LMFDB - Embedded newform 6015.2.a.h.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.45937 q^{2} +1.00000 q^{3} +0.129770 q^{4} -1.00000 q^{5} -1.45937 q^{6} +4.22534 q^{7} +2.72936 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.45937 q^{2} +1.00000 q^{3} +0.129770 q^{4} -1.00000 q^{5} -1.45937 q^{6} +4.22534 q^{7} +2.72936 q^{8} +1.00000 q^{9} +1.45937 q^{10} +5.03973 q^{11} +0.129770 q^{12} +2.78562 q^{13} -6.16635 q^{14} -1.00000 q^{15} -4.24270 q^{16} -2.25766 q^{17} -1.45937 q^{18} -4.42475 q^{19} -0.129770 q^{20} +4.22534 q^{21} -7.35484 q^{22} +3.01376 q^{23} +2.72936 q^{24} +1.00000 q^{25} -4.06525 q^{26} +1.00000 q^{27} +0.548323 q^{28} +4.42787 q^{29} +1.45937 q^{30} +7.05921 q^{31} +0.732956 q^{32} +5.03973 q^{33} +3.29476 q^{34} -4.22534 q^{35} +0.129770 q^{36} +4.87023 q^{37} +6.45737 q^{38} +2.78562 q^{39} -2.72936 q^{40} -2.84348 q^{41} -6.16635 q^{42} +9.33179 q^{43} +0.654006 q^{44} -1.00000 q^{45} -4.39819 q^{46} -3.28978 q^{47} -4.24270 q^{48} +10.8535 q^{49} -1.45937 q^{50} -2.25766 q^{51} +0.361490 q^{52} -5.95224 q^{53} -1.45937 q^{54} -5.03973 q^{55} +11.5325 q^{56} -4.42475 q^{57} -6.46192 q^{58} +14.9921 q^{59} -0.129770 q^{60} -7.34289 q^{61} -10.3020 q^{62} +4.22534 q^{63} +7.41574 q^{64} -2.78562 q^{65} -7.35484 q^{66} -2.58240 q^{67} -0.292976 q^{68} +3.01376 q^{69} +6.16635 q^{70} -3.18373 q^{71} +2.72936 q^{72} +8.59784 q^{73} -7.10748 q^{74} +1.00000 q^{75} -0.574201 q^{76} +21.2946 q^{77} -4.06525 q^{78} -6.03923 q^{79} +4.24270 q^{80} +1.00000 q^{81} +4.14970 q^{82} -0.267206 q^{83} +0.548323 q^{84} +2.25766 q^{85} -13.6186 q^{86} +4.42787 q^{87} +13.7552 q^{88} +11.3060 q^{89} +1.45937 q^{90} +11.7702 q^{91} +0.391095 q^{92} +7.05921 q^{93} +4.80102 q^{94} +4.42475 q^{95} +0.732956 q^{96} -8.87254 q^{97} -15.8394 q^{98} +5.03973 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9} - q^{11} + 48 q^{12} + 30 q^{13} + 8 q^{14} - 39 q^{15} + 58 q^{16} + 32 q^{17} + 27 q^{19} - 48 q^{20} + 22 q^{21} + 23 q^{22} - 8 q^{23} + 3 q^{24} + 39 q^{25} - 4 q^{26} + 39 q^{27} + 60 q^{28} - 9 q^{29} + 19 q^{31} + q^{32} - q^{33} + 26 q^{34} - 22 q^{35} + 48 q^{36} + 44 q^{37} + 14 q^{38} + 30 q^{39} - 3 q^{40} + 31 q^{41} + 8 q^{42} + 75 q^{43} + q^{44} - 39 q^{45} + 19 q^{46} - 16 q^{47} + 58 q^{48} + 91 q^{49} + 32 q^{51} + 94 q^{52} + 17 q^{53} + q^{55} + 27 q^{56} + 27 q^{57} + 26 q^{58} - q^{59} - 48 q^{60} + 55 q^{61} + 11 q^{62} + 22 q^{63} + 77 q^{64} - 30 q^{65} + 23 q^{66} + 84 q^{67} + 36 q^{68} - 8 q^{69} - 8 q^{70} - 2 q^{71} + 3 q^{72} + 79 q^{73} + 20 q^{74} + 39 q^{75} + 58 q^{76} + 32 q^{77} - 4 q^{78} + 29 q^{79} - 58 q^{80} + 39 q^{81} + 53 q^{82} + 9 q^{83} + 60 q^{84} - 32 q^{85} - 17 q^{86} - 9 q^{87} + 57 q^{88} + 37 q^{89} + 71 q^{91} + 7 q^{92} + 19 q^{93} + 32 q^{94} - 27 q^{95} + q^{96} + 91 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9 - q^11 + 48 * q^12 + 30 * q^13 + 8 * q^14 - 39 * q^15 + 58 * q^16 + 32 * q^17 + 27 * q^19 - 48 * q^20 + 22 * q^21 + 23 * q^22 - 8 * q^23 + 3 * q^24 + 39 * q^25 - 4 * q^26 + 39 * q^27 + 60 * q^28 - 9 * q^29 + 19 * q^31 + q^32 - q^33 + 26 * q^34 - 22 * q^35 + 48 * q^36 + 44 * q^37 + 14 * q^38 + 30 * q^39 - 3 * q^40 + 31 * q^41 + 8 * q^42 + 75 * q^43 + q^44 - 39 * q^45 + 19 * q^46 - 16 * q^47 + 58 * q^48 + 91 * q^49 + 32 * q^51 + 94 * q^52 + 17 * q^53 + q^55 + 27 * q^56 + 27 * q^57 + 26 * q^58 - q^59 - 48 * q^60 + 55 * q^61 + 11 * q^62 + 22 * q^63 + 77 * q^64 - 30 * q^65 + 23 * q^66 + 84 * q^67 + 36 * q^68 - 8 * q^69 - 8 * q^70 - 2 * q^71 + 3 * q^72 + 79 * q^73 + 20 * q^74 + 39 * q^75 + 58 * q^76 + 32 * q^77 - 4 * q^78 + 29 * q^79 - 58 * q^80 + 39 * q^81 + 53 * q^82 + 9 * q^83 + 60 * q^84 - 32 * q^85 - 17 * q^86 - 9 * q^87 + 57 * q^88 + 37 * q^89 + 71 * q^91 + 7 * q^92 + 19 * q^93 + 32 * q^94 - 27 * q^95 + q^96 + 91 * q^97 - 9 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.45937	−1.03193	−0.515966	−	0.856609i	$-0.672567\pi$
$2$	−1.45937	−1.03193	−0.515966	+	0.856609i	$0.672567\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.129770	0.0648851
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.45937	−0.595787
$7$	4.22534	1.59703	0.798515	−	0.601975i	$-0.205619\pi$
$7$	4.22534	1.59703	0.798515	+	0.601975i	$0.205619\pi$
$8$	2.72936	0.964976
$9$	1.00000	0.333333
$10$	1.45937	0.461494
$11$	5.03973	1.51954	0.759768	−	0.650195i	$-0.225313\pi$
$11$	5.03973	1.51954	0.759768	+	0.650195i	$0.225313\pi$
$12$	0.129770	0.0374614
$13$	2.78562	0.772591	0.386296	−	0.922375i	$-0.373754\pi$
$13$	2.78562	0.772591	0.386296	+	0.922375i	$0.373754\pi$
$14$	−6.16635	−1.64803
$15$	−1.00000	−0.258199
$16$	−4.24270	−1.06067
$17$	−2.25766	−0.547562	−0.273781	−	0.961792i	$-0.588274\pi$
$17$	−2.25766	−0.547562	−0.273781	+	0.961792i	$0.588274\pi$
$18$	−1.45937	−0.343978
$19$	−4.42475	−1.01511	−0.507554	−	0.861620i	$-0.669450\pi$
$19$	−4.42475	−1.01511	−0.507554	+	0.861620i	$0.669450\pi$
$20$	−0.129770	−0.0290175
$21$	4.22534	0.922046
$22$	−7.35484	−1.56806
$23$	3.01376	0.628411	0.314206	−	0.949355i	$-0.398262\pi$
$23$	3.01376	0.628411	0.314206	+	0.949355i	$0.398262\pi$
$24$	2.72936	0.557129
$25$	1.00000	0.200000
$26$	−4.06525	−0.797262
$27$	1.00000	0.192450
$28$	0.548323	0.103623
$29$	4.42787	0.822236	0.411118	−	0.911582i	$-0.365138\pi$
$29$	4.42787	0.822236	0.411118	+	0.911582i	$0.365138\pi$
$30$	1.45937	0.266444
$31$	7.05921	1.26787	0.633935	−	0.773386i	$-0.281439\pi$
$31$	7.05921	1.26787	0.633935	+	0.773386i	$0.281439\pi$
$32$	0.732956	0.129570
$33$	5.03973	0.877304
$34$	3.29476	0.565047
$35$	−4.22534	−0.714214
$36$	0.129770	0.0216284
$37$	4.87023	0.800661	0.400330	−	0.916371i	$-0.368895\pi$
$37$	4.87023	0.800661	0.400330	+	0.916371i	$0.368895\pi$
$38$	6.45737	1.04752
$39$	2.78562	0.446056
$40$	−2.72936	−0.431550
$41$	−2.84348	−0.444077	−0.222038	−	0.975038i	$-0.571271\pi$
$41$	−2.84348	−0.444077	−0.222038	+	0.975038i	$0.571271\pi$
$42$	−6.16635	−0.951489
$43$	9.33179	1.42308	0.711542	−	0.702643i	$-0.247997\pi$
$43$	9.33179	1.42308	0.711542	+	0.702643i	$0.247997\pi$
$44$	0.654006	0.0985951
$45$	−1.00000	−0.149071
$46$	−4.39819	−0.648478
$47$	−3.28978	−0.479864	−0.239932	−	0.970790i	$-0.577125\pi$
$47$	−3.28978	−0.479864	−0.239932	+	0.970790i	$0.577125\pi$
$48$	−4.24270	−0.612381
$49$	10.8535	1.55051
$50$	−1.45937	−0.206387
$51$	−2.25766	−0.316135
$52$	0.361490	0.0501296
$53$	−5.95224	−0.817603	−0.408802	−	0.912623i	$-0.634053\pi$
$53$	−5.95224	−0.817603	−0.408802	+	0.912623i	$0.634053\pi$
$54$	−1.45937	−0.198596
$55$	−5.03973	−0.679557
$56$	11.5325	1.54110
$57$	−4.42475	−0.586073
$58$	−6.46192	−0.848492
$59$	14.9921	1.95181	0.975905	−	0.218194i	$-0.0700166\pi$
$59$	14.9921	1.95181	0.975905	+	0.218194i	$0.0700166\pi$
$60$	−0.129770	−0.0167532
$61$	−7.34289	−0.940160	−0.470080	−	0.882624i	$-0.655775\pi$
$61$	−7.34289	−0.940160	−0.470080	+	0.882624i	$0.655775\pi$
$62$	−10.3020	−1.30836
$63$	4.22534	0.532343
$64$	7.41574	0.926968
$65$	−2.78562	−0.345513
$66$	−7.35484	−0.905319
$67$	−2.58240	−0.315490	−0.157745	−	0.987480i	$-0.550422\pi$
$67$	−2.58240	−0.315490	−0.157745	+	0.987480i	$0.550422\pi$
$68$	−0.292976	−0.0355286
$69$	3.01376	0.362814
$70$	6.16635	0.737020
$71$	−3.18373	−0.377839	−0.188919	−	0.981993i	$-0.560498\pi$
$71$	−3.18373	−0.377839	−0.188919	+	0.981993i	$0.560498\pi$
$72$	2.72936	0.321659
$73$	8.59784	1.00630	0.503151	−	0.864199i	$-0.332174\pi$
$73$	8.59784	1.00630	0.503151	+	0.864199i	$0.332174\pi$
$74$	−7.10748	−0.826228
$75$	1.00000	0.115470
$76$	−0.574201	−0.0658654
$77$	21.2946	2.42674
$78$	−4.06525	−0.460299
$79$	−6.03923	−0.679467	−0.339733	−	0.940522i	$-0.610337\pi$
$79$	−6.03923	−0.679467	−0.339733	+	0.940522i	$0.610337\pi$
$80$	4.24270	0.474348
$81$	1.00000	0.111111
$82$	4.14970	0.458258
$83$	−0.267206	−0.0293296	−0.0146648	−	0.999892i	$-0.504668\pi$
$83$	−0.267206	−0.0293296	−0.0146648	+	0.999892i	$0.504668\pi$
$84$	0.548323	0.0598270
$85$	2.25766	0.244877
$86$	−13.6186	−1.46853
$87$	4.42787	0.474718
$88$	13.7552	1.46631
$89$	11.3060	1.19843	0.599215	−	0.800588i	$-0.295479\pi$
$89$	11.3060	1.19843	0.599215	+	0.800588i	$0.295479\pi$
$90$	1.45937	0.153831
$91$	11.7702	1.23385
$92$	0.391095	0.0407745
$93$	7.05921	0.732005
$94$	4.80102	0.495188
$95$	4.42475	0.453970
$96$	0.732956	0.0748070
$97$	−8.87254	−0.900870	−0.450435	−	0.892809i	$-0.648731\pi$
$97$	−8.87254	−0.900870	−0.450435	+	0.892809i	$0.648731\pi$
$98$	−15.8394	−1.60002
$99$	5.03973	0.506512
$100$	0.129770	0.0129770
$101$	−2.14295	−0.213231	−0.106616	−	0.994300i	$-0.534001\pi$
$101$	−2.14295	−0.213231	−0.106616	+	0.994300i	$0.534001\pi$
$102$	3.29476	0.326230
$103$	−4.76190	−0.469204	−0.234602	−	0.972091i	$-0.575379\pi$
$103$	−4.76190	−0.469204	−0.234602	+	0.972091i	$0.575379\pi$
$104$	7.60296	0.745532
$105$	−4.22534	−0.412351
$106$	8.68654	0.843712
$107$	−20.3122	−1.96365	−0.981827	−	0.189780i	$-0.939222\pi$
$107$	−20.3122	−1.96365	−0.981827	+	0.189780i	$0.939222\pi$
$108$	0.129770	0.0124871
$109$	14.2741	1.36721	0.683604	−	0.729853i	$-0.260412\pi$
$109$	14.2741	1.36721	0.683604	+	0.729853i	$0.260412\pi$
$110$	7.35484	0.701257
$111$	4.87023	0.462262
$112$	−17.9269	−1.69393
$113$	−2.26202	−0.212793	−0.106396	−	0.994324i	$-0.533931\pi$
$113$	−2.26202	−0.212793	−0.106396	+	0.994324i	$0.533931\pi$
$114$	6.45737	0.604788
$115$	−3.01376	−0.281034
$116$	0.574606	0.0533508
$117$	2.78562	0.257530
$118$	−21.8791	−2.01414
$119$	−9.53937	−0.874473
$120$	−2.72936	−0.249156
$121$	14.3989	1.30899
$122$	10.7160	0.970182
$123$	−2.84348	−0.256388
$124$	0.916074	0.0822659
$125$	−1.00000	−0.0894427
$126$	−6.16635	−0.549343
$127$	19.9781	1.77277	0.886385	−	0.462949i	$-0.153209\pi$
$127$	19.9781	1.77277	0.886385	+	0.462949i	$0.153209\pi$
$128$	−12.2882	−1.08614
$129$	9.33179	0.821619
$130$	4.06525	0.356546
$131$	−22.1773	−1.93764	−0.968821	−	0.247762i	$-0.920305\pi$
$131$	−22.1773	−1.93764	−0.968821	+	0.247762i	$0.920305\pi$
$132$	0.654006	0.0569239
$133$	−18.6961	−1.62116
$134$	3.76868	0.325564
$135$	−1.00000	−0.0860663
$136$	−6.16196	−0.528384
$137$	−12.4151	−1.06069	−0.530346	−	0.847781i	$-0.677938\pi$
$137$	−12.4151	−1.06069	−0.530346	+	0.847781i	$0.677938\pi$
$138$	−4.39819	−0.374399
$139$	18.3499	1.55642	0.778209	−	0.628005i	$-0.216128\pi$
$139$	18.3499	1.55642	0.778209	+	0.628005i	$0.216128\pi$
$140$	−0.548323	−0.0463418
$141$	−3.28978	−0.277050
$142$	4.64624	0.389904
$143$	14.0388	1.17398
$144$	−4.24270	−0.353558
$145$	−4.42787	−0.367715
$146$	−12.5475	−1.03843
$147$	10.8535	0.895185
$148$	0.632010	0.0519509
$149$	−20.9634	−1.71739	−0.858694	−	0.512488i	$-0.828724\pi$
$149$	−20.9634	−1.71739	−0.858694	+	0.512488i	$0.828724\pi$
$150$	−1.45937	−0.119157
$151$	−8.01202	−0.652009	−0.326005	−	0.945368i	$-0.605703\pi$
$151$	−8.01202	−0.652009	−0.326005	+	0.945368i	$0.605703\pi$
$152$	−12.0768	−0.979555
$153$	−2.25766	−0.182521
$154$	−31.0768	−2.50424
$155$	−7.05921	−0.567009
$156$	0.361490	0.0289423
$157$	−14.6789	−1.17151	−0.585753	−	0.810490i	$-0.699201\pi$
$157$	−14.6789	−1.17151	−0.585753	+	0.810490i	$0.699201\pi$
$158$	8.81349	0.701164
$159$	−5.95224	−0.472043
$160$	−0.732956	−0.0579452
$161$	12.7342	1.00359
$162$	−1.45937	−0.114659
$163$	−10.0689	−0.788659	−0.394329	−	0.918969i	$-0.629023\pi$
$163$	−10.0689	−0.788659	−0.394329	+	0.918969i	$0.629023\pi$
$164$	−0.368999	−0.0288140
$165$	−5.03973	−0.392342
$166$	0.389953	0.0302662
$167$	9.65349	0.747010	0.373505	−	0.927628i	$-0.378156\pi$
$167$	9.65349	0.747010	0.373505	+	0.927628i	$0.378156\pi$
$168$	11.5325	0.889752
$169$	−5.24034	−0.403103
$170$	−3.29476	−0.252697
$171$	−4.42475	−0.338369
$172$	1.21099	0.0923370
$173$	4.88601	0.371476	0.185738	−	0.982599i	$-0.440532\pi$
$173$	4.88601	0.371476	0.185738	+	0.982599i	$0.440532\pi$
$174$	−6.46192	−0.489877
$175$	4.22534	0.319406
$176$	−21.3821	−1.61173
$177$	14.9921	1.12688
$178$	−16.4996	−1.23670
$179$	−24.2228	−1.81050	−0.905248	−	0.424884i	$-0.860315\pi$
$179$	−24.2228	−1.81050	−0.905248	+	0.424884i	$0.860315\pi$
$180$	−0.129770	−0.00967249
$181$	−7.00332	−0.520553	−0.260276	−	0.965534i	$-0.583814\pi$
$181$	−7.00332	−0.520553	−0.260276	+	0.965534i	$0.583814\pi$
$182$	−17.1771	−1.27325
$183$	−7.34289	−0.542802
$184$	8.22563	0.606402
$185$	−4.87023	−0.358066
$186$	−10.3020	−0.755380
$187$	−11.3780	−0.832040
$188$	−0.426916	−0.0311360
$189$	4.22534	0.307349
$190$	−6.45737	−0.468467
$191$	−0.421647	−0.0305093	−0.0152546	−	0.999884i	$-0.504856\pi$
$191$	−0.421647	−0.0305093	−0.0152546	+	0.999884i	$0.504856\pi$
$192$	7.41574	0.535185
$193$	7.58263	0.545810	0.272905	−	0.962041i	$-0.412016\pi$
$193$	7.58263	0.545810	0.272905	+	0.962041i	$0.412016\pi$
$194$	12.9484	0.929637
$195$	−2.78562	−0.199482
$196$	1.40846	0.100605
$197$	−14.6330	−1.04256	−0.521279	−	0.853386i	$-0.674545\pi$
$197$	−14.6330	−1.04256	−0.521279	+	0.853386i	$0.674545\pi$
$198$	−7.35484	−0.522686
$199$	22.0657	1.56419	0.782097	−	0.623157i	$-0.214150\pi$
$199$	22.0657	1.56419	0.782097	+	0.623157i	$0.214150\pi$
$200$	2.72936	0.192995
$201$	−2.58240	−0.182148
$202$	3.12736	0.220040
$203$	18.7093	1.31314
$204$	−0.292976	−0.0205124
$205$	2.84348	0.198597
$206$	6.94940	0.484187
$207$	3.01376	0.209470
$208$	−11.8185	−0.819468
$209$	−22.2996	−1.54249
$210$	6.16635	0.425519
$211$	15.0804	1.03818	0.519090	−	0.854720i	$-0.326271\pi$
$211$	15.0804	1.03818	0.519090	+	0.854720i	$0.326271\pi$
$212$	−0.772423	−0.0530502
$213$	−3.18373	−0.218145
$214$	29.6431	2.02636
$215$	−9.33179	−0.636423
$216$	2.72936	0.185710
$217$	29.8276	2.02483
$218$	−20.8312	−1.41087
$219$	8.59784	0.580988
$220$	−0.654006	−0.0440931
$221$	−6.28896	−0.423041
$222$	−7.10748	−0.477023
$223$	−2.89154	−0.193632	−0.0968160	−	0.995302i	$-0.530866\pi$
$223$	−2.89154	−0.193632	−0.0968160	+	0.995302i	$0.530866\pi$
$224$	3.09699	0.206926
$225$	1.00000	0.0666667
$226$	3.30113	0.219588
$227$	−15.8602	−1.05268	−0.526341	−	0.850274i	$-0.676436\pi$
$227$	−15.8602	−1.05268	−0.526341	+	0.850274i	$0.676436\pi$
$228$	−0.574201	−0.0380274
$229$	−9.19780	−0.607808	−0.303904	−	0.952703i	$-0.598290\pi$
$229$	−9.19780	−0.607808	−0.303904	+	0.952703i	$0.598290\pi$
$230$	4.39819	0.290008
$231$	21.2946	1.40108
$232$	12.0853	0.793437
$233$	−1.37462	−0.0900542	−0.0450271	−	0.998986i	$-0.514337\pi$
$233$	−1.37462	−0.0900542	−0.0450271	+	0.998986i	$0.514337\pi$
$234$	−4.06525	−0.265754
$235$	3.28978	0.214602
$236$	1.94553	0.126643
$237$	−6.03923	−0.392290
$238$	13.9215	0.902397
$239$	25.4539	1.64648	0.823239	−	0.567696i	$-0.192165\pi$
$239$	25.4539	1.64648	0.823239	+	0.567696i	$0.192165\pi$
$240$	4.24270	0.273865
$241$	−6.39681	−0.412055	−0.206028	−	0.978546i	$-0.566054\pi$
$241$	−6.39681	−0.412055	−0.206028	+	0.978546i	$0.566054\pi$
$242$	−21.0133	−1.35079
$243$	1.00000	0.0641500
$244$	−0.952887	−0.0610024
$245$	−10.8535	−0.693407
$246$	4.14970	0.264575
$247$	−12.3257	−0.784264
$248$	19.2671	1.22346
$249$	−0.267206	−0.0169335
$250$	1.45937	0.0922989
$251$	26.0252	1.64270	0.821349	−	0.570427i	$-0.193222\pi$
$251$	26.0252	1.64270	0.821349	+	0.570427i	$0.193222\pi$
$252$	0.548323	0.0345411
$253$	15.1885	0.954893
$254$	−29.1555	−1.82938
$255$	2.25766	0.141380
$256$	3.10165	0.193853
$257$	−23.4060	−1.46003	−0.730014	−	0.683432i	$-0.760487\pi$
$257$	−23.4060	−1.46003	−0.730014	+	0.683432i	$0.760487\pi$
$258$	−13.6186	−0.847855
$259$	20.5784	1.27868
$260$	−0.361490	−0.0224186
$261$	4.42787	0.274079
$262$	32.3650	1.99952
$263$	−2.60124	−0.160399	−0.0801996	−	0.996779i	$-0.525556\pi$
$263$	−2.60124	−0.160399	−0.0801996	+	0.996779i	$0.525556\pi$
$264$	13.7552	0.846577
$265$	5.95224	0.365643
$266$	27.2846	1.67293
$267$	11.3060	0.691914
$268$	−0.335118	−0.0204706
$269$	−18.4772	−1.12658	−0.563288	−	0.826261i	$-0.690464\pi$
$269$	−18.4772	−1.12658	−0.563288	+	0.826261i	$0.690464\pi$
$270$	1.45937	0.0888146
$271$	−3.49361	−0.212221	−0.106111	−	0.994354i	$-0.533840\pi$
$271$	−3.49361	−0.212221	−0.106111	+	0.994354i	$0.533840\pi$
$272$	9.57856	0.580785
$273$	11.7702	0.712364
$274$	18.1182	1.09456
$275$	5.03973	0.303907
$276$	0.391095	0.0235412
$277$	1.60133	0.0962146	0.0481073	−	0.998842i	$-0.484681\pi$
$277$	1.60133	0.0962146	0.0481073	+	0.998842i	$0.484681\pi$
$278$	−26.7794	−1.60612
$279$	7.05921	0.422624
$280$	−11.5325	−0.689199
$281$	7.17049	0.427756	0.213878	−	0.976860i	$-0.431391\pi$
$281$	7.17049	0.427756	0.213878	+	0.976860i	$0.431391\pi$
$282$	4.80102	0.285897
$283$	−1.01042	−0.0600635	−0.0300317	−	0.999549i	$-0.509561\pi$
$283$	−1.01042	−0.0600635	−0.0300317	+	0.999549i	$0.509561\pi$
$284$	−0.413153	−0.0245161
$285$	4.42475	0.262100
$286$	−20.4878	−1.21147
$287$	−12.0147	−0.709204
$288$	0.732956	0.0431898
$289$	−11.9030	−0.700176
$290$	6.46192	0.379457
$291$	−8.87254	−0.520118
$292$	1.11574	0.0652939
$293$	23.5976	1.37859	0.689293	−	0.724482i	$-0.257921\pi$
$293$	23.5976	1.37859	0.689293	+	0.724482i	$0.257921\pi$
$294$	−15.8394	−0.923770
$295$	−14.9921	−0.872876
$296$	13.2926	0.772618
$297$	5.03973	0.292435
$298$	30.5934	1.77223
$299$	8.39517	0.485505
$300$	0.129770	0.00749228
$301$	39.4300	2.27271
$302$	11.6925	0.672830
$303$	−2.14295	−0.123109
$304$	18.7729	1.07670
$305$	7.34289	0.420452
$306$	3.29476	0.188349
$307$	18.9003	1.07870	0.539348	−	0.842083i	$-0.318671\pi$
$307$	18.9003	1.07870	0.539348	+	0.842083i	$0.318671\pi$
$308$	2.76340	0.157459
$309$	−4.76190	−0.270895
$310$	10.3020	0.585115
$311$	−13.5793	−0.770009	−0.385005	−	0.922915i	$-0.625800\pi$
$311$	−13.5793	−0.770009	−0.385005	+	0.922915i	$0.625800\pi$
$312$	7.60296	0.430433
$313$	9.75239	0.551238	0.275619	−	0.961267i	$-0.411117\pi$
$313$	9.75239	0.551238	0.275619	+	0.961267i	$0.411117\pi$
$314$	21.4220	1.20891
$315$	−4.22534	−0.238071
$316$	−0.783712	−0.0440872
$317$	−4.54253	−0.255134	−0.127567	−	0.991830i	$-0.540717\pi$
$317$	−4.54253	−0.255134	−0.127567	+	0.991830i	$0.540717\pi$
$318$	8.68654	0.487117
$319$	22.3153	1.24942
$320$	−7.41574	−0.414553
$321$	−20.3122	−1.13372
$322$	−18.5839	−1.03564
$323$	9.98957	0.555835
$324$	0.129770	0.00720945
$325$	2.78562	0.154518
$326$	14.6943	0.813843
$327$	14.2741	0.789357
$328$	−7.76089	−0.428523
$329$	−13.9005	−0.766358
$330$	7.35484	0.404871
$331$	14.5240	0.798309	0.399155	−	0.916884i	$-0.369304\pi$
$331$	14.5240	0.798309	0.399155	+	0.916884i	$0.369304\pi$
$332$	−0.0346753	−0.00190305
$333$	4.87023	0.266887
$334$	−14.0881	−0.770864
$335$	2.58240	0.141091
$336$	−17.9269	−0.977991
$337$	−5.06604	−0.275965	−0.137982	−	0.990435i	$-0.544062\pi$
$337$	−5.06604	−0.275965	−0.137982	+	0.990435i	$0.544062\pi$
$338$	7.64761	0.415975
$339$	−2.26202	−0.122856
$340$	0.292976	0.0158889
$341$	35.5765	1.92657
$342$	6.45737	0.349174
$343$	16.2825	0.879174
$344$	25.4699	1.37324
$345$	−3.01376	−0.162255
$346$	−7.13050	−0.383338
$347$	−4.71142	−0.252922	−0.126461	−	0.991972i	$-0.540362\pi$
$347$	−4.71142	−0.252922	−0.126461	+	0.991972i	$0.540362\pi$
$348$	0.574606	0.0308021
$349$	−6.12452	−0.327838	−0.163919	−	0.986474i	$-0.552414\pi$
$349$	−6.12452	−0.327838	−0.163919	+	0.986474i	$0.552414\pi$
$350$	−6.16635	−0.329606
$351$	2.78562	0.148685
$352$	3.69390	0.196885
$353$	29.9822	1.59579	0.797895	−	0.602797i	$-0.205947\pi$
$353$	29.9822	1.59579	0.797895	+	0.602797i	$0.205947\pi$
$354$	−21.8791	−1.16286
$355$	3.18373	0.168975
$356$	1.46718	0.0777602
$357$	−9.53937	−0.504877
$358$	35.3501	1.86831
$359$	−1.42833	−0.0753845	−0.0376922	−	0.999289i	$-0.512001\pi$
$359$	−1.42833	−0.0753845	−0.0376922	+	0.999289i	$0.512001\pi$
$360$	−2.72936	−0.143850
$361$	0.578452	0.0304449
$362$	10.2205	0.537175
$363$	14.3989	0.755744
$364$	1.52742	0.0800585
$365$	−8.59784	−0.450032
$366$	10.7160	0.560135
$367$	22.7812	1.18917	0.594584	−	0.804033i	$-0.297317\pi$
$367$	22.7812	1.18917	0.594584	+	0.804033i	$0.297317\pi$
$368$	−12.7865	−0.666540
$369$	−2.84348	−0.148026
$370$	7.10748	0.369500
$371$	−25.1503	−1.30574
$372$	0.916074	0.0474962
$373$	−8.74510	−0.452804	−0.226402	−	0.974034i	$-0.572696\pi$
$373$	−8.74510	−0.452804	−0.226402	+	0.974034i	$0.572696\pi$
$374$	16.6047	0.858609
$375$	−1.00000	−0.0516398
$376$	−8.97902	−0.463057
$377$	12.3344	0.635252
$378$	−6.16635	−0.317163
$379$	2.02911	0.104228	0.0521141	−	0.998641i	$-0.483404\pi$
$379$	2.02911	0.104228	0.0521141	+	0.998641i	$0.483404\pi$
$380$	0.574201	0.0294559
$381$	19.9781	1.02351
$382$	0.615340	0.0314835
$383$	−1.38798	−0.0709227	−0.0354613	−	0.999371i	$-0.511290\pi$
$383$	−1.38798	−0.0709227	−0.0354613	+	0.999371i	$0.511290\pi$
$384$	−12.2882	−0.627082
$385$	−21.2946	−1.08527
$386$	−11.0659	−0.563239
$387$	9.33179	0.474362
$388$	−1.15139	−0.0584530
$389$	−9.44502	−0.478882	−0.239441	−	0.970911i	$-0.576964\pi$
$389$	−9.44502	−0.478882	−0.239441	+	0.970911i	$0.576964\pi$
$390$	4.06525	0.205852
$391$	−6.80402	−0.344094
$392$	29.6232	1.49620
$393$	−22.1773	−1.11870
$394$	21.3550	1.07585
$395$	6.03923	0.303867
$396$	0.654006	0.0328650
$397$	33.0741	1.65994	0.829970	−	0.557809i	$-0.188358\pi$
$397$	33.0741	1.65994	0.829970	+	0.557809i	$0.188358\pi$
$398$	−32.2020	−1.61414
$399$	−18.6961	−0.935976
$400$	−4.24270	−0.212135
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	3.76868	0.187965
$403$	19.6642	0.979546
$404$	−0.278090	−0.0138355
$405$	−1.00000	−0.0496904
$406$	−27.3038	−1.35507
$407$	24.5446	1.21663
$408$	−6.16196	−0.305063
$409$	−22.8313	−1.12893	−0.564466	−	0.825456i	$-0.690918\pi$
$409$	−22.8313	−1.12893	−0.564466	+	0.825456i	$0.690918\pi$
$410$	−4.14970	−0.204939
$411$	−12.4151	−0.612391
$412$	−0.617953	−0.0304444
$413$	63.3470	3.11710
$414$	−4.39819	−0.216159
$415$	0.267206	0.0131166
$416$	2.04173	0.100104
$417$	18.3499	0.898599
$418$	32.5434	1.59175
$419$	−16.3767	−0.800053	−0.400026	−	0.916504i	$-0.630999\pi$
$419$	−16.3767	−0.800053	−0.400026	+	0.916504i	$0.630999\pi$
$420$	−0.548323	−0.0267554
$421$	16.6389	0.810932	0.405466	−	0.914110i	$-0.367109\pi$
$421$	16.6389	0.810932	0.405466	+	0.914110i	$0.367109\pi$
$422$	−22.0080	−1.07133
$423$	−3.28978	−0.159955
$424$	−16.2458	−0.788967
$425$	−2.25766	−0.109512
$426$	4.64624	0.225111
$427$	−31.0262	−1.50146
$428$	−2.63591	−0.127412
$429$	14.0388	0.677797
$430$	13.6186	0.656746
$431$	2.61060	0.125748	0.0628740	−	0.998021i	$-0.479973\pi$
$431$	2.61060	0.125748	0.0628740	+	0.998021i	$0.479973\pi$
$432$	−4.24270	−0.204127
$433$	4.79681	0.230520	0.115260	−	0.993335i	$-0.463230\pi$
$433$	4.79681	0.230520	0.115260	+	0.993335i	$0.463230\pi$
$434$	−43.5296	−2.08949
$435$	−4.42787	−0.212300
$436$	1.85235	0.0887113
$437$	−13.3351	−0.637906
$438$	−12.5475	−0.599541
$439$	−12.5612	−0.599513	−0.299756	−	0.954016i	$-0.596905\pi$
$439$	−12.5612	−0.599513	−0.299756	+	0.954016i	$0.596905\pi$
$440$	−13.7552	−0.655756
$441$	10.8535	0.516835
$442$	9.17795	0.436550
$443$	41.2233	1.95858	0.979288	−	0.202472i	$-0.0648975\pi$
$443$	41.2233	1.95858	0.979288	+	0.202472i	$0.0648975\pi$
$444$	0.632010	0.0299939
$445$	−11.3060	−0.535954
$446$	4.21984	0.199815
$447$	−20.9634	−0.991535
$448$	31.3341	1.48040
$449$	−7.86156	−0.371010	−0.185505	−	0.982643i	$-0.559392\pi$
$449$	−7.86156	−0.371010	−0.185505	+	0.982643i	$0.559392\pi$
$450$	−1.45937	−0.0687955
$451$	−14.3304	−0.674791
$452$	−0.293543	−0.0138071
$453$	−8.01202	−0.376438
$454$	23.1460	1.08630
$455$	−11.7702	−0.551795
$456$	−12.0768	−0.565546
$457$	−15.1607	−0.709186	−0.354593	−	0.935021i	$-0.615381\pi$
$457$	−15.1607	−0.709186	−0.354593	+	0.935021i	$0.615381\pi$
$458$	13.4230	0.627217
$459$	−2.25766	−0.105378
$460$	−0.391095	−0.0182349
$461$	−0.259984	−0.0121087	−0.00605434	−	0.999982i	$-0.501927\pi$
$461$	−0.259984	−0.0121087	−0.00605434	+	0.999982i	$0.501927\pi$
$462$	−31.0768	−1.44582
$463$	−3.24349	−0.150738	−0.0753688	−	0.997156i	$-0.524013\pi$
$463$	−3.24349	−0.150738	−0.0753688	+	0.997156i	$0.524013\pi$
$464$	−18.7861	−0.872125
$465$	−7.05921	−0.327363
$466$	2.00608	0.0929299
$467$	12.6195	0.583963	0.291981	−	0.956424i	$-0.405685\pi$
$467$	12.6195	0.583963	0.291981	+	0.956424i	$0.405685\pi$
$468$	0.361490	0.0167099
$469$	−10.9115	−0.503847
$470$	−4.80102	−0.221455
$471$	−14.6789	−0.676369
$472$	40.9190	1.88345
$473$	47.0297	2.16243
$474$	8.81349	0.404817
$475$	−4.42475	−0.203022
$476$	−1.23793	−0.0567402
$477$	−5.95224	−0.272534
$478$	−37.1468	−1.69905
$479$	18.0083	0.822819	0.411410	−	0.911451i	$-0.365037\pi$
$479$	18.0083	0.822819	0.411410	+	0.911451i	$0.365037\pi$
$480$	−0.732956	−0.0334547
$481$	13.5666	0.618583
$482$	9.33534	0.425213
$483$	12.7342	0.579424
$484$	1.86854	0.0849337
$485$	8.87254	0.402881
$486$	−1.45937	−0.0661985
$487$	−30.7559	−1.39368	−0.696841	−	0.717226i	$-0.745412\pi$
$487$	−30.7559	−1.39368	−0.696841	+	0.717226i	$0.745412\pi$
$488$	−20.0414	−0.907232
$489$	−10.0689	−0.455332
$490$	15.8394	0.715549
$491$	−18.3555	−0.828370	−0.414185	−	0.910193i	$-0.635933\pi$
$491$	−18.3555	−0.828370	−0.414185	+	0.910193i	$0.635933\pi$
$492$	−0.368999	−0.0166357
$493$	−9.99662	−0.450225
$494$	17.9878	0.809307
$495$	−5.03973	−0.226519
$496$	−29.9501	−1.34480
$497$	−13.4523	−0.603420
$498$	0.389953	0.0174742
$499$	34.1116	1.52704	0.763522	−	0.645782i	$-0.223468\pi$
$499$	34.1116	1.52704	0.763522	+	0.645782i	$0.223468\pi$
$500$	−0.129770	−0.00580350
$501$	9.65349	0.431286
$502$	−37.9805	−1.69515
$503$	22.9352	1.02263	0.511316	−	0.859393i	$-0.329158\pi$
$503$	22.9352	1.02263	0.511316	+	0.859393i	$0.329158\pi$
$504$	11.5325	0.513698
$505$	2.14295	0.0953599
$506$	−22.1657	−0.985386
$507$	−5.24034	−0.232732
$508$	2.59256	0.115026
$509$	41.8823	1.85640	0.928200	−	0.372081i	$-0.121356\pi$
$509$	41.8823	1.85640	0.928200	+	0.372081i	$0.121356\pi$
$510$	−3.29476	−0.145895
$511$	36.3288	1.60709
$512$	20.0500	0.886094
$513$	−4.42475	−0.195358
$514$	34.1581	1.50665
$515$	4.76190	0.209835
$516$	1.21099	0.0533108
$517$	−16.5796	−0.729171
$518$	−30.0316	−1.31951
$519$	4.88601	0.214472
$520$	−7.60296	−0.333412
$521$	13.3198	0.583549	0.291775	−	0.956487i	$-0.405754\pi$
$521$	13.3198	0.583549	0.291775	+	0.956487i	$0.405754\pi$
$522$	−6.46192	−0.282831
$523$	−8.85824	−0.387344	−0.193672	−	0.981066i	$-0.562040\pi$
$523$	−8.85824	−0.387344	−0.193672	+	0.981066i	$0.562040\pi$
$524$	−2.87795	−0.125724
$525$	4.22534	0.184409
$526$	3.79618	0.165521
$527$	−15.9373	−0.694238
$528$	−21.3821	−0.930534
$529$	−13.9173	−0.605099
$530$	−8.68654	−0.377319
$531$	14.9921	0.650604
$532$	−2.42620	−0.105189
$533$	−7.92085	−0.343090
$534$	−16.4996	−0.714009
$535$	20.3122	0.878172
$536$	−7.04830	−0.304440
$537$	−24.2228	−1.04529
$538$	26.9652	1.16255
$539$	54.6989	2.35605
$540$	−0.129770	−0.00558442
$541$	−19.0385	−0.818529	−0.409264	−	0.912416i	$-0.634215\pi$
$541$	−19.0385	−0.818529	−0.409264	+	0.912416i	$0.634215\pi$
$542$	5.09847	0.218998
$543$	−7.00332	−0.300541
$544$	−1.65476	−0.0709473
$545$	−14.2741	−0.611434
$546$	−17.1771	−0.735112
$547$	32.4937	1.38933	0.694666	−	0.719332i	$-0.255552\pi$
$547$	32.4937	1.38933	0.694666	+	0.719332i	$0.255552\pi$
$548$	−1.61111	−0.0688231
$549$	−7.34289	−0.313387
$550$	−7.35484	−0.313612
$551$	−19.5923	−0.834658
$552$	8.22563	0.350106
$553$	−25.5178	−1.08513
$554$	−2.33694	−0.0992870
$555$	−4.87023	−0.206730
$556$	2.38127	0.100988
$557$	30.9988	1.31346	0.656731	−	0.754125i	$-0.271939\pi$
$557$	30.9988	1.31346	0.656731	+	0.754125i	$0.271939\pi$
$558$	−10.3020	−0.436119
$559$	25.9948	1.09946
$560$	17.9269	0.757549
$561$	−11.3780	−0.480378
$562$	−10.4644	−0.441415
$563$	−25.4462	−1.07243	−0.536214	−	0.844082i	$-0.680146\pi$
$563$	−25.4462	−1.07243	−0.536214	+	0.844082i	$0.680146\pi$
$564$	−0.426916	−0.0179764
$565$	2.26202	0.0951639
$566$	1.47459	0.0619814
$567$	4.22534	0.177448
$568$	−8.68955	−0.364605
$569$	−40.2393	−1.68692	−0.843459	−	0.537193i	$-0.819485\pi$
$569$	−40.2393	−1.68692	−0.843459	+	0.537193i	$0.819485\pi$
$570$	−6.45737	−0.270469
$571$	22.3600	0.935735	0.467867	−	0.883799i	$-0.345022\pi$
$571$	22.3600	0.935735	0.467867	+	0.883799i	$0.345022\pi$
$572$	1.82181	0.0761737
$573$	−0.421647	−0.0176145
$574$	17.5339	0.731851
$575$	3.01376	0.125682
$576$	7.41574	0.308989
$577$	−36.2414	−1.50875	−0.754374	−	0.656444i	$-0.772060\pi$
$577$	−36.2414	−1.50875	−0.754374	+	0.656444i	$0.772060\pi$
$578$	17.3709	0.722534
$579$	7.58263	0.315123
$580$	−0.574606	−0.0238592
$581$	−1.12904	−0.0468403
$582$	12.9484	0.536726
$583$	−29.9977	−1.24238
$584$	23.4666	0.971056
$585$	−2.78562	−0.115171
$586$	−34.4377	−1.42261
$587$	−44.8233	−1.85006	−0.925029	−	0.379897i	$-0.875959\pi$
$587$	−44.8233	−1.85006	−0.925029	+	0.379897i	$0.875959\pi$
$588$	1.40846	0.0580841
$589$	−31.2353	−1.28703
$590$	21.8791	0.900750
$591$	−14.6330	−0.601921
$592$	−20.6629	−0.849241
$593$	−2.22088	−0.0912004	−0.0456002	−	0.998960i	$-0.514520\pi$
$593$	−2.22088	−0.0912004	−0.0456002	+	0.998960i	$0.514520\pi$
$594$	−7.35484	−0.301773
$595$	9.53937	0.391076
$596$	−2.72042	−0.111433
$597$	22.0657	0.903088
$598$	−12.2517	−0.501009
$599$	−14.9429	−0.610551	−0.305276	−	0.952264i	$-0.598749\pi$
$599$	−14.9429	−0.610551	−0.305276	+	0.952264i	$0.598749\pi$
$600$	2.72936	0.111426
$601$	−15.7502	−0.642465	−0.321232	−	0.947000i	$-0.604097\pi$
$601$	−15.7502	−0.642465	−0.321232	+	0.947000i	$0.604097\pi$
$602$	−57.5431	−2.34528
$603$	−2.58240	−0.105163
$604$	−1.03972	−0.0423057
$605$	−14.3989	−0.585397
$606$	3.12736	0.127040
$607$	33.9260	1.37701	0.688506	−	0.725231i	$-0.258267\pi$
$607$	33.9260	1.37701	0.688506	+	0.725231i	$0.258267\pi$
$608$	−3.24315	−0.131527
$609$	18.7093	0.758139
$610$	−10.7160	−0.433879
$611$	−9.16408	−0.370739
$612$	−0.292976	−0.0118429
$613$	−5.72585	−0.231265	−0.115633	−	0.993292i	$-0.536890\pi$
$613$	−5.72585	−0.231265	−0.115633	+	0.993292i	$0.536890\pi$
$614$	−27.5826	−1.11314
$615$	2.84348	0.114660
$616$	58.1207	2.34175
$617$	−15.3117	−0.616426	−0.308213	−	0.951317i	$-0.599731\pi$
$617$	−15.3117	−0.616426	−0.308213	+	0.951317i	$0.599731\pi$
$618$	6.94940	0.279546
$619$	−21.5348	−0.865555	−0.432778	−	0.901501i	$-0.642466\pi$
$619$	−21.5348	−0.865555	−0.432778	+	0.901501i	$0.642466\pi$
$620$	−0.916074	−0.0367904
$621$	3.01376	0.120938
$622$	19.8172	0.794598
$623$	47.7716	1.91393
$624$	−11.8185	−0.473120
$625$	1.00000	0.0400000
$626$	−14.2324	−0.568840
$627$	−22.2996	−0.890559
$628$	−1.90489	−0.0760132
$629$	−10.9953	−0.438411
$630$	6.16635	0.245673
$631$	27.6786	1.10187	0.550933	−	0.834549i	$-0.314272\pi$
$631$	27.6786	1.10187	0.550933	+	0.834549i	$0.314272\pi$
$632$	−16.4833	−0.655669
$633$	15.0804	0.599394
$634$	6.62925	0.263281
$635$	−19.9781	−0.792807
$636$	−0.772423	−0.0306286
$637$	30.2338	1.19791
$638$	−32.5663	−1.28931
$639$	−3.18373	−0.125946
$640$	12.2882	0.485736
$641$	−38.6726	−1.52748	−0.763739	−	0.645525i	$-0.776638\pi$
$641$	−38.6726	−1.52748	−0.763739	+	0.645525i	$0.776638\pi$
$642$	29.6431	1.16992
$643$	26.6665	1.05162	0.525811	−	0.850601i	$-0.323762\pi$
$643$	26.6665	1.05162	0.525811	+	0.850601i	$0.323762\pi$
$644$	1.65251	0.0651181
$645$	−9.33179	−0.367439
$646$	−14.5785	−0.573584
$647$	31.9601	1.25648	0.628241	−	0.778019i	$-0.283775\pi$
$647$	31.9601	1.25648	0.628241	+	0.778019i	$0.283775\pi$
$648$	2.72936	0.107220
$649$	75.5563	2.96585
$650$	−4.06525	−0.159452
$651$	29.8276	1.16903
$652$	−1.30665	−0.0511722
$653$	35.1260	1.37458	0.687292	−	0.726381i	$-0.258799\pi$
$653$	35.1260	1.37458	0.687292	+	0.726381i	$0.258799\pi$
$654$	−20.8312	−0.814564
$655$	22.1773	0.866540
$656$	12.0640	0.471021
$657$	8.59784	0.335434
$658$	20.2860	0.790830
$659$	−44.9499	−1.75100	−0.875501	−	0.483217i	$-0.839468\pi$
$659$	−44.9499	−1.75100	−0.875501	+	0.483217i	$0.839468\pi$
$660$	−0.654006	−0.0254572
$661$	−43.8357	−1.70501	−0.852505	−	0.522719i	$-0.824918\pi$
$661$	−43.8357	−1.70501	−0.852505	+	0.522719i	$0.824918\pi$
$662$	−21.1959	−0.823801
$663$	−6.28896	−0.244243
$664$	−0.729301	−0.0283024
$665$	18.6961	0.725004
$666$	−7.10748	−0.275409
$667$	13.3445	0.516702
$668$	1.25274	0.0484698
$669$	−2.89154	−0.111794
$670$	−3.76868	−0.145597
$671$	−37.0062	−1.42861
$672$	3.09699	0.119469
$673$	19.8144	0.763790	0.381895	−	0.924206i	$-0.375272\pi$
$673$	19.8144	0.763790	0.381895	+	0.924206i	$0.375272\pi$
$674$	7.39324	0.284777
$675$	1.00000	0.0384900
$676$	−0.680039	−0.0261554
$677$	9.55120	0.367083	0.183541	−	0.983012i	$-0.441244\pi$
$677$	9.55120	0.367083	0.183541	+	0.983012i	$0.441244\pi$
$678$	3.30113	0.126779
$679$	−37.4896	−1.43872
$680$	6.16196	0.236300
$681$	−15.8602	−0.607766
$682$	−51.9194	−1.98809
$683$	−7.73550	−0.295991	−0.147995	−	0.988988i	$-0.547282\pi$
$683$	−7.73550	−0.295991	−0.147995	+	0.988988i	$0.547282\pi$
$684$	−0.574201	−0.0219551
$685$	12.4151	0.474356
$686$	−23.7623	−0.907248
$687$	−9.19780	−0.350918
$688$	−39.5920	−1.50943
$689$	−16.5807	−0.631673
$690$	4.39819	0.167436
$691$	17.5947	0.669333	0.334666	−	0.942337i	$-0.391376\pi$
$691$	17.5947	0.669333	0.334666	+	0.942337i	$0.391376\pi$
$692$	0.634057	0.0241032
$693$	21.2946	0.808915
$694$	6.87572	0.260999
$695$	−18.3499	−0.696052
$696$	12.0853	0.458091
$697$	6.41960	0.243160
$698$	8.93797	0.338307
$699$	−1.37462	−0.0519928
$700$	0.548323	0.0207247
$701$	−8.67519	−0.327657	−0.163829	−	0.986489i	$-0.552384\pi$
$701$	−8.67519	−0.327657	−0.163829	+	0.986489i	$0.552384\pi$
$702$	−4.06525	−0.153433
$703$	−21.5496	−0.812757
$704$	37.3733	1.40856
$705$	3.28978	0.123900
$706$	−43.7552	−1.64675
$707$	−9.05469	−0.340537
$708$	1.94553	0.0731176
$709$	37.6577	1.41427	0.707133	−	0.707081i	$-0.249988\pi$
$709$	37.6577	1.41427	0.707133	+	0.707081i	$0.249988\pi$
$710$	−4.64624	−0.174370
$711$	−6.03923	−0.226489
$712$	30.8581	1.15646
$713$	21.2747	0.796744
$714$	13.9215	0.520999
$715$	−14.0388	−0.525020
$716$	−3.14339	−0.117474
$717$	25.4539	0.950594
$718$	2.08447	0.0777917
$719$	−42.8519	−1.59811	−0.799053	−	0.601261i	$-0.794665\pi$
$719$	−42.8519	−1.59811	−0.799053	+	0.601261i	$0.794665\pi$
$720$	4.24270	0.158116
$721$	−20.1207	−0.749334
$722$	−0.844178	−0.0314171
$723$	−6.39681	−0.237900
$724$	−0.908822	−0.0337761
$725$	4.42787	0.164447
$726$	−21.0133	−0.779877
$727$	−9.79780	−0.363380	−0.181690	−	0.983356i	$-0.558157\pi$
$727$	−9.79780	−0.363380	−0.181690	+	0.983356i	$0.558157\pi$
$728$	32.1251	1.19064
$729$	1.00000	0.0370370
$730$	12.5475	0.464402
$731$	−21.0680	−0.779227
$732$	−0.952887	−0.0352197
$733$	−1.43431	−0.0529776	−0.0264888	−	0.999649i	$-0.508433\pi$
$733$	−1.43431	−0.0529776	−0.0264888	+	0.999649i	$0.508433\pi$
$734$	−33.2463	−1.22714
$735$	−10.8535	−0.400339
$736$	2.20895	0.0814230
$737$	−13.0146	−0.479398
$738$	4.14970	0.152753
$739$	−6.10335	−0.224515	−0.112258	−	0.993679i	$-0.535808\pi$
$739$	−6.10335	−0.224515	−0.112258	+	0.993679i	$0.535808\pi$
$740$	−0.632010	−0.0232332
$741$	−12.3257	−0.452795
$742$	36.7036	1.34743
$743$	−24.7188	−0.906845	−0.453423	−	0.891296i	$-0.649797\pi$
$743$	−24.7188	−0.906845	−0.453423	+	0.891296i	$0.649797\pi$
$744$	19.2671	0.706367
$745$	20.9634	0.768040
$746$	12.7624	0.467264
$747$	−0.267206	−0.00977654
$748$	−1.47652	−0.0539869
$749$	−85.8260	−3.13601
$750$	1.45937	0.0532888
$751$	8.73818	0.318861	0.159430	−	0.987209i	$-0.449034\pi$
$751$	8.73818	0.318861	0.159430	+	0.987209i	$0.449034\pi$
$752$	13.9576	0.508980
$753$	26.0252	0.948412
$754$	−18.0004	−0.655537
$755$	8.01202	0.291587
$756$	0.548323	0.0199423
$757$	10.1322	0.368263	0.184131	−	0.982902i	$-0.441053\pi$
$757$	10.1322	0.368263	0.184131	+	0.982902i	$0.441053\pi$
$758$	−2.96123	−0.107557
$759$	15.1885	0.551308
$760$	12.0768	0.438070
$761$	46.3613	1.68060	0.840298	−	0.542125i	$-0.182380\pi$
$761$	46.3613	1.68060	0.840298	+	0.542125i	$0.182380\pi$
$762$	−29.1555	−1.05619
$763$	60.3128	2.18347
$764$	−0.0547171	−0.00197960
$765$	2.25766	0.0816257
$766$	2.02559	0.0731874
$767$	41.7624	1.50795
$768$	3.10165	0.111921
$769$	−17.9722	−0.648094	−0.324047	−	0.946041i	$-0.605044\pi$
$769$	−17.9722	−0.648094	−0.324047	+	0.946041i	$0.605044\pi$
$770$	31.0768	1.11993
$771$	−23.4060	−0.842948
$772$	0.983999	0.0354149
$773$	−2.14178	−0.0770344	−0.0385172	−	0.999258i	$-0.512263\pi$
$773$	−2.14178	−0.0770344	−0.0385172	+	0.999258i	$0.512263\pi$
$774$	−13.6186	−0.489509
$775$	7.05921	0.253574
$776$	−24.2164	−0.869318
$777$	20.5784	0.738246
$778$	13.7838	0.494174
$779$	12.5817	0.450786
$780$	−0.361490	−0.0129434
$781$	−16.0451	−0.574139
$782$	9.92961	0.355082
$783$	4.42787	0.158239
$784$	−46.0483	−1.64458
$785$	14.6789	0.523913
$786$	32.3650	1.15442
$787$	45.7057	1.62923	0.814616	−	0.580000i	$-0.196947\pi$
$787$	45.7057	1.62923	0.814616	+	0.580000i	$0.196947\pi$
$788$	−1.89893	−0.0676464
$789$	−2.60124	−0.0926065
$790$	−8.81349	−0.313570
$791$	−9.55781	−0.339837
$792$	13.7552	0.488772
$793$	−20.4545	−0.726359
$794$	−48.2674	−1.71295
$795$	5.95224	0.211104
$796$	2.86346	0.101493
$797$	34.3558	1.21694	0.608472	−	0.793575i	$-0.291783\pi$
$797$	34.3558	1.21694	0.608472	+	0.793575i	$0.291783\pi$
$798$	27.2846	0.965865
$799$	7.42720	0.262756
$800$	0.732956	0.0259139
$801$	11.3060	0.399477
$802$	1.45937	0.0515323
$803$	43.3308	1.52911
$804$	−0.335118	−0.0118187
$805$	−12.7342	−0.448820
$806$	−28.6975	−1.01083
$807$	−18.4772	−0.650429
$808$	−5.84888	−0.205763
$809$	−8.81590	−0.309951	−0.154975	−	0.987918i	$-0.549530\pi$
$809$	−8.81590	−0.309951	−0.154975	+	0.987918i	$0.549530\pi$
$810$	1.45937	0.0512771
$811$	52.8384	1.85541	0.927703	−	0.373318i	$-0.121780\pi$
$811$	52.8384	1.85541	0.927703	+	0.373318i	$0.121780\pi$
$812$	2.42791	0.0852029
$813$	−3.49361	−0.122526
$814$	−35.8198	−1.25548
$815$	10.0689	0.352699
$816$	9.57856	0.335317
$817$	−41.2909	−1.44459
$818$	33.3193	1.16498
$819$	11.7702	0.411284
$820$	0.368999	0.0128860
$821$	−47.8340	−1.66942	−0.834710	−	0.550690i	$-0.814365\pi$
$821$	−47.8340	−1.66942	−0.834710	+	0.550690i	$0.814365\pi$
$822$	18.1182	0.631946
$823$	27.9711	0.975010	0.487505	−	0.873120i	$-0.337907\pi$
$823$	27.9711	0.975010	0.487505	+	0.873120i	$0.337907\pi$
$824$	−12.9970	−0.452771
$825$	5.03973	0.175461
$826$	−92.4469	−3.21664
$827$	15.8958	0.552751	0.276376	−	0.961050i	$-0.410867\pi$
$827$	15.8958	0.552751	0.276376	+	0.961050i	$0.410867\pi$
$828$	0.391095	0.0135915
$829$	37.9606	1.31843	0.659214	−	0.751956i	$-0.270889\pi$
$829$	37.9606	1.31843	0.659214	+	0.751956i	$0.270889\pi$
$830$	−0.389953	−0.0135355
$831$	1.60133	0.0555495
$832$	20.6574	0.716167
$833$	−24.5036	−0.848998
$834$	−26.7794	−0.927293
$835$	−9.65349	−0.334073
$836$	−2.89382	−0.100085
$837$	7.05921	0.244002
$838$	23.8997	0.825600
$839$	50.8735	1.75635	0.878174	−	0.478341i	$-0.158762\pi$
$839$	50.8735	1.75635	0.878174	+	0.478341i	$0.158762\pi$
$840$	−11.5325	−0.397909
$841$	−9.39393	−0.323929
$842$	−24.2824	−0.836828
$843$	7.17049	0.246965
$844$	1.95699	0.0673624
$845$	5.24034	0.180273
$846$	4.80102	0.165063
$847$	60.8402	2.09049
$848$	25.2536	0.867211
$849$	−1.01042	−0.0346777
$850$	3.29476	0.113009
$851$	14.6777	0.503144
$852$	−0.413153	−0.0141544
$853$	−12.7174	−0.435434	−0.217717	−	0.976012i	$-0.569861\pi$
$853$	−12.7174	−0.435434	−0.217717	+	0.976012i	$0.569861\pi$
$854$	45.2788	1.54941
$855$	4.42475	0.151323
$856$	−55.4393	−1.89488
$857$	−15.1036	−0.515929	−0.257965	−	0.966154i	$-0.583052\pi$
$857$	−15.1036	−0.515929	−0.257965	+	0.966154i	$0.583052\pi$
$858$	−20.4878	−0.699441
$859$	19.9690	0.681334	0.340667	−	0.940184i	$-0.389347\pi$
$859$	19.9690	0.681334	0.340667	+	0.940184i	$0.389347\pi$
$860$	−1.21099	−0.0412943
$861$	−12.0147	−0.409459
$862$	−3.80983	−0.129763
$863$	29.1660	0.992823	0.496411	−	0.868087i	$-0.334651\pi$
$863$	29.1660	0.992823	0.496411	+	0.868087i	$0.334651\pi$
$864$	0.732956	0.0249357
$865$	−4.88601	−0.166129
$866$	−7.00034	−0.237881
$867$	−11.9030	−0.404247
$868$	3.87073	0.131381
$869$	−30.4361	−1.03247
$870$	6.46192	0.219080
$871$	−7.19357	−0.243745
$872$	38.9591	1.31932
$873$	−8.87254	−0.300290
$874$	19.4609	0.658276
$875$	−4.22534	−0.142843
$876$	1.11574	0.0376975
$877$	−56.9456	−1.92292	−0.961458	−	0.274952i	$-0.911338\pi$
$877$	−56.9456	−1.92292	−0.961458	+	0.274952i	$0.911338\pi$
$878$	18.3315	0.618657
$879$	23.5976	0.795928
$880$	21.3821	0.720789
$881$	−47.4170	−1.59752	−0.798760	−	0.601649i	$-0.794511\pi$
$881$	−47.4170	−1.59752	−0.798760	+	0.601649i	$0.794511\pi$
$882$	−15.8394	−0.533339
$883$	3.31001	0.111391	0.0556953	−	0.998448i	$-0.482262\pi$
$883$	3.31001	0.111391	0.0556953	+	0.998448i	$0.482262\pi$
$884$	−0.816120	−0.0274491
$885$	−14.9921	−0.503955
$886$	−60.1601	−2.02112
$887$	−7.60984	−0.255513	−0.127757	−	0.991806i	$-0.540778\pi$
$887$	−7.60984	−0.255513	−0.127757	+	0.991806i	$0.540778\pi$
$888$	13.2926	0.446071
$889$	84.4144	2.83117
$890$	16.4996	0.553069
$891$	5.03973	0.168837
$892$	−0.375236	−0.0125638
$893$	14.5565	0.487114
$894$	30.5934	1.02320
$895$	24.2228	0.809678
$896$	−51.9221	−1.73460
$897$	8.39517	0.280307
$898$	11.4730	0.382857
$899$	31.2573	1.04249
$900$	0.129770	0.00432567
$901$	13.4381	0.447688
$902$	20.9134	0.696339
$903$	39.4300	1.31215
$904$	−6.17387	−0.205340
$905$	7.00332	0.232798
$906$	11.6925	0.388458
$907$	27.8979	0.926335	0.463167	−	0.886271i	$-0.346713\pi$
$907$	27.8979	0.926335	0.463167	+	0.886271i	$0.346713\pi$
$908$	−2.05819	−0.0683033
$909$	−2.14295	−0.0710771
$910$	17.1771	0.569415
$911$	−8.22550	−0.272523	−0.136261	−	0.990673i	$-0.543509\pi$
$911$	−8.22550	−0.272523	−0.136261	+	0.990673i	$0.543509\pi$
$912$	18.7729	0.621633
$913$	−1.34664	−0.0445674
$914$	22.1251	0.731832
$915$	7.34289	0.242748
$916$	−1.19360	−0.0394376
$917$	−93.7068	−3.09447
$918$	3.29476	0.108743
$919$	11.1437	0.367597	0.183798	−	0.982964i	$-0.441161\pi$
$919$	11.1437	0.367597	0.183798	+	0.982964i	$0.441161\pi$
$920$	−8.22563	−0.271191
$921$	18.9003	0.622786
$922$	0.379414	0.0124953
$923$	−8.86864	−0.291915
$924$	2.76340	0.0909092
$925$	4.87023	0.160132
$926$	4.73346	0.155551
$927$	−4.76190	−0.156401
$928$	3.24544	0.106537
$929$	−15.8318	−0.519423	−0.259712	−	0.965686i	$-0.583628\pi$
$929$	−15.8318	−0.519423	−0.259712	+	0.965686i	$0.583628\pi$
$930$	10.3020	0.337816
$931$	−48.0242	−1.57393
$932$	−0.178384	−0.00584317
$933$	−13.5793	−0.444565
$934$	−18.4166	−0.602610
$935$	11.3780	0.372099
$936$	7.60296	0.248511
$937$	−15.4853	−0.505881	−0.252941	−	0.967482i	$-0.581398\pi$
$937$	−15.4853	−0.505881	−0.252941	+	0.967482i	$0.581398\pi$
$938$	15.9240	0.519936
$939$	9.75239	0.318257
$940$	0.426916	0.0139245
$941$	−7.41948	−0.241868	−0.120934	−	0.992661i	$-0.538589\pi$
$941$	−7.41948	−0.241868	−0.120934	+	0.992661i	$0.538589\pi$
$942$	21.4220	0.697967
$943$	−8.56955	−0.279063
$944$	−63.6072	−2.07024
$945$	−4.22534	−0.137450
$946$	−68.6339	−2.23148
$947$	−32.3014	−1.04966	−0.524828	−	0.851208i	$-0.675870\pi$
$947$	−32.3014	−1.04966	−0.524828	+	0.851208i	$0.675870\pi$
$948$	−0.783712	−0.0254538
$949$	23.9503	0.777459
$950$	6.45737	0.209505
$951$	−4.54253	−0.147302
$952$	−26.0364	−0.843845
$953$	30.7027	0.994559	0.497279	−	0.867591i	$-0.334332\pi$
$953$	30.7027	0.994559	0.497279	+	0.867591i	$0.334332\pi$
$954$	8.68654	0.281237
$955$	0.421647	0.0136442
$956$	3.30316	0.106832
$957$	22.3153	0.721351
$958$	−26.2808	−0.849094
$959$	−52.4580	−1.69396
$960$	−7.41574	−0.239342
$961$	18.8324	0.607496
$962$	−19.7987	−0.638336
$963$	−20.3122	−0.654551
$964$	−0.830115	−0.0267362
$965$	−7.58263	−0.244093
$966$	−18.5839	−0.597927
$967$	31.5145	1.01344	0.506719	−	0.862111i	$-0.330858\pi$
$967$	31.5145	1.01344	0.506719	+	0.862111i	$0.330858\pi$
$968$	39.2997	1.26314
$969$	9.98957	0.320911
$970$	−12.9484	−0.415746
$971$	−44.9164	−1.44144	−0.720718	−	0.693228i	$-0.756188\pi$
$971$	−44.9164	−1.44144	−0.720718	+	0.693228i	$0.756188\pi$
$972$	0.129770	0.00416238
$973$	77.5347	2.48565
$974$	44.8843	1.43819
$975$	2.78562	0.0892111
$976$	31.1537	0.997205
$977$	−7.04880	−0.225511	−0.112756	−	0.993623i	$-0.535968\pi$
$977$	−7.04880	−0.225511	−0.112756	+	0.993623i	$0.535968\pi$
$978$	14.6943	0.469872
$979$	56.9790	1.82106
$980$	−1.40846	−0.0449918
$981$	14.2741	0.455736
$982$	26.7875	0.854822
$983$	43.9894	1.40304	0.701522	−	0.712647i	$-0.252504\pi$
$983$	43.9894	1.40304	0.701522	+	0.712647i	$0.252504\pi$
$984$	−7.76089	−0.247408
$985$	14.6330	0.466246
$986$	14.5888	0.464602
$987$	−13.9005	−0.442457
$988$	−1.59950	−0.0508870
$989$	28.1237	0.894283
$990$	7.35484	0.233752
$991$	−48.1603	−1.52986	−0.764931	−	0.644112i	$-0.777227\pi$
$991$	−48.1603	−1.52986	−0.764931	+	0.644112i	$0.777227\pi$
$992$	5.17409	0.164277
$993$	14.5240	0.460904
$994$	19.6320	0.622689
$995$	−22.0657	−0.699529
$996$	−0.0346753	−0.00109873
$997$	19.5953	0.620590	0.310295	−	0.950640i	$-0.399572\pi$
$997$	19.5953	0.620590	0.310295	+	0.950640i	$0.399572\pi$
$998$	−49.7815	−1.57581
$999$	4.87023	0.154087

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.h.1.12	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.h.1.12	✓	39	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.45937 q^{2} +1.00000 q^{3} +0.129770 q^{4} -1.00000 q^{5} -1.45937 q^{6} +4.22534 q^{7} +2.72936 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.45937 q^{2} +1.00000 q^{3} +0.129770 q^{4} -1.00000 q^{5} -1.45937 q^{6} +4.22534 q^{7} +2.72936 q^{8} +1.00000 q^{9} +1.45937 q^{10} +5.03973 q^{11} +0.129770 q^{12} +2.78562 q^{13} -6.16635 q^{14} -1.00000 q^{15} -4.24270 q^{16} -2.25766 q^{17} -1.45937 q^{18} -4.42475 q^{19} -0.129770 q^{20} +4.22534 q^{21} -7.35484 q^{22} +3.01376 q^{23} +2.72936 q^{24} +1.00000 q^{25} -4.06525 q^{26} +1.00000 q^{27} +0.548323 q^{28} +4.42787 q^{29} +1.45937 q^{30} +7.05921 q^{31} +0.732956 q^{32} +5.03973 q^{33} +3.29476 q^{34} -4.22534 q^{35} +0.129770 q^{36} +4.87023 q^{37} +6.45737 q^{38} +2.78562 q^{39} -2.72936 q^{40} -2.84348 q^{41} -6.16635 q^{42} +9.33179 q^{43} +0.654006 q^{44} -1.00000 q^{45} -4.39819 q^{46} -3.28978 q^{47} -4.24270 q^{48} +10.8535 q^{49} -1.45937 q^{50} -2.25766 q^{51} +0.361490 q^{52} -5.95224 q^{53} -1.45937 q^{54} -5.03973 q^{55} +11.5325 q^{56} -4.42475 q^{57} -6.46192 q^{58} +14.9921 q^{59} -0.129770 q^{60} -7.34289 q^{61} -10.3020 q^{62} +4.22534 q^{63} +7.41574 q^{64} -2.78562 q^{65} -7.35484 q^{66} -2.58240 q^{67} -0.292976 q^{68} +3.01376 q^{69} +6.16635 q^{70} -3.18373 q^{71} +2.72936 q^{72} +8.59784 q^{73} -7.10748 q^{74} +1.00000 q^{75} -0.574201 q^{76} +21.2946 q^{77} -4.06525 q^{78} -6.03923 q^{79} +4.24270 q^{80} +1.00000 q^{81} +4.14970 q^{82} -0.267206 q^{83} +0.548323 q^{84} +2.25766 q^{85} -13.6186 q^{86} +4.42787 q^{87} +13.7552 q^{88} +11.3060 q^{89} +1.45937 q^{90} +11.7702 q^{91} +0.391095 q^{92} +7.05921 q^{93} +4.80102 q^{94} +4.42475 q^{95} +0.732956 q^{96} -8.87254 q^{97} -15.8394 q^{98} +5.03973 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9} - q^{11} + 48 q^{12} + 30 q^{13} + 8 q^{14} - 39 q^{15} + 58 q^{16} + 32 q^{17} + 27 q^{19} - 48 q^{20} + 22 q^{21} + 23 q^{22} - 8 q^{23} + 3 q^{24} + 39 q^{25} - 4 q^{26} + 39 q^{27} + 60 q^{28} - 9 q^{29} + 19 q^{31} + q^{32} - q^{33} + 26 q^{34} - 22 q^{35} + 48 q^{36} + 44 q^{37} + 14 q^{38} + 30 q^{39} - 3 q^{40} + 31 q^{41} + 8 q^{42} + 75 q^{43} + q^{44} - 39 q^{45} + 19 q^{46} - 16 q^{47} + 58 q^{48} + 91 q^{49} + 32 q^{51} + 94 q^{52} + 17 q^{53} + q^{55} + 27 q^{56} + 27 q^{57} + 26 q^{58} - q^{59} - 48 q^{60} + 55 q^{61} + 11 q^{62} + 22 q^{63} + 77 q^{64} - 30 q^{65} + 23 q^{66} + 84 q^{67} + 36 q^{68} - 8 q^{69} - 8 q^{70} - 2 q^{71} + 3 q^{72} + 79 q^{73} + 20 q^{74} + 39 q^{75} + 58 q^{76} + 32 q^{77} - 4 q^{78} + 29 q^{79} - 58 q^{80} + 39 q^{81} + 53 q^{82} + 9 q^{83} + 60 q^{84} - 32 q^{85} - 17 q^{86} - 9 q^{87} + 57 q^{88} + 37 q^{89} + 71 q^{91} + 7 q^{92} + 19 q^{93} + 32 q^{94} - 27 q^{95} + q^{96} + 91 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9 - q^11 + 48 * q^12 + 30 * q^13 + 8 * q^14 - 39 * q^15 + 58 * q^16 + 32 * q^17 + 27 * q^19 - 48 * q^20 + 22 * q^21 + 23 * q^22 - 8 * q^23 + 3 * q^24 + 39 * q^25 - 4 * q^26 + 39 * q^27 + 60 * q^28 - 9 * q^29 + 19 * q^31 + q^32 - q^33 + 26 * q^34 - 22 * q^35 + 48 * q^36 + 44 * q^37 + 14 * q^38 + 30 * q^39 - 3 * q^40 + 31 * q^41 + 8 * q^42 + 75 * q^43 + q^44 - 39 * q^45 + 19 * q^46 - 16 * q^47 + 58 * q^48 + 91 * q^49 + 32 * q^51 + 94 * q^52 + 17 * q^53 + q^55 + 27 * q^56 + 27 * q^57 + 26 * q^58 - q^59 - 48 * q^60 + 55 * q^61 + 11 * q^62 + 22 * q^63 + 77 * q^64 - 30 * q^65 + 23 * q^66 + 84 * q^67 + 36 * q^68 - 8 * q^69 - 8 * q^70 - 2 * q^71 + 3 * q^72 + 79 * q^73 + 20 * q^74 + 39 * q^75 + 58 * q^76 + 32 * q^77 - 4 * q^78 + 29 * q^79 - 58 * q^80 + 39 * q^81 + 53 * q^82 + 9 * q^83 + 60 * q^84 - 32 * q^85 - 17 * q^86 - 9 * q^87 + 57 * q^88 + 37 * q^89 + 71 * q^91 + 7 * q^92 + 19 * q^93 + 32 * q^94 - 27 * q^95 + q^96 + 91 * q^97 - 9 * q^98 - q^99

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