912560	0.263433
$13$	−1.70016	−0.471539	−0.235769	−	0.971809i	$-0.575761\pi$
$13$	−1.70016	−0.471539	−0.235769	+	0.971809i	$0.575761\pi$
$14$	1.65863	0.443287
$15$	1.21505	0.313725
$16$	−4.93802	−1.23451
$17$	4.99037	1.21034	0.605172	−	0.796095i	$-0.293104\pi$
$17$	4.99037	1.21034	0.605172	+	0.796095i	$0.293104\pi$
$18$	2.52716	0.595657
$19$	−0.872568	−0.200181	−0.100090	−	0.994978i	$-0.531913\pi$
$19$	−0.872568	−0.200181	−0.100090	+	0.994978i	$0.531913\pi$
$20$	0.751045	0.167939
$21$	−1.21505	−0.265146
$22$	8.33493	1.77701
$23$	−2.73016	−0.569279	−0.284639	−	0.958635i	$-0.591874\pi$
$23$	−2.73016	−0.569279	−0.284639	+	0.958635i	$0.591874\pi$
$24$	2.51705	0.513790
$25$	1.00000	0.200000
$26$	2.81993	0.553033
$27$	−5.49647	−1.05780
$28$	−0.751045	−0.141934
$29$	0.150614	0.0279682	0.0139841	−	0.999902i	$-0.495549\pi$
$29$	0.150614	0.0279682	0.0139841	+	0.999902i	$0.495549\pi$
$30$	−2.01532	−0.367946
$31$	7.20088	1.29332	0.646658	−	0.762780i	$-0.276166\pi$
$31$	7.20088	1.29332	0.646658	+	0.762780i	$0.276166\pi$
$32$	4.04724	0.715457
$33$	−6.10588	−1.06290
$34$	−8.27717	−1.41952
$35$	−1.00000	−0.169031
$36$	−1.14433	−0.190721
$37$	4.43604	0.729280	0.364640	−	0.931149i	$-0.381192\pi$
$37$	4.43604	0.729280	0.364640	+	0.931149i	$0.381192\pi$
$38$	1.44727	0.234778
$39$	−2.06578	−0.330790
$40$	2.07155	0.327541
$41$	6.95313	1.08590	0.542948	−	0.839766i	$-0.317308\pi$
$41$	6.95313	1.08590	0.542948	+	0.839766i	$0.317308\pi$
$42$	2.01532	0.310971
$43$	3.64530	0.555903	0.277952	−	0.960595i	$-0.410344\pi$
$43$	3.64530	0.555903	0.277952	+	0.960595i	$0.410344\pi$
$44$	−3.77415	−0.568974
$45$	−1.52365	−0.227132
$46$	4.52833	0.667665
$47$	−4.69774	−0.685236	−0.342618	−	0.939475i	$-0.611314\pi$
$47$	−4.69774	−0.685236	−0.342618	+	0.939475i	$0.611314\pi$
$48$	−5.99996	−0.866020
$49$	1.00000	0.142857
$50$	−1.65863	−0.234565
$51$	6.06357	0.849070
$52$	−1.27689	−0.177073
$53$	5.70549	0.783710	0.391855	−	0.920027i	$-0.371833\pi$
$53$	5.70549	0.783710	0.391855	+	0.920027i	$0.371833\pi$
$54$	9.11660	1.24061
$55$	−5.02519	−0.677597
$56$	−2.07155	−0.276823
$57$	−1.06022	−0.140429
$58$	−0.249812	−0.0328019
$59$	12.3536	1.60830	0.804148	−	0.594428i	$-0.202622\pi$
$59$	12.3536	1.60830	0.804148	+	0.594428i	$0.202622\pi$
$60$	0.912560	0.117811
$61$	−0.319003	−0.0408441	−0.0204220	−	0.999791i	$-0.506501\pi$
$61$	−0.319003	−0.0408441	−0.0204220	+	0.999791i	$0.506501\pi$
$62$	−11.9436	−1.51684
$63$	1.52365	0.191961
$64$	3.16319	0.395398
$65$	−1.70016	−0.210878
$66$	10.1274	1.24659
$67$	1.80573	0.220605	0.110302	−	0.993898i	$-0.464818\pi$
$67$	1.80573	0.220605	0.110302	+	0.993898i	$0.464818\pi$
$68$	3.74800	0.454511
$69$	−3.31730	−0.399355
$70$	1.65863	0.198244
$71$	−3.63277	−0.431130	−0.215565	−	0.976489i	$-0.569159\pi$
$71$	−3.63277	−0.431130	−0.215565	+	0.976489i	$0.569159\pi$
$72$	−3.15631	−0.371975
$73$	−6.37006	−0.745559	−0.372779	−	0.927920i	$-0.621595\pi$
$73$	−6.37006	−0.745559	−0.372779	+	0.927920i	$0.621595\pi$
$74$	−7.35773	−0.855319
$75$	1.21505	0.140302
$76$	−0.655338	−0.0751725
$77$	5.02519	0.572674
$78$	3.42636	0.387959
$79$	6.92372	0.778980	0.389490	−	0.921031i	$-0.372651\pi$
$79$	6.92372	0.778980	0.389490	+	0.921031i	$0.372651\pi$
$80$	−4.93802	−0.552088
$81$	−2.10757	−0.234174
$82$	−11.5327	−1.27357
$83$	−2.79360	−0.306637	−0.153318	−	0.988177i	$-0.548996\pi$
$83$	−2.79360	−0.306637	−0.153318	+	0.988177i	$0.548996\pi$
$84$	−0.912560	−0.0995684
$85$	4.99037	0.541282
$86$	−6.04620	−0.651978
$87$	0.183003	0.0196200
$88$	−10.4099	−1.10970
$89$	−7.82447	−0.829392	−0.414696	−	0.909960i	$-0.636112\pi$
$89$	−7.82447	−0.829392	−0.414696	+	0.909960i	$0.636112\pi$
$90$	2.52716	0.266386
$91$	1.70016	0.178225
$92$	−2.05048	−0.213777
$93$	8.74946	0.907276
$94$	7.79180	0.803663
$95$	−0.872568	−0.0895236
$96$	4.91761	0.501901
$97$	−7.30500	−0.741711	−0.370855	−	0.928691i	$-0.620935\pi$
$97$	−7.30500	−0.741711	−0.370855	+	0.928691i	$0.620935\pi$
$98$	−1.65863	−0.167547
$99$	7.65661	0.769519
$100$	0.751045	0.0751045
$101$	11.7964	1.17379	0.586895	−	0.809663i	$-0.300350\pi$
$101$	11.7964	1.17379	0.586895	+	0.809663i	$0.300350\pi$
$102$	−10.0572	−0.995812
$103$	0.896701	0.0883545	0.0441773	−	0.999024i	$-0.485933\pi$
$103$	0.896701	0.0883545	0.0441773	+	0.999024i	$0.485933\pi$
$104$	−3.52196	−0.345357
$105$	−1.21505	−0.118577
$106$	−9.46329	−0.919156
$107$	4.97270	0.480729	0.240365	−	0.970683i	$-0.422733\pi$
$107$	4.97270	0.480729	0.240365	+	0.970683i	$0.422733\pi$
$108$	−4.12810	−0.397226
$109$	−7.68157	−0.735761	−0.367881	−	0.929873i	$-0.619917\pi$
$109$	−7.68157	−0.735761	−0.367881	+	0.929873i	$0.619917\pi$
$110$	8.33493	0.794704
$111$	5.39002	0.511598
$112$	4.93802	0.466599
$113$	−10.9958	−1.03440	−0.517200	−	0.855865i	$-0.673026\pi$
$113$	−10.9958	−1.03440	−0.517200	+	0.855865i	$0.673026\pi$
$114$	1.75851	0.164699
$115$	−2.73016	−0.254589
$116$	0.113118	0.0105027
$117$	2.59044	0.239486
$118$	−20.4900	−1.88625
$119$	−4.99037	−0.457467
$120$	2.51705	0.229774
$121$	14.2526	1.29569
$122$	0.529106	0.0479030
$123$	8.44843	0.761769
$124$	5.40819	0.485670
$125$	1.00000	0.0894427
$126$	−2.52716	−0.225137
$127$	−5.49972	−0.488021	−0.244011	−	0.969773i	$-0.578463\pi$
$127$	−5.49972	−0.488021	−0.244011	+	0.969773i	$0.578463\pi$
$128$	−13.3410	−1.17919
$129$	4.42924	0.389973
$130$	2.81993	0.247324
$131$	−0.261585	−0.0228548	−0.0114274	−	0.999935i	$-0.503638\pi$
$131$	−0.261585	−0.0228548	−0.0114274	+	0.999935i	$0.503638\pi$
$132$	−4.58579	−0.399142
$133$	0.872568	0.0756613
$134$	−2.99503	−0.258731
$135$	−5.49647	−0.473061
$136$	10.3378	0.886460
$137$	7.10756	0.607240	0.303620	−	0.952793i	$-0.401805\pi$
$137$	7.10756	0.607240	0.303620	+	0.952793i	$0.401805\pi$
$138$	5.50216	0.468375
$139$	−12.6087	−1.06945	−0.534727	−	0.845025i	$-0.679585\pi$
$139$	−12.6087	−1.06945	−0.534727	+	0.845025i	$0.679585\pi$
$140$	−0.751045	−0.0634749
$141$	−5.70801	−0.480701
$142$	6.02541	0.505641
$143$	8.54362	0.714453
$144$	7.52379	0.626983
$145$	0.150614	0.0125078
$146$	10.5656	0.874411
$147$	1.21505	0.100216
$148$	3.33166	0.273861
$149$	−14.9123	−1.22167	−0.610834	−	0.791759i	$-0.709166\pi$
$149$	−14.9123	−1.22167	−0.610834	+	0.791759i	$0.709166\pi$
$150$	−2.01532	−0.164550
$151$	−5.47497	−0.445546	−0.222773	−	0.974870i	$-0.571511\pi$
$151$	−5.47497	−0.445546	−0.222773	+	0.974870i	$0.571511\pi$
$152$	−1.80757	−0.146613
$153$	−7.60356	−0.614711
$154$	−8.33493	−0.671647
$155$	7.20088	0.578389
$156$	−1.55149	−0.124219
$157$	−22.2155	−1.77299	−0.886494	−	0.462740i	$-0.846866\pi$
$157$	−22.2155	−1.77299	−0.886494	+	0.462740i	$0.846866\pi$
$158$	−11.4839	−0.913608
$159$	6.93248	0.549782
$160$	4.04724	0.319962
$161$	2.73016	0.215167
$162$	3.49567	0.274646
$163$	13.5382	1.06039	0.530195	−	0.847876i	$-0.322119\pi$
$163$	13.5382	1.06039	0.530195	+	0.847876i	$0.322119\pi$
$164$	5.22211	0.407779
$165$	−6.10588	−0.475342
$166$	4.63353	0.359632
$167$	−14.0446	−1.08681	−0.543403	−	0.839472i	$-0.682864\pi$
$167$	−14.0446	−1.08681	−0.543403	+	0.839472i	$0.682864\pi$
$168$	−2.51705	−0.194194
$169$	−10.1095	−0.777651
$170$	−8.27717	−0.634830
$171$	1.32948	0.101668
$172$	2.73779	0.208754
$173$	−8.46616	−0.643670	−0.321835	−	0.946796i	$-0.604300\pi$
$173$	−8.46616	−0.643670	−0.321835	+	0.946796i	$0.604300\pi$
$174$	−0.303535	−0.0230109
$175$	−1.00000	−0.0755929
$176$	24.8145	1.87046
$177$	15.0102	1.12824
$178$	12.9779	0.972733
$179$	−21.9781	−1.64272	−0.821361	−	0.570408i	$-0.806785\pi$
$179$	−21.9781	−1.64272	−0.821361	+	0.570408i	$0.806785\pi$
$180$	−1.14433	−0.0852930
$181$	−8.86449	−0.658893	−0.329446	−	0.944174i	$-0.606862\pi$
$181$	−8.86449	−0.658893	−0.329446	+	0.944174i	$0.606862\pi$
$182$	−2.81993	−0.209027
$183$	−0.387605	−0.0286526
$184$	−5.65567	−0.416942
$185$	4.43604	0.326144
$186$	−14.5121	−1.06408
$187$	−25.0776	−1.83386
$188$	−3.52822	−0.257322
$189$	5.49647	0.399809
$190$	1.44727	0.104996
$191$	−14.0637	−1.01762	−0.508809	−	0.860880i	$-0.669914\pi$
$191$	−14.0637	−1.01762	−0.508809	+	0.860880i	$0.669914\pi$
$192$	3.84344	0.277376
$193$	−24.7721	−1.78314	−0.891568	−	0.452887i	$-0.850394\pi$
$193$	−24.7721	−1.78314	−0.891568	+	0.452887i	$0.850394\pi$
$194$	12.1163	0.869898
$195$	−2.06578	−0.147934
$196$	0.751045	0.0536461
$197$	−23.5829	−1.68021	−0.840105	−	0.542423i	$-0.817507\pi$
$197$	−23.5829	−1.68021	−0.840105	+	0.542423i	$0.817507\pi$
$198$	−12.6995	−0.902512
$199$	18.8295	1.33479	0.667393	−	0.744705i	$-0.267410\pi$
$199$	18.8295	1.33479	0.667393	+	0.744705i	$0.267410\pi$
$200$	2.07155	0.146481
$201$	2.19406	0.154757
$202$	−19.5659	−1.37665
$203$	−0.150614	−0.0105710
$204$	4.55402	0.318845
$205$	6.95313	0.485628
$206$	−1.48729	−0.103625
$207$	4.15980	0.289126
$208$	8.39541	0.582117
$209$	4.38483	0.303305
$210$	2.01532	0.139070
$211$	3.62575	0.249607	0.124804	−	0.992181i	$-0.460170\pi$
$211$	3.62575	0.249607	0.124804	+	0.992181i	$0.460170\pi$
$212$	4.28508	0.294301
$213$	−4.41401	−0.302443
$214$	−8.24786	−0.563812
$215$	3.64530	0.248608
$216$	−11.3862	−0.774734
$217$	−7.20088	−0.488828
$218$	12.7409	0.862921
$219$	−7.73996	−0.523018
$220$	−3.77415	−0.254453
$221$	−8.48442	−0.570724
$222$	−8.94004	−0.600016
$223$	4.86031	0.325470	0.162735	−	0.986670i	$-0.447968\pi$
$223$	4.86031	0.325470	0.162735	+	0.986670i	$0.447968\pi$
$224$	−4.04724	−0.270417
$225$	−1.52365	−0.101576
$226$	18.2380	1.21317
$227$	−9.30596	−0.617658	−0.308829	−	0.951118i	$-0.599937\pi$
$227$	−9.30596	−0.617658	−0.308829	+	0.951118i	$0.599937\pi$
$228$	−0.796271	−0.0527343
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	4.52833	0.298589
$231$	6.10588	0.401737
$232$	0.312004	0.0204840
$233$	−5.21376	−0.341565	−0.170782	−	0.985309i	$-0.554630\pi$
$233$	−5.21376	−0.341565	−0.170782	+	0.985309i	$0.554630\pi$
$234$	−4.29657	−0.280875
$235$	−4.69774	−0.306447
$236$	9.27808	0.603952
$237$	8.41269	0.546463
$238$	8.27717	0.536529
$239$	−10.5541	−0.682689	−0.341345	−	0.939938i	$-0.610882\pi$
$239$	−10.5541	−0.682689	−0.341345	+	0.939938i	$0.610882\pi$
$240$	−5.99996	−0.387296
$241$	−5.55369	−0.357745	−0.178872	−	0.983872i	$-0.557245\pi$
$241$	−5.55369	−0.357745	−0.178872	+	0.983872i	$0.557245\pi$
$242$	−23.6397	−1.51962
$243$	13.9286	0.893520
$244$	−0.239585	−0.0153379
$245$	1.00000	0.0638877
$246$	−14.0128	−0.893423
$247$	1.48350	0.0943930
$248$	14.9170	0.947230
$249$	−3.39437	−0.215109
$250$	−1.65863	−0.104901
$251$	−8.32321	−0.525356	−0.262678	−	0.964884i	$-0.584606\pi$
$251$	−8.32321	−0.525356	−0.262678	+	0.964884i	$0.584606\pi$
$252$	1.14433	0.0720858
$253$	13.7196	0.862544
$254$	9.12198	0.572364
$255$	6.06357	0.379716
$256$	15.8014	0.987588
$257$	−23.0902	−1.44033	−0.720163	−	0.693804i	$-0.755933\pi$
$257$	−23.0902	−1.44033	−0.720163	+	0.693804i	$0.755933\pi$
$258$	−7.34646	−0.457370
$259$	−4.43604	−0.275642
$260$	−1.27689	−0.0791896
$261$	−0.229482	−0.0142046
$262$	0.433872	0.0268047
$263$	18.6423	1.14953	0.574766	−	0.818318i	$-0.305093\pi$
$263$	18.6423	1.14953	0.574766	+	0.818318i	$0.305093\pi$
$264$	−12.6486	−0.778470
$265$	5.70549	0.350486
$266$	−1.44727	−0.0887376
$267$	−9.50715	−0.581828
$268$	1.35618	0.0828420
$269$	−18.9260	−1.15394	−0.576970	−	0.816765i	$-0.695765\pi$
$269$	−18.9260	−1.15394	−0.576970	+	0.816765i	$0.695765\pi$
$270$	9.11660	0.554818
$271$	18.0889	1.09882	0.549411	−	0.835552i	$-0.314852\pi$
$271$	18.0889	1.09882	0.549411	+	0.835552i	$0.314852\pi$
$272$	−24.6426	−1.49418
$273$	2.06578	0.125027
$274$	−11.7888	−0.712187
$275$	−5.02519	−0.303031
$276$	−2.49144	−0.149967
$277$	−19.5547	−1.17493	−0.587465	−	0.809250i	$-0.699874\pi$
$277$	−19.5547	−1.17493	−0.587465	+	0.809250i	$0.699874\pi$
$278$	20.9131	1.25428
$279$	−10.9716	−0.656852
$280$	−2.07155	−0.123799
$281$	−19.7364	−1.17737	−0.588686	−	0.808362i	$-0.700355\pi$
$281$	−19.7364	−1.17737	−0.588686	+	0.808362i	$0.700355\pi$
$282$	9.46746	0.563779
$283$	−9.33887	−0.555138	−0.277569	−	0.960706i	$-0.589529\pi$
$283$	−9.33887	−0.555138	−0.277569	+	0.960706i	$0.589529\pi$
$284$	−2.72837	−0.161899
$285$	−1.06022	−0.0628019
$286$	−14.1707	−0.837930
$287$	−6.95313	−0.410430
$288$	−6.16655	−0.363368
$289$	7.90384	0.464932
$290$	−0.249812	−0.0146695
$291$	−8.87597	−0.520319
$292$	−4.78420	−0.279974
$293$	28.1335	1.64358	0.821789	−	0.569792i	$-0.192976\pi$
$293$	28.1335	1.64358	0.821789	+	0.569792i	$0.192976\pi$
$294$	−2.01532	−0.117536
$295$	12.3536	0.719252
$296$	9.18948	0.534128
$297$	27.6208	1.60272
$298$	24.7340	1.43280
$299$	4.64171	0.268437
$300$	0.912560	0.0526867
$301$	−3.64530	−0.210112
$302$	9.08093	0.522549
$303$	14.3333	0.823427
$304$	4.30876	0.247124
$305$	−0.319003	−0.0182660
$306$	12.6115	0.720950
$307$	24.4472	1.39527	0.697636	−	0.716452i	$-0.254235\pi$
$307$	24.4472	1.39527	0.697636	+	0.716452i	$0.254235\pi$
$308$	3.77415	0.215052
$309$	1.08954	0.0619817
$310$	−11.9436	−0.678350
$311$	14.0233	0.795188	0.397594	−	0.917561i	$-0.369845\pi$
$311$	14.0233	0.795188	0.397594	+	0.917561i	$0.369845\pi$
$312$	−4.27937	−0.242272
$313$	8.22973	0.465172	0.232586	−	0.972576i	$-0.425281\pi$
$313$	8.22973	0.465172	0.232586	+	0.972576i	$0.425281\pi$
$314$	36.8472	2.07941
$315$	1.52365	0.0858477
$316$	5.20003	0.292524
$317$	−12.4250	−0.697857	−0.348929	−	0.937149i	$-0.613454\pi$
$317$	−12.4250	−0.697857	−0.348929	+	0.937149i	$0.613454\pi$
$318$	−11.4984	−0.644798
$319$	−0.756862	−0.0423762
$320$	3.16319	0.176827
$321$	6.04210	0.337237
$322$	−4.52833	−0.252354
$323$	−4.35444	−0.242288
$324$	−1.58288	−0.0879378
$325$	−1.70016	−0.0943077
$326$	−22.4548	−1.24365
$327$	−9.33352	−0.516145
$328$	14.4038	0.795315
$329$	4.69774	0.258995
$330$	10.1274	0.557494
$331$	−7.91705	−0.435160	−0.217580	−	0.976042i	$-0.569816\pi$
$331$	−7.91705	−0.435160	−0.217580	+	0.976042i	$0.569816\pi$
$332$	−2.09812	−0.115149
$333$	−6.75895	−0.370388
$334$	23.2948	1.27464
$335$	1.80573	0.0986574
$336$	5.99996	0.327325
$337$	13.5018	0.735492	0.367746	−	0.929926i	$-0.380130\pi$
$337$	13.5018	0.735492	0.367746	+	0.929926i	$0.380130\pi$
$338$	16.7678	0.912050
$339$	−13.3605	−0.725643
$340$	3.74800	0.203264
$341$	−36.1858	−1.95957
$342$	−2.20512	−0.119239
$343$	−1.00000	−0.0539949
$344$	7.55143	0.407146
$345$	−3.31730	−0.178597
$346$	14.0422	0.754913
$347$	1.35139	0.0725465	0.0362733	−	0.999342i	$-0.488451\pi$
$347$	1.35139	0.0725465	0.0362733	+	0.999342i	$0.488451\pi$
$348$	0.137444	0.00736776
$349$	−9.43001	−0.504777	−0.252388	−	0.967626i	$-0.581216\pi$
$349$	−9.43001	−0.504777	−0.252388	+	0.967626i	$0.581216\pi$
$350$	1.65863	0.0886574
$351$	9.34486	0.498792
$352$	−20.3381	−1.08403
$353$	7.36841	0.392181	0.196090	−	0.980586i	$-0.437175\pi$
$353$	7.36841	0.392181	0.196090	+	0.980586i	$0.437175\pi$
$354$	−24.8964	−1.32323
$355$	−3.63277	−0.192807
$356$	−5.87653	−0.311456
$357$	−6.06357	−0.320918
$358$	36.4535	1.92663
$359$	−12.4539	−0.657293	−0.328647	−	0.944453i	$-0.606592\pi$
$359$	−12.4539	−0.657293	−0.328647	+	0.944453i	$0.606592\pi$
$360$	−3.15631	−0.166352
$361$	−18.2386	−0.959928
$362$	14.7029	0.772767
$363$	17.3177	0.908941
$364$	1.27689	0.0669274
$365$	−6.37006	−0.333424
$366$	0.642893	0.0336045
$367$	−31.0310	−1.61980	−0.809901	−	0.586566i	$-0.800479\pi$
$367$	−31.0310	−1.61980	−0.809901	+	0.586566i	$0.800479\pi$
$368$	13.4816	0.702777
$369$	−10.5941	−0.551507
$370$	−7.35773	−0.382510
$371$	−5.70549	−0.296215
$372$	6.57124	0.340703
$373$	8.74985	0.453050	0.226525	−	0.974005i	$-0.427263\pi$
$373$	8.74985	0.453050	0.226525	+	0.974005i	$0.427263\pi$
$374$	41.5944	2.15080
$375$	1.21505	0.0627451
$376$	−9.73161	−0.501870
$377$	−0.256067	−0.0131881
$378$	−9.11660	−0.468907
$379$	−18.4306	−0.946717	−0.473358	−	0.880870i	$-0.656958\pi$
$379$	−18.4306	−0.946717	−0.473358	+	0.880870i	$0.656958\pi$
$380$	−0.655338	−0.0336181
$381$	−6.68245	−0.342352
$382$	23.3265	1.19349
$383$	36.5615	1.86820	0.934102	−	0.357006i	$-0.116203\pi$
$383$	36.5615	1.86820	0.934102	+	0.357006i	$0.116203\pi$
$384$	−16.2101	−0.827216
$385$	5.02519	0.256108
$386$	41.0877	2.09131
$387$	−5.55415	−0.282333
$388$	−5.48639	−0.278529
$389$	−1.03793	−0.0526250	−0.0263125	−	0.999654i	$-0.508376\pi$
$389$	−1.03793	−0.0526250	−0.0263125	+	0.999654i	$0.508376\pi$
$390$	3.42636	0.173501
$391$	−13.6245	−0.689023
$392$	2.07155	0.104629
$393$	−0.317839	−0.0160329
$394$	39.1152	1.97060
$395$	6.92372	0.348370
$396$	5.75046	0.288972
$397$	2.33209	0.117044	0.0585222	−	0.998286i	$-0.481361\pi$
$397$	2.33209	0.117044	0.0585222	+	0.998286i	$0.481361\pi$
$398$	−31.2311	−1.56547
$399$	1.06022	0.0530773
$400$	−4.93802	−0.246901
$401$	−29.0573	−1.45105	−0.725527	−	0.688194i	$-0.758404\pi$
$401$	−29.0573	−1.45105	−0.725527	+	0.688194i	$0.758404\pi$
$402$	−3.63912	−0.181503
$403$	−12.2426	−0.609849
$404$	8.85966	0.440784
$405$	−2.10757	−0.104726
$406$	0.249812	0.0123979
$407$	−22.2920	−1.10497
$408$	12.5610	0.621862
$409$	31.3405	1.54969	0.774844	−	0.632152i	$-0.217828\pi$
$409$	31.3405	1.54969	0.774844	+	0.632152i	$0.217828\pi$
$410$	−11.5327	−0.569557
$411$	8.63607	0.425986
$412$	0.673463	0.0331791
$413$	−12.3536	−0.607879
$414$	−6.89956	−0.339095
$415$	−2.79360	−0.137132
$416$	−6.88094	−0.337366
$417$	−15.3202	−0.750234
$418$	−7.27279	−0.355724
$419$	34.0865	1.66523	0.832617	−	0.553849i	$-0.186841\pi$
$419$	34.0865	1.66523	0.832617	+	0.553849i	$0.186841\pi$
$420$	−0.912560	−0.0445284
$421$	2.48878	0.121296	0.0606480	−	0.998159i	$-0.480683\pi$
$421$	2.48878	0.121296	0.0606480	+	0.998159i	$0.480683\pi$
$422$	−6.01377	−0.292746
$423$	7.15769	0.348019
$424$	11.8192	0.573992
$425$	4.99037	0.242069
$426$	7.32119	0.354713
$427$	0.319003	0.0154376
$428$	3.73472	0.180525
$429$	10.3810	0.501197
$430$	−6.04620	−0.291574
$431$	19.4439	0.936582	0.468291	−	0.883574i	$-0.344870\pi$
$431$	19.4439	0.936582	0.468291	+	0.883574i	$0.344870\pi$
$432$	27.1417	1.30586
$433$	−25.1890	−1.21051	−0.605254	−	0.796032i	$-0.706929\pi$
$433$	−25.1890	−1.21051	−0.605254	+	0.796032i	$0.706929\pi$
$434$	11.9436	0.573310
$435$	0.183003	0.00877435
$436$	−5.76921	−0.276295
$437$	2.38226	0.113959
$438$	12.8377	0.613410
$439$	−7.01654	−0.334881	−0.167441	−	0.985882i	$-0.553550\pi$
$439$	−7.01654	−0.334881	−0.167441	+	0.985882i	$0.553550\pi$
$440$	−10.4099	−0.496275
$441$	−1.52365	−0.0725545
$442$	14.0725	0.669360
$443$	40.7907	1.93802	0.969012	−	0.247014i	$-0.0794494\pi$
$443$	40.7907	1.93802	0.969012	+	0.247014i	$0.0794494\pi$
$444$	4.04815	0.192117
$445$	−7.82447	−0.370916
$446$	−8.06144	−0.381720
$447$	−18.1193	−0.857013
$448$	−3.16319	−0.149446
$449$	4.25078	0.200607	0.100303	−	0.994957i	$-0.468019\pi$
$449$	4.25078	0.200607	0.100303	+	0.994957i	$0.468019\pi$
$450$	2.52716	0.119131
$451$	−34.9408	−1.64530
$452$	−8.25836	−0.388440
$453$	−6.65238	−0.312556
$454$	15.4351	0.724406
$455$	1.70016	0.0797046
$456$	−2.19629	−0.102851
$457$	10.6884	0.499983	0.249992	−	0.968248i	$-0.419572\pi$
$457$	10.6884	0.499983	0.249992	+	0.968248i	$0.419572\pi$
$458$	−1.65863	−0.0775026
$459$	−27.4294	−1.28030
$460$	−2.05048	−0.0956040
$461$	−37.6453	−1.75332	−0.876659	−	0.481112i	$-0.840233\pi$
$461$	−37.6453	−1.75332	−0.876659	+	0.481112i	$0.840233\pi$
$462$	−10.1274	−0.471168
$463$	2.20013	0.102249	0.0511243	−	0.998692i	$-0.483720\pi$
$463$	2.20013	0.102249	0.0511243	+	0.998692i	$0.483720\pi$
$464$	−0.743733	−0.0345269
$465$	8.74946	0.405746
$466$	8.64768	0.400596
$467$	34.9376	1.61672	0.808359	−	0.588690i	$-0.200356\pi$
$467$	34.9376	1.61672	0.808359	+	0.588690i	$0.200356\pi$
$468$	1.94553	0.0899323
$469$	−1.80573	−0.0833807
$470$	7.79180	0.359409
$471$	−26.9930	−1.24377
$472$	25.5910	1.17792
$473$	−18.3184	−0.842279
$474$	−13.9535	−0.640907
$475$	−0.872568	−0.0400362
$476$	−3.74800	−0.171789
$477$	−8.69315	−0.398032
$478$	17.5054	0.800676
$479$	−19.1177	−0.873512	−0.436756	−	0.899580i	$-0.643873\pi$
$479$	−19.1177	−0.873512	−0.436756	+	0.899580i	$0.643873\pi$
$480$	4.91761	0.224457
$481$	−7.54196	−0.343884
$482$	9.21150	0.419573
$483$	3.31730	0.150942
$484$	10.7043	0.486561
$485$	−7.30500	−0.331703
$486$	−23.1024	−1.04794
$487$	9.05251	0.410209	0.205104	−	0.978740i	$-0.434247\pi$
$487$	9.05251	0.410209	0.205104	+	0.978740i	$0.434247\pi$
$488$	−0.660830	−0.0299144
$489$	16.4496	0.743876
$490$	−1.65863	−0.0749292
$491$	4.07512	0.183908	0.0919539	−	0.995763i	$-0.470689\pi$
$491$	4.07512	0.183908	0.0919539	+	0.995763i	$0.470689\pi$
$492$	6.34515	0.286061
$493$	0.751618	0.0338512
$494$	−2.46058	−0.110707
$495$	7.65661	0.344139
$496$	−35.5581	−1.59661
$497$	3.63277	0.162952
$498$	5.62999	0.252286
$499$	−17.0471	−0.763135	−0.381567	−	0.924341i	$-0.624616\pi$
$499$	−17.0471	−0.763135	−0.381567	+	0.924341i	$0.624616\pi$
$500$	0.751045	0.0335878
$501$	−17.0650	−0.762407
$502$	13.8051	0.616152
$503$	33.5332	1.49517	0.747585	−	0.664166i	$-0.231213\pi$
$503$	33.5332	1.49517	0.747585	+	0.664166i	$0.231213\pi$
$504$	3.15631	0.140593
$505$	11.7964	0.524935
$506$	−22.7557	−1.01162
$507$	−12.2835	−0.545531
$508$	−4.13054	−0.183263
$509$	8.72420	0.386693	0.193347	−	0.981131i	$-0.438066\pi$
$509$	8.72420	0.386693	0.193347	+	0.981131i	$0.438066\pi$
$510$	−10.0572	−0.445341
$511$	6.37006	0.281795
$512$	0.473388	0.0209210
$513$	4.79605	0.211751
$514$	38.2980	1.68925
$515$	0.896701	0.0395133
$516$	3.32656	0.146444
$517$	23.6071	1.03824
$518$	7.35773	0.323280
$519$	−10.2868	−0.451542
$520$	−3.52196	−0.154448
$521$	40.8803	1.79100	0.895498	−	0.445065i	$-0.146819\pi$
$521$	40.8803	1.79100	0.895498	+	0.445065i	$0.146819\pi$
$522$	0.380624	0.0166595
$523$	−33.0981	−1.44728	−0.723640	−	0.690177i	$-0.757533\pi$
$523$	−33.0981	−1.44728	−0.723640	+	0.690177i	$0.757533\pi$
$524$	−0.196462	−0.00858248
$525$	−1.21505	−0.0530293
$526$	−30.9206	−1.34820
$527$	35.9351	1.56536
$528$	30.1510	1.31215
$529$	−15.5462	−0.675922
$530$	−9.46329	−0.411059
$531$	−18.8224	−0.816825
$532$	0.655338	0.0284125
$533$	−11.8214	−0.512042
$534$	15.7688	0.682384
$535$	4.97270	0.214989
$536$	3.74066	0.161572
$537$	−26.7046	−1.15239
$538$	31.3912	1.35337
$539$	−5.02519	−0.216450
$540$	−4.12810	−0.177645
$541$	−30.1649	−1.29689	−0.648444	−	0.761262i	$-0.724580\pi$
$541$	−30.1649	−1.29689	−0.648444	+	0.761262i	$0.724580\pi$
$542$	−30.0027	−1.28873
$543$	−10.7708	−0.462221
$544$	20.1972	0.865949
$545$	−7.68157	−0.329042
$546$	−3.42636	−0.146635
$547$	−19.0670	−0.815247	−0.407624	−	0.913150i	$-0.633642\pi$
$547$	−19.0670	−0.815247	−0.407624	+	0.913150i	$0.633642\pi$
$548$	5.33810	0.228032
$549$	0.486047	0.0207440
$550$	8.33493	0.355402
$551$	−0.131421	−0.00559871
$552$	−6.87195	−0.292489
$553$	−6.92372	−0.294427
$554$	32.4340	1.37799
$555$	5.39002	0.228794
$556$	−9.46968	−0.401604
$557$	3.85176	0.163204	0.0816021	−	0.996665i	$-0.473996\pi$
$557$	3.85176	0.163204	0.0816021	+	0.996665i	$0.473996\pi$
$558$	18.1978	0.770374
$559$	−6.19759	−0.262130
$560$	4.93802	0.208669
$561$	−30.4706	−1.28647
$562$	32.7353	1.38085
$563$	16.7403	0.705521	0.352760	−	0.935714i	$-0.385243\pi$
$563$	16.7403	0.705521	0.352760	+	0.935714i	$0.385243\pi$
$564$	−4.28697	−0.180514
$565$	−10.9958	−0.462598
$566$	15.4897	0.651081
$567$	2.10757	0.0885096
$568$	−7.52546	−0.315761
$569$	−25.3109	−1.06109	−0.530544	−	0.847658i	$-0.678012\pi$
$569$	−25.3109	−1.06109	−0.530544	+	0.847658i	$0.678012\pi$
$570$	1.75851	0.0736557
$571$	25.8518	1.08186	0.540932	−	0.841067i	$-0.318072\pi$
$571$	25.8518	1.08186	0.540932	+	0.841067i	$0.318072\pi$
$572$	6.41664	0.268293
$573$	−17.0882	−0.713870
$574$	11.5327	0.481364
$575$	−2.73016	−0.113856
$576$	−4.81957	−0.200816
$577$	12.0272	0.500699	0.250349	−	0.968156i	$-0.419454\pi$
$577$	12.0272	0.500699	0.250349	+	0.968156i	$0.419454\pi$
$578$	−13.1095	−0.545285
$579$	−30.0994	−1.25089
$580$	0.113118	0.00469695
$581$	2.79360	0.115898
$582$	14.7219	0.610244
$583$	−28.6712	−1.18744
$584$	−13.1959	−0.546050
$585$	2.59044	0.107101
$586$	−46.6630	−1.92763
$587$	−42.9133	−1.77122	−0.885611	−	0.464429i	$-0.846260\pi$
$587$	−42.9133	−1.77122	−0.885611	+	0.464429i	$0.846260\pi$
$588$	0.912560	0.0376333
$589$	−6.28326	−0.258897
$590$	−20.4900	−0.843558
$591$	−28.6545	−1.17869
$592$	−21.9053	−0.900300
$593$	−19.0270	−0.781345	−0.390672	−	0.920530i	$-0.627757\pi$
$593$	−19.0270	−0.781345	−0.390672	+	0.920530i	$0.627757\pi$
$594$	−45.8127	−1.87972
$595$	−4.99037	−0.204585
$596$	−11.1998	−0.458764
$597$	22.8788	0.936368
$598$	−7.69886	−0.314830
$599$	38.2261	1.56188	0.780938	−	0.624609i	$-0.214742\pi$
$599$	38.2261	1.56188	0.780938	+	0.624609i	$0.214742\pi$
$600$	2.51705	0.102758
$601$	44.0930	1.79859	0.899296	−	0.437341i	$-0.144080\pi$
$601$	44.0930	1.79859	0.899296	+	0.437341i	$0.144080\pi$
$602$	6.04620	0.246425
$603$	−2.75129	−0.112041
$604$	−4.11195	−0.167313
$605$	14.2526	0.579450
$606$	−23.7736	−0.965737
$607$	10.6675	0.432980	0.216490	−	0.976285i	$-0.430539\pi$
$607$	10.6675	0.432980	0.216490	+	0.976285i	$0.430539\pi$
$608$	−3.53149	−0.143221
$609$	−0.183003	−0.00741568
$610$	0.529106	0.0214229
$611$	7.98690	0.323115
$612$	−5.71062	−0.230838
$613$	−14.0442	−0.567239	−0.283619	−	0.958937i	$-0.591535\pi$
$613$	−14.0442	−0.567239	−0.283619	+	0.958937i	$0.591535\pi$
$614$	−40.5487	−1.63641
$615$	8.44843	0.340673
$616$	10.4099	0.419429
$617$	−18.0009	−0.724687	−0.362344	−	0.932045i	$-0.618023\pi$
$617$	−18.0009	−0.724687	−0.362344	+	0.932045i	$0.618023\pi$
$618$	−1.80714	−0.0726938
$619$	15.6157	0.627647	0.313824	−	0.949481i	$-0.398390\pi$
$619$	15.6157	0.627647	0.313824	+	0.949481i	$0.398390\pi$
$620$	5.40819	0.217198
$621$	15.0063	0.602181
$622$	−23.2594	−0.932618
$623$	7.82447	0.313481
$624$	10.2009	0.408362
$625$	1.00000	0.0400000
$626$	−13.6500	−0.545566
$627$	5.32780	0.212772
$628$	−16.6848	−0.665797
$629$	22.1375	0.882680
$630$	−2.52716	−0.100684
$631$	−31.8288	−1.26708	−0.633542	−	0.773708i	$-0.718400\pi$
$631$	−31.8288	−1.26708	−0.633542	+	0.773708i	$0.718400\pi$
$632$	14.3428	0.570528
$633$	4.40548	0.175102
$634$	20.6084	0.818466
$635$	−5.49972	−0.218250
$636$	5.20661	0.206455
$637$	−1.70016	−0.0673627
$638$	1.25535	0.0496999
$639$	5.53505	0.218963
$640$	−13.3410	−0.527350
$641$	−9.24708	−0.365238	−0.182619	−	0.983184i	$-0.558457\pi$
$641$	−9.24708	−0.365238	−0.182619	+	0.983184i	$0.558457\pi$
$642$	−10.0216	−0.395521
$643$	27.1515	1.07075	0.535375	−	0.844615i	$-0.320170\pi$
$643$	27.1515	1.07075	0.535375	+	0.844615i	$0.320170\pi$
$644$	2.05048	0.0808001
$645$	4.42924	0.174401
$646$	7.22240	0.284162
$647$	17.3905	0.683692	0.341846	−	0.939756i	$-0.388948\pi$
$647$	17.3905	0.683692	0.341846	+	0.939756i	$0.388948\pi$
$648$	−4.36594	−0.171510
$649$	−62.0791	−2.43682
$650$	2.81993	0.110607
$651$	−8.74946	−0.342918
$652$	10.1678	0.398201
$653$	28.6581	1.12148	0.560739	−	0.827993i	$-0.310517\pi$
$653$	28.6581	1.12148	0.560739	+	0.827993i	$0.310517\pi$
$654$	15.4808	0.605349
$655$	−0.261585	−0.0102210
$656$	−34.3347	−1.34055
$657$	9.70571	0.378656
$658$	−7.79180	−0.303756
$659$	10.4048	0.405312	0.202656	−	0.979250i	$-0.435043\pi$
$659$	10.4048	0.405312	0.202656	+	0.979250i	$0.435043\pi$
$660$	−4.58579	−0.178502
$661$	−27.6371	−1.07496	−0.537480	−	0.843276i	$-0.680624\pi$
$661$	−27.6371	−1.07496	−0.537480	+	0.843276i	$0.680624\pi$
$662$	13.1314	0.510368
$663$	−10.3090	−0.400369
$664$	−5.78707	−0.224582
$665$	0.872568	0.0338368
$666$	11.2106	0.434401
$667$	−0.411200	−0.0159217
$668$	−10.5482	−0.408120
$669$	5.90553	0.228321
$670$	−2.99503	−0.115708
$671$	1.60305	0.0618851
$672$	−4.91761	−0.189701
$673$	−31.1142	−1.19937	−0.599683	−	0.800238i	$-0.704707\pi$
$673$	−31.1142	−1.19937	−0.599683	+	0.800238i	$0.704707\pi$
$674$	−22.3945	−0.862605
$675$	−5.49647	−0.211559
$676$	−7.59267	−0.292026
$677$	−20.2121	−0.776814	−0.388407	−	0.921488i	$-0.626975\pi$
$677$	−20.2121	−0.776814	−0.388407	+	0.921488i	$0.626975\pi$
$678$	22.1601	0.851054
$679$	7.30500	0.280340
$680$	10.3378	0.396437
$681$	−11.3072	−0.433294
$682$	60.0188	2.29824
$683$	4.85747	0.185866	0.0929329	−	0.995672i	$-0.470376\pi$
$683$	4.85747	0.185866	0.0929329	+	0.995672i	$0.470376\pi$
$684$	0.998503	0.0381787
$685$	7.10756	0.271566
$686$	1.65863	0.0633267
$687$	1.21505	0.0463572
$688$	−18.0006	−0.686266
$689$	−9.70024	−0.369550
$690$	5.50216	0.209464
$691$	−2.20867	−0.0840217	−0.0420108	−	0.999117i	$-0.513376\pi$
$691$	−2.20867	−0.0840217	−0.0420108	+	0.999117i	$0.513376\pi$
$692$	−6.35847	−0.241713
$693$	−7.65661	−0.290851
$694$	−2.24146	−0.0850845
$695$	−12.6087	−0.478274
$696$	0.379101	0.0143698
$697$	34.6987	1.31431
$698$	15.6409	0.592016
$699$	−6.33500	−0.239612
$700$	−0.751045	−0.0283868
$701$	−26.6295	−1.00578	−0.502891	−	0.864350i	$-0.667730\pi$
$701$	−26.6295	−1.00578	−0.502891	+	0.864350i	$0.667730\pi$
$702$	−15.4996	−0.584996
$703$	−3.87075	−0.145988
$704$	−15.8956	−0.599089
$705$	−5.70801	−0.214976
$706$	−12.2214	−0.459960
$707$	−11.7964	−0.443651
$708$	11.2734	0.423679
$709$	6.06761	0.227874	0.113937	−	0.993488i	$-0.463654\pi$
$709$	6.06761	0.227874	0.113937	+	0.993488i	$0.463654\pi$
$710$	6.02541	0.226129
$711$	−10.5493	−0.395630
$712$	−16.2088	−0.607450
$713$	−19.6596	−0.736258
$714$	10.0572	0.376382
$715$	8.54362	0.319513
$716$	−16.5066	−0.616879
$717$	−12.8238	−0.478914
$718$	20.6564	0.770891
$719$	−1.59690	−0.0595542	−0.0297771	−	0.999557i	$-0.509480\pi$
$719$	−1.59690	−0.0595542	−0.0297771	+	0.999557i	$0.509480\pi$
$720$	7.52379	0.280395
$721$	−0.896701	−0.0333949
$722$	30.2511	1.12583
$723$	−6.74803	−0.250962
$724$	−6.65763	−0.247429
$725$	0.150614	0.00559365
$726$	−28.7235	−1.06603
$727$	−38.4621	−1.42648	−0.713241	−	0.700919i	$-0.752773\pi$
$727$	−38.4621	−1.42648	−0.713241	+	0.700919i	$0.752773\pi$
$728$	3.52196	0.130533
$729$	23.2467	0.860989
$730$	10.5656	0.391049
$731$	18.1914	0.672834
$732$	−0.291109	−0.0107597
$733$	−1.63890	−0.0605340	−0.0302670	−	0.999542i	$-0.509636\pi$
$733$	−1.63890	−0.0605340	−0.0302670	+	0.999542i	$0.509636\pi$
$734$	51.4688	1.89975
$735$	1.21505	0.0448179
$736$	−11.0496	−0.407294
$737$	−9.07413	−0.334250
$738$	17.5717	0.646822
$739$	17.2983	0.636326	0.318163	−	0.948036i	$-0.396934\pi$
$739$	17.2983	0.636326	0.318163	+	0.948036i	$0.396934\pi$
$740$	3.33166	0.122474
$741$	1.80254	0.0662178
$742$	9.46329	0.347408
$743$	14.6426	0.537185	0.268592	−	0.963254i	$-0.413442\pi$
$743$	14.6426	0.537185	0.268592	+	0.963254i	$0.413442\pi$
$744$	18.1249	0.664493
$745$	−14.9123	−0.546346
$746$	−14.5127	−0.531349
$747$	4.25645	0.155735
$748$	−18.8344	−0.688654
$749$	−4.97270	−0.181699
$750$	−2.01532	−0.0735891
$751$	−18.5400	−0.676535	−0.338267	−	0.941050i	$-0.609841\pi$
$751$	−18.5400	−0.676535	−0.338267	+	0.941050i	$0.609841\pi$
$752$	23.1976	0.845928
$753$	−10.1131	−0.368543
$754$	0.424719	0.0154674
$755$	−5.47497	−0.199254
$756$	4.12810	0.150137
$757$	−4.02812	−0.146404	−0.0732022	−	0.997317i	$-0.523322\pi$
$757$	−4.02812	−0.146404	−0.0732022	+	0.997317i	$0.523322\pi$
$758$	30.5695	1.11033
$759$	16.6701	0.605085
$760$	−1.80757	−0.0655675
$761$	51.1001	1.85238	0.926189	−	0.377061i	$-0.123065\pi$
$761$	51.1001	1.85238	0.926189	+	0.377061i	$0.123065\pi$
$762$	11.0837	0.401520
$763$	7.68157	0.278092
$764$	−10.5625	−0.382138
$765$	−7.60356	−0.274907
$766$	−60.6419	−2.19108
$767$	−21.0030	−0.758374
$768$	19.1996	0.692804
$769$	9.44888	0.340735	0.170368	−	0.985381i	$-0.445504\pi$
$769$	9.44888	0.340735	0.170368	+	0.985381i	$0.445504\pi$
$770$	−8.33493	−0.300370
$771$	−28.0558	−1.01041
$772$	−18.6050	−0.669608
$773$	29.7999	1.07183	0.535914	−	0.844272i	$-0.319967\pi$
$773$	29.7999	1.07183	0.535914	+	0.844272i	$0.319967\pi$
$774$	9.21226	0.331128
$775$	7.20088	0.258663
$776$	−15.1327	−0.543232
$777$	−5.39002	−0.193366
$778$	1.72153	0.0617200
$779$	−6.06708	−0.217376
$780$	−1.55149	−0.0555524
$781$	18.2554	0.653228
$782$	22.5980	0.808104
$783$	−0.827843	−0.0295847
$784$	−4.93802	−0.176358
$785$	−22.2155	−0.792904
$786$	0.527177	0.0188038
$787$	7.12015	0.253806	0.126903	−	0.991915i	$-0.459496\pi$
$787$	7.12015	0.253806	0.126903	+	0.991915i	$0.459496\pi$
$788$	−17.7118	−0.630957
$789$	22.6514	0.806410
$790$	−11.4839	−0.408578
$791$	10.9958	0.390966
$792$	15.8611	0.563598
$793$	0.542354	0.0192596
$794$	−3.86807	−0.137273
$795$	6.93248	0.245870
$796$	14.1418	0.501243
$797$	−13.8655	−0.491139	−0.245570	−	0.969379i	$-0.578975\pi$
$797$	−13.8655	−0.491139	−0.245570	+	0.969379i	$0.578975\pi$
$798$	−1.75851	−0.0622504
$799$	−23.4435	−0.829371
$800$	4.04724	0.143091
$801$	11.9217	0.421233
$802$	48.1953	1.70183
$803$	32.0108	1.12964
$804$	1.64783	0.0581146
$805$	2.73016	0.0962256
$806$	20.3060	0.715247
$807$	−22.9961	−0.809502
$808$	24.4369	0.859688
$809$	5.36388	0.188584	0.0942920	−	0.995545i	$-0.469941\pi$
$809$	5.36388	0.188584	0.0942920	+	0.995545i	$0.469941\pi$
$810$	3.49567	0.122825
$811$	−40.9501	−1.43795	−0.718976	−	0.695035i	$-0.755389\pi$
$811$	−40.9501	−1.43795	−0.718976	+	0.695035i	$0.755389\pi$
$812$	−0.113118	−0.00396965
$813$	21.9790	0.770836
$814$	36.9741	1.29594
$815$	13.5382	0.474221
$816$	−29.9420	−1.04818
$817$	−3.18078	−0.111281
$818$	−51.9822	−1.81752
$819$	−2.59044	−0.0905171
$820$	5.22211	0.182364
$821$	34.5940	1.20734	0.603669	−	0.797235i	$-0.293705\pi$
$821$	34.5940	1.20734	0.603669	+	0.797235i	$0.293705\pi$
$822$	−14.3240	−0.499608
$823$	−15.9027	−0.554333	−0.277166	−	0.960822i	$-0.589395\pi$
$823$	−15.9027	−0.554333	−0.277166	+	0.960822i	$0.589395\pi$
$824$	1.85756	0.0647112
$825$	−6.10588	−0.212579
$826$	20.4900	0.712937
$827$	−14.0016	−0.486882	−0.243441	−	0.969916i	$-0.578276\pi$
$827$	−14.0016	−0.486882	−0.243441	+	0.969916i	$0.578276\pi$
$828$	3.12420	0.108573
$829$	−33.8009	−1.17395	−0.586976	−	0.809604i	$-0.699682\pi$
$829$	−33.8009	−1.17395	−0.586976	+	0.809604i	$0.699682\pi$
$830$	4.63353	0.160832
$831$	−23.7600	−0.824226
$832$	−5.37791	−0.186446
$833$	4.99037	0.172906
$834$	25.4105	0.879894
$835$	−14.0446	−0.486034
$836$	3.29320	0.113898
$837$	−39.5794	−1.36807
$838$	−56.5368	−1.95303
$839$	40.1411	1.38583	0.692913	−	0.721022i	$-0.256327\pi$
$839$	40.1411	1.38583	0.692913	+	0.721022i	$0.256327\pi$
$840$	−2.51705	−0.0868463
$841$	−28.9773	−0.999218
$842$	−4.12797	−0.142259
$843$	−23.9807	−0.825940
$844$	2.72310	0.0937331
$845$	−10.1095	−0.347776
$846$	−11.8719	−0.408166
$847$	−14.2526	−0.489725
$848$	−28.1739	−0.967494
$849$	−11.3472	−0.389436
$850$	−8.27717	−0.283905
$851$	−12.1111	−0.415164
$852$	−3.31512	−0.113574
$853$	−1.04976	−0.0359432	−0.0179716	−	0.999838i	$-0.505721\pi$
$853$	−1.04976	−0.0359432	−0.0179716	+	0.999838i	$0.505721\pi$
$854$	−0.529106	−0.0181056
$855$	1.32948	0.0454674
$856$	10.3012	0.352088
$857$	−38.5066	−1.31536	−0.657680	−	0.753297i	$-0.728462\pi$
$857$	−38.5066	−1.31536	−0.657680	+	0.753297i	$0.728462\pi$
$858$	−17.2181	−0.587817
$859$	−15.1391	−0.516540	−0.258270	−	0.966073i	$-0.583152\pi$
$859$	−15.1391	−0.516540	−0.258270	+	0.966073i	$0.583152\pi$
$860$	2.73779	0.0933578
$861$	−8.44843	−0.287922
$862$	−32.2503	−1.09845
$863$	11.0233	0.375236	0.187618	−	0.982242i	$-0.439923\pi$
$863$	11.0233	0.375236	0.187618	+	0.982242i	$0.439923\pi$
$864$	−22.2455	−0.756808
$865$	−8.46616	−0.287858
$866$	41.7792	1.41972
$867$	9.60359	0.326155
$868$	−5.40819	−0.183566
$869$	−34.7931	−1.18027
$870$	−0.303535	−0.0102908
$871$	−3.07002	−0.104024
$872$	−15.9128	−0.538874
$873$	11.1302	0.376701
$874$	−3.95127	−0.133654
$875$	−1.00000	−0.0338062
$876$	−5.81306	−0.196405
$877$	11.7458	0.396629	0.198314	−	0.980138i	$-0.436453\pi$
$877$	11.7458	0.396629	0.198314	+	0.980138i	$0.436453\pi$
$878$	11.6378	0.392758
$879$	34.1837	1.15299
$880$	24.8145	0.836497
$881$	−23.5509	−0.793449	−0.396725	−	0.917938i	$-0.629853\pi$
$881$	−23.5509	−0.793449	−0.396725	+	0.917938i	$0.629853\pi$
$882$	2.52716	0.0850939
$883$	11.2005	0.376925	0.188463	−	0.982080i	$-0.439650\pi$
$883$	11.2005	0.376925	0.188463	+	0.982080i	$0.439650\pi$
$884$	−6.37218	−0.214320
$885$	15.0102	0.504564
$886$	−67.6565	−2.27297
$887$	42.0723	1.41265	0.706325	−	0.707888i	$-0.250352\pi$
$887$	42.0723	1.41265	0.706325	+	0.707888i	$0.250352\pi$
$888$	11.1657	0.374697
$889$	5.49972	0.184455
$890$	12.9779	0.435020
$891$	10.5909	0.354810
$892$	3.65031	0.122221
$893$	4.09910	0.137171
$894$	30.0532	1.00513
$895$	−21.9781	−0.734648
$896$	13.3410	0.445692
$897$	5.63992	0.188312
$898$	−7.05046	−0.235277
$899$	1.08455	0.0361718
$900$	−1.14433	−0.0381442
$901$	28.4726	0.948558
$902$	57.9538	1.92965
$903$	−4.42924	−0.147396
$904$	−22.7784	−0.757598
$905$	−8.86449	−0.294666
$906$	11.0338	0.366574
$907$	49.0892	1.62998	0.814991	−	0.579474i	$-0.196742\pi$
$907$	49.0892	1.62998	0.814991	+	0.579474i	$0.196742\pi$
$908$	−6.98920	−0.231945
$909$	−17.9736	−0.596146
$910$	−2.81993	−0.0934797
$911$	−18.6477	−0.617826	−0.308913	−	0.951090i	$-0.599965\pi$
$911$	−18.6477	−0.617826	−0.308913	+	0.951090i	$0.599965\pi$
$912$	5.23538	0.173361
$913$	14.0384	0.464602
$914$	−17.7281	−0.586393
$915$	−0.387605	−0.0128138
$916$	0.751045	0.0248152
$917$	0.261585	0.00863829
$918$	45.4952	1.50157
$919$	−54.8892	−1.81063	−0.905313	−	0.424744i	$-0.860364\pi$
$919$	−54.8892	−1.81063	−0.905313	+	0.424744i	$0.860364\pi$
$920$	−5.65567	−0.186462
$921$	29.7046	0.978800
$922$	62.4396	2.05634
$923$	6.17627	0.203294
$924$	4.58579	0.150861
$925$	4.43604	0.145856
$926$	−3.64920	−0.119920
$927$	−1.36625	−0.0448737
$928$	0.609569	0.0200101
$929$	30.4511	0.999068	0.499534	−	0.866294i	$-0.333505\pi$
$929$	30.4511	0.999068	0.499534	+	0.866294i	$0.333505\pi$
$930$	−14.5121	−0.475870
$931$	−0.872568	−0.0285973
$932$	−3.91577	−0.128265
$933$	17.0391	0.557834
$934$	−57.9484	−1.89613
$935$	−25.0776	−0.820125
$936$	5.36622	0.175400
$937$	−54.7632	−1.78904	−0.894519	−	0.447031i	$-0.852481\pi$
$937$	−54.7632	−1.78904	−0.894519	+	0.447031i	$0.852481\pi$
$938$	2.99503	0.0977912
$939$	9.99956	0.326323
$940$	−3.52822	−0.115078
$941$	−3.95297	−0.128863	−0.0644315	−	0.997922i	$-0.520523\pi$
$941$	−3.95297	−0.128863	−0.0644315	+	0.997922i	$0.520523\pi$
$942$	44.7713	1.45873
$943$	−18.9832	−0.618178
$944$	−61.0022	−1.98545
$945$	5.49647	0.178800
$946$	30.3833	0.987847
$947$	−56.7247	−1.84331	−0.921653	−	0.388015i	$-0.873161\pi$
$947$	−56.7247	−1.84331	−0.921653	+	0.388015i	$0.873161\pi$
$948$	6.31831	0.205209
$949$	10.8301	0.351560
$950$	1.44727	0.0469555
$951$	−15.0970	−0.489555
$952$	−10.3378	−0.335051
$953$	−2.76322	−0.0895094	−0.0447547	−	0.998998i	$-0.514251\pi$
$953$	−2.76322	−0.0895094	−0.0447547	+	0.998998i	$0.514251\pi$
$954$	14.4187	0.466823
$955$	−14.0637	−0.455092
$956$	−7.92662	−0.256365
$957$	−0.919628	−0.0297274
$958$	31.7092	1.02448
$959$	−7.10756	−0.229515
$960$	3.84344	0.124046
$961$	20.8527	0.672668
$962$	12.5093	0.403316
$963$	−7.57663	−0.244154
$964$	−4.17107	−0.134341
$965$	−24.7721	−0.797443
$966$	−5.50216	−0.177029
$967$	−2.58758	−0.0832110	−0.0416055	−	0.999134i	$-0.513247\pi$
$967$	−2.58758	−0.0832110	−0.0416055	+	0.999134i	$0.513247\pi$
$968$	29.5250	0.948968
$969$	−5.29088	−0.169968
$970$	12.1163	0.389030
$971$	−17.7784	−0.570537	−0.285268	−	0.958448i	$-0.592083\pi$
$971$	−17.7784	−0.570537	−0.285268	+	0.958448i	$0.592083\pi$
$972$	10.4610	0.335537
$973$	12.6087	0.404215
$974$	−15.0147	−0.481104
$975$	−2.06578	−0.0661579
$976$	1.57524	0.0504223
$977$	20.4642	0.654709	0.327354	−	0.944902i	$-0.393843\pi$
$977$	20.4642	0.654709	0.327354	+	0.944902i	$0.393843\pi$
$978$	−27.2837	−0.872438
$979$	39.3195	1.25666
$980$	0.751045	0.0239913
$981$	11.7040	0.373680
$982$	−6.75911	−0.215692
$983$	5.85030	0.186595	0.0932977	−	0.995638i	$-0.470259\pi$
$983$	5.85030	0.186595	0.0932977	+	0.995638i	$0.470259\pi$
$984$	17.5013	0.557922
$985$	−23.5829	−0.751413
$986$	−1.24665	−0.0397016
$987$	5.70801	0.181688
$988$	1.11418	0.0354467
$989$	−9.95228	−0.316464
$990$	−12.6995	−0.403616
$991$	15.4363	0.490352	0.245176	−	0.969479i	$-0.421154\pi$
$991$	15.4363	0.490352	0.245176	+	0.969479i	$0.421154\pi$
$992$	29.1437	0.925313
$993$	−9.61964	−0.305270
$994$	−6.02541	−0.191114
$995$	18.8295	0.596935
$996$	−2.54932	−0.0807784
$997$	10.6859	0.338427	0.169213	−	0.985579i	$-0.445877\pi$
$997$	10.6859	0.338427	0.169213	+	0.985579i	$0.445877\pi$
$998$	28.2748	0.895025
$999$	−24.3826	−0.771430

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.i.1.10	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.i.1.10	✓	44	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.65863 q^{2} +1.21505 q^{3} +0.751045 q^{4} +1.00000 q^{5} -2.01532 q^{6} -1.00000 q^{7} +2.07155 q^{8} -1.52365 q^{9} +O(q^{10})\)	\(q-1.65863 q^{2} +1.21505 q^{3} +0.751045 q^{4} +1.00000 q^{5} -2.01532 q^{6} -1.00000 q^{7} +2.07155 q^{8} -1.52365 q^{9} -1.65863 q^{10} -5.02519 q^{11} +0.912560 q^{12} -1.70016 q^{13} +1.65863 q^{14} +1.21505 q^{15} -4.93802 q^{16} +4.99037 q^{17} +2.52716 q^{18} -0.872568 q^{19} +0.751045 q^{20} -1.21505 q^{21} +8.33493 q^{22} -2.73016 q^{23} +2.51705 q^{24} +1.00000 q^{25} +2.81993 q^{26} -5.49647 q^{27} -0.751045 q^{28} +0.150614 q^{29} -2.01532 q^{30} +7.20088 q^{31} +4.04724 q^{32} -6.10588 q^{33} -8.27717 q^{34} -1.00000 q^{35} -1.14433 q^{36} +4.43604 q^{37} +1.44727 q^{38} -2.06578 q^{39} +2.07155 q^{40} +6.95313 q^{41} +2.01532 q^{42} +3.64530 q^{43} -3.77415 q^{44} -1.52365 q^{45} +4.52833 q^{46} -4.69774 q^{47} -5.99996 q^{48} +1.00000 q^{49} -1.65863 q^{50} +6.06357 q^{51} -1.27689 q^{52} +5.70549 q^{53} +9.11660 q^{54} -5.02519 q^{55} -2.07155 q^{56} -1.06022 q^{57} -0.249812 q^{58} +12.3536 q^{59} +0.912560 q^{60} -0.319003 q^{61} -11.9436 q^{62} +1.52365 q^{63} +3.16319 q^{64} -1.70016 q^{65} +10.1274 q^{66} +1.80573 q^{67} +3.74800 q^{68} -3.31730 q^{69} +1.65863 q^{70} -3.63277 q^{71} -3.15631 q^{72} -6.37006 q^{73} -7.35773 q^{74} +1.21505 q^{75} -0.655338 q^{76} +5.02519 q^{77} +3.42636 q^{78} +6.92372 q^{79} -4.93802 q^{80} -2.10757 q^{81} -11.5327 q^{82} -2.79360 q^{83} -0.912560 q^{84} +4.99037 q^{85} -6.04620 q^{86} +0.183003 q^{87} -10.4099 q^{88} -7.82447 q^{89} +2.52716 q^{90} +1.70016 q^{91} -2.05048 q^{92} +8.74946 q^{93} +7.79180 q^{94} -0.872568 q^{95} +4.91761 q^{96} -7.30500 q^{97} -1.65863 q^{98} +7.65661 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9 - 2 * q^10 - 15 * q^11 - 3 * q^12 - 17 * q^13 + 2 * q^14 + 10 * q^16 - 7 * q^17 - 16 * q^18 - 32 * q^19 + 30 * q^20 - 14 * q^22 + 8 * q^23 - 35 * q^24 + 44 * q^25 - 27 * q^26 + 6 * q^27 - 30 * q^28 - 42 * q^29 - 7 * q^30 - 43 * q^31 - 8 * q^32 - 33 * q^33 - 33 * q^34 - 44 * q^35 - 11 * q^36 - 44 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 - 62 * q^41 + 7 * q^42 - 7 * q^43 - 45 * q^44 + 16 * q^45 - 15 * q^46 + 2 * q^47 - 26 * q^48 + 44 * q^49 - 2 * q^50 - 25 * q^51 - 35 * q^52 - 25 * q^53 - 76 * q^54 - 15 * q^55 + 3 * q^56 - 7 * q^57 - 2 * q^58 - 35 * q^59 - 3 * q^60 - 86 * q^61 - 23 * q^62 - 16 * q^63 - 5 * q^64 - 17 * q^65 - 6 * q^66 + 2 * q^67 - q^68 - 75 * q^69 + 2 * q^70 - 54 * q^71 - 3 * q^72 - 52 * q^73 - 22 * q^74 - 77 * q^76 + 15 * q^77 + 2 * q^78 + 46 * q^79 + 10 * q^80 - 72 * q^81 - 16 * q^82 + 26 * q^83 + 3 * q^84 - 7 * q^85 - 33 * q^86 - 8 * q^87 - 23 * q^88 - 105 * q^89 - 16 * q^90 + 17 * q^91 - 41 * q^92 - 11 * q^93 - 47 * q^94 - 32 * q^95 - 39 * q^96 - 80 * q^97 - 2 * q^98 - 53 * q^99

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