LMFDB - Embedded newform 1805.2.a.u.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 12x^{7} - 4x^{6} + 48x^{5} + 27x^{4} - 72x^{3} - 51x^{2} + 27x + 19 $ x^9 - 12x^7 - 4x^6 + 48x^5 + 27x^4 - 72x^3 - 51x^2 + 27*x + 19
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.19408$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.19408 q^{2} -2.27318 q^{3} -0.574177 q^{4} -1.00000 q^{5} -2.71435 q^{6} -2.19649 q^{7} -3.07377 q^{8} +2.16734 q^{9} +O(q^{10})$	\(q+1.19408 q^{2} -2.27318 q^{3} -0.574177 q^{4} -1.00000 q^{5} -2.71435 q^{6} -2.19649 q^{7} -3.07377 q^{8} +2.16734 q^{9} -1.19408 q^{10} -2.82648 q^{11} +1.30521 q^{12} -4.08121 q^{13} -2.62278 q^{14} +2.27318 q^{15} -2.52197 q^{16} +0.382631 q^{17} +2.58797 q^{18} +0.574177 q^{20} +4.99302 q^{21} -3.37504 q^{22} -2.97594 q^{23} +6.98723 q^{24} +1.00000 q^{25} -4.87328 q^{26} +1.89278 q^{27} +1.26118 q^{28} -8.57501 q^{29} +2.71435 q^{30} +4.69244 q^{31} +3.13611 q^{32} +6.42509 q^{33} +0.456891 q^{34} +2.19649 q^{35} -1.24444 q^{36} +10.7694 q^{37} +9.27731 q^{39} +3.07377 q^{40} -3.13533 q^{41} +5.96205 q^{42} +2.00902 q^{43} +1.62290 q^{44} -2.16734 q^{45} -3.55350 q^{46} -10.8977 q^{47} +5.73288 q^{48} -2.17543 q^{49} +1.19408 q^{50} -0.869788 q^{51} +2.34334 q^{52} -7.47576 q^{53} +2.26013 q^{54} +2.82648 q^{55} +6.75150 q^{56} -10.2392 q^{58} +12.9788 q^{59} -1.30521 q^{60} +5.97594 q^{61} +5.60313 q^{62} -4.76054 q^{63} +8.78870 q^{64} +4.08121 q^{65} +7.67206 q^{66} -1.04943 q^{67} -0.219698 q^{68} +6.76484 q^{69} +2.62278 q^{70} +7.82756 q^{71} -6.66191 q^{72} -14.0896 q^{73} +12.8595 q^{74} -2.27318 q^{75} +6.20833 q^{77} +11.0778 q^{78} +13.4384 q^{79} +2.52197 q^{80} -10.8047 q^{81} -3.74383 q^{82} -5.55613 q^{83} -2.86688 q^{84} -0.382631 q^{85} +2.39893 q^{86} +19.4925 q^{87} +8.68794 q^{88} +6.56407 q^{89} -2.58797 q^{90} +8.96433 q^{91} +1.70872 q^{92} -10.6667 q^{93} -13.0127 q^{94} -7.12895 q^{96} -14.4463 q^{97} -2.59763 q^{98} -6.12594 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} - 12 q^{8} + 6 q^{9}+O(q^{10}) $ 9 * q + 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 - 12 * q^8 + 6 * q^9	$ 9 q + 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} - 12 q^{8} + 6 q^{9} + 6 q^{12} - 3 q^{13} + 12 q^{14} - 3 q^{15} - 12 q^{16} - 9 q^{17} + 6 q^{18} - 6 q^{20} + 12 q^{21} + 12 q^{22} + 15 q^{24} + 9 q^{25} + 21 q^{26} + 6 q^{27} - 15 q^{28} + 15 q^{29} + 12 q^{30} + 30 q^{31} - 9 q^{32} + 9 q^{33} - 6 q^{36} + 30 q^{37} + 6 q^{39} + 12 q^{40} + 18 q^{41} + 36 q^{42} - 6 q^{43} - 24 q^{44} - 6 q^{45} + 21 q^{46} + 21 q^{47} + 15 q^{48} + 3 q^{49} + 18 q^{51} - 3 q^{52} - 9 q^{53} - 9 q^{54} + 36 q^{56} + 18 q^{58} + 27 q^{59} - 6 q^{60} + 12 q^{61} - 6 q^{62} - 15 q^{63} + 24 q^{64} + 3 q^{65} + 3 q^{66} + 36 q^{67} + 3 q^{68} + 27 q^{69} - 12 q^{70} - 6 q^{71} + 12 q^{72} - 9 q^{73} - 9 q^{74} + 3 q^{75} + 12 q^{77} + 54 q^{78} + 45 q^{79} + 12 q^{80} - 15 q^{81} - 48 q^{82} - 12 q^{84} + 9 q^{85} - 9 q^{86} + 45 q^{87} + 39 q^{88} - 9 q^{89} - 6 q^{90} + 51 q^{91} - 54 q^{92} + 9 q^{93} + 33 q^{94} - 9 q^{96} + 45 q^{97} + 33 q^{98} + 12 q^{99}+O(q^{100}) $ 9 * q + 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 - 12 * q^8 + 6 * q^9 + 6 * q^12 - 3 * q^13 + 12 * q^14 - 3 * q^15 - 12 * q^16 - 9 * q^17 + 6 * q^18 - 6 * q^20 + 12 * q^21 + 12 * q^22 + 15 * q^24 + 9 * q^25 + 21 * q^26 + 6 * q^27 - 15 * q^28 + 15 * q^29 + 12 * q^30 + 30 * q^31 - 9 * q^32 + 9 * q^33 - 6 * q^36 + 30 * q^37 + 6 * q^39 + 12 * q^40 + 18 * q^41 + 36 * q^42 - 6 * q^43 - 24 * q^44 - 6 * q^45 + 21 * q^46 + 21 * q^47 + 15 * q^48 + 3 * q^49 + 18 * q^51 - 3 * q^52 - 9 * q^53 - 9 * q^54 + 36 * q^56 + 18 * q^58 + 27 * q^59 - 6 * q^60 + 12 * q^61 - 6 * q^62 - 15 * q^63 + 24 * q^64 + 3 * q^65 + 3 * q^66 + 36 * q^67 + 3 * q^68 + 27 * q^69 - 12 * q^70 - 6 * q^71 + 12 * q^72 - 9 * q^73 - 9 * q^74 + 3 * q^75 + 12 * q^77 + 54 * q^78 + 45 * q^79 + 12 * q^80 - 15 * q^81 - 48 * q^82 - 12 * q^84 + 9 * q^85 - 9 * q^86 + 45 * q^87 + 39 * q^88 - 9 * q^89 - 6 * q^90 + 51 * q^91 - 54 * q^92 + 9 * q^93 + 33 * q^94 - 9 * q^96 + 45 * q^97 + 33 * q^98 + 12 * 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 $

$2$	1.19408	0.844341	0.422170	−	0.906517i	$-0.361268\pi$
$2$	1.19408	0.844341	0.422170	+	0.906517i	$0.361268\pi$
$3$	−2.27318	−1.31242	−0.656210	−	0.754578i	$-0.727842\pi$
$3$	−2.27318	−1.31242	−0.656210	+	0.754578i	$0.727842\pi$
$4$	−0.574177	−0.287089
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.71435	−1.10813
$7$	−2.19649	−0.830195	−0.415098	−	0.909777i	$-0.636253\pi$
$7$	−2.19649	−0.830195	−0.415098	+	0.909777i	$0.636253\pi$
$8$	−3.07377	−1.08674
$9$	2.16734	0.722447
$10$	−1.19408	−0.377601
$11$	−2.82648	−0.852215	−0.426108	−	0.904672i	$-0.640116\pi$
$11$	−2.82648	−0.852215	−0.426108	+	0.904672i	$0.640116\pi$
$12$	1.30521	0.376781
$13$	−4.08121	−1.13192	−0.565962	−	0.824432i	$-0.691495\pi$
$13$	−4.08121	−1.13192	−0.565962	+	0.824432i	$0.691495\pi$
$14$	−2.62278	−0.700968
$15$	2.27318	0.586932
$16$	−2.52197	−0.630491
$17$	0.382631	0.0928015	0.0464008	−	0.998923i	$-0.485225\pi$
$17$	0.382631	0.0928015	0.0464008	+	0.998923i	$0.485225\pi$
$18$	2.58797	0.609992
$19$	0	0
$19$	0	0
$20$	0.574177	0.128390
$21$	4.99302	1.08957
$22$	−3.37504	−0.719560
$23$	−2.97594	−0.620526	−0.310263	−	0.950651i	$-0.600417\pi$
$23$	−2.97594	−0.620526	−0.310263	+	0.950651i	$0.600417\pi$
$24$	6.98723	1.42626
$25$	1.00000	0.200000
$26$	−4.87328	−0.955729
$27$	1.89278	0.364266
$28$	1.26118	0.238340
$29$	−8.57501	−1.59234	−0.796169	−	0.605074i	$-0.793144\pi$
$29$	−8.57501	−1.59234	−0.796169	+	0.605074i	$0.793144\pi$
$30$	2.71435	0.495571
$31$	4.69244	0.842786	0.421393	−	0.906878i	$-0.361541\pi$
$31$	4.69244	0.842786	0.421393	+	0.906878i	$0.361541\pi$
$32$	3.13611	0.554392
$33$	6.42509	1.11846
$34$	0.456891	0.0783561
$35$	2.19649	0.371275
$36$	−1.24444	−0.207406
$37$	10.7694	1.77048	0.885242	−	0.465131i	$-0.153993\pi$
$37$	10.7694	1.77048	0.885242	+	0.465131i	$0.153993\pi$
$38$	0	0
$39$	9.27731	1.48556
$40$	3.07377	0.486006
$41$	−3.13533	−0.489657	−0.244828	−	0.969566i	$-0.578732\pi$
$41$	−3.13533	−0.489657	−0.244828	+	0.969566i	$0.578732\pi$
$42$	5.96205	0.919964
$43$	2.00902	0.306373	0.153186	−	0.988197i	$-0.451047\pi$
$43$	2.00902	0.306373	0.153186	+	0.988197i	$0.451047\pi$
$44$	1.62290	0.244661
$45$	−2.16734	−0.323088
$46$	−3.55350	−0.523936
$47$	−10.8977	−1.58959	−0.794794	−	0.606879i	$-0.792421\pi$
$47$	−10.8977	−1.58959	−0.794794	+	0.606879i	$0.792421\pi$
$48$	5.73288	0.827470
$49$	−2.17543	−0.310776
$50$	1.19408	0.168868
$51$	−0.869788	−0.121795
$52$	2.34334	0.324962
$53$	−7.47576	−1.02687	−0.513437	−	0.858127i	$-0.671628\pi$
$53$	−7.47576	−1.02687	−0.513437	+	0.858127i	$0.671628\pi$
$54$	2.26013	0.307565
$55$	2.82648	0.381122
$56$	6.75150	0.902208
$57$	0	0
$58$	−10.2392	−1.34448
$59$	12.9788	1.68969	0.844846	−	0.535009i	$-0.179692\pi$
$59$	12.9788	1.68969	0.844846	+	0.535009i	$0.179692\pi$
$60$	−1.30521	−0.168502
$61$	5.97594	0.765141	0.382570	−	0.923926i	$-0.375039\pi$
$61$	5.97594	0.765141	0.382570	+	0.923926i	$0.375039\pi$
$62$	5.60313	0.711599
$63$	−4.76054	−0.599772
$64$	8.78870	1.09859
$65$	4.08121	0.506211
$66$	7.67206	0.944365
$67$	−1.04943	−0.128208	−0.0641039	−	0.997943i	$-0.520419\pi$
$67$	−1.04943	−0.128208	−0.0641039	+	0.997943i	$0.520419\pi$
$68$	−0.219698	−0.0266423
$69$	6.76484	0.814391
$70$	2.62278	0.313482
$71$	7.82756	0.928960	0.464480	−	0.885583i	$-0.346241\pi$
$71$	7.82756	0.928960	0.464480	+	0.885583i	$0.346241\pi$
$72$	−6.66191	−0.785113
$73$	−14.0896	−1.64906	−0.824531	−	0.565817i	$-0.808561\pi$
$73$	−14.0896	−1.64906	−0.824531	+	0.565817i	$0.808561\pi$
$74$	12.8595	1.49489
$75$	−2.27318	−0.262484
$76$	0	0
$77$	6.20833	0.707505
$78$	11.0778	1.25432
$79$	13.4384	1.51194	0.755969	−	0.654607i	$-0.227166\pi$
$79$	13.4384	1.51194	0.755969	+	0.654607i	$0.227166\pi$
$80$	2.52197	0.281964
$81$	−10.8047	−1.20052
$82$	−3.74383	−0.413437
$83$	−5.55613	−0.609865	−0.304932	−	0.952374i	$-0.598634\pi$
$83$	−5.55613	−0.609865	−0.304932	+	0.952374i	$0.598634\pi$
$84$	−2.86688	−0.312802
$85$	−0.382631	−0.0415021
$86$	2.39893	0.258683
$87$	19.4925	2.08982
$88$	8.68794	0.926138
$89$	6.56407	0.695790	0.347895	−	0.937533i	$-0.386897\pi$
$89$	6.56407	0.695790	0.347895	+	0.937533i	$0.386897\pi$
$90$	−2.58797	−0.272797
$91$	8.96433	0.939717
$92$	1.70872	0.178146
$93$	−10.6667	−1.10609
$94$	−13.0127	−1.34215
$95$	0	0
$96$	−7.12895	−0.727595
$97$	−14.4463	−1.46679	−0.733397	−	0.679800i	$-0.762067\pi$
$97$	−14.4463	−1.46679	−0.733397	+	0.679800i	$0.762067\pi$
$98$	−2.59763	−0.262401
$99$	−6.12594	−0.615681
$100$	−0.574177	−0.0574177
$101$	4.25040	0.422930	0.211465	−	0.977386i	$-0.432177\pi$
$101$	4.25040	0.422930	0.211465	+	0.977386i	$0.432177\pi$
$102$	−1.03859	−0.102836
$103$	14.6706	1.44553	0.722767	−	0.691092i	$-0.242870\pi$
$103$	14.6706	1.44553	0.722767	+	0.691092i	$0.242870\pi$
$104$	12.5447	1.23011
$105$	−4.99302	−0.487268
$106$	−8.92664	−0.867032
$107$	6.18046	0.597488	0.298744	−	0.954333i	$-0.403432\pi$
$107$	6.18046	0.597488	0.298744	+	0.954333i	$0.403432\pi$
$108$	−1.08679	−0.104577
$109$	−0.753864	−0.0722071	−0.0361035	−	0.999348i	$-0.511495\pi$
$109$	−0.753864	−0.0722071	−0.0361035	+	0.999348i	$0.511495\pi$
$110$	3.37504	0.321797
$111$	−24.4808	−2.32362
$112$	5.53947	0.523431
$113$	−0.870003	−0.0818430	−0.0409215	−	0.999162i	$-0.513029\pi$
$113$	−0.870003	−0.0818430	−0.0409215	+	0.999162i	$0.513029\pi$
$114$	0	0
$115$	2.97594	0.277508
$116$	4.92357	0.457142
$117$	−8.84537	−0.817755
$118$	15.4977	1.42668
$119$	−0.840444	−0.0770434
$120$	−6.98723	−0.637844
$121$	−3.01102	−0.273729
$122$	7.13574	0.646040
$123$	7.12717	0.642635
$124$	−2.69429	−0.241954
$125$	−1.00000	−0.0894427
$126$	−5.68446	−0.506412
$127$	3.44442	0.305642	0.152821	−	0.988254i	$-0.451164\pi$
$127$	3.44442	0.305642	0.152821	+	0.988254i	$0.451164\pi$
$128$	4.22216	0.373190
$129$	−4.56686	−0.402090
$130$	4.87328	0.427415
$131$	10.3008	0.899981	0.449991	−	0.893033i	$-0.351427\pi$
$131$	10.3008	0.899981	0.449991	+	0.893033i	$0.351427\pi$
$132$	−3.68914	−0.321099
$133$	0	0
$134$	−1.25310	−0.108251
$135$	−1.89278	−0.162905
$136$	−1.17612	−0.100851
$137$	1.46792	0.125413	0.0627065	−	0.998032i	$-0.480027\pi$
$137$	1.46792	0.125413	0.0627065	+	0.998032i	$0.480027\pi$
$138$	8.07775	0.687624
$139$	−7.32762	−0.621520	−0.310760	−	0.950488i	$-0.600584\pi$
$139$	−7.32762	−0.621520	−0.310760	+	0.950488i	$0.600584\pi$
$140$	−1.26118	−0.106589
$141$	24.7723	2.08621
$142$	9.34672	0.784359
$143$	11.5354	0.964642
$144$	−5.46596	−0.455497
$145$	8.57501	0.712115
$146$	−16.8241	−1.39237
$147$	4.94514	0.407868
$148$	−6.18356	−0.508286
$149$	9.99186	0.818565	0.409283	−	0.912408i	$-0.365779\pi$
$149$	9.99186	0.818565	0.409283	+	0.912408i	$0.365779\pi$
$150$	−2.71435	−0.221626
$151$	−15.0689	−1.22629	−0.613144	−	0.789971i	$-0.710095\pi$
$151$	−15.0689	−1.22629	−0.613144	+	0.789971i	$0.710095\pi$
$152$	0	0
$153$	0.829291	0.0670442
$154$	7.41324	0.597376
$155$	−4.69244	−0.376905
$156$	−5.32682	−0.426487
$157$	10.3445	0.825585	0.412792	−	0.910825i	$-0.364554\pi$
$157$	10.3445	0.825585	0.412792	+	0.910825i	$0.364554\pi$
$158$	16.0465	1.27659
$159$	16.9937	1.34769
$160$	−3.13611	−0.247932
$161$	6.53662	0.515158
$162$	−12.9016	−1.01365
$163$	−6.90009	−0.540457	−0.270228	−	0.962796i	$-0.587099\pi$
$163$	−6.90009	−0.540457	−0.270228	+	0.962796i	$0.587099\pi$
$164$	1.80024	0.140575
$165$	−6.42509	−0.500193
$166$	−6.63446	−0.514934
$167$	−11.8620	−0.917911	−0.458955	−	0.888459i	$-0.651776\pi$
$167$	−11.8620	−0.917911	−0.458955	+	0.888459i	$0.651776\pi$
$168$	−15.3474	−1.18408
$169$	3.65625	0.281250
$170$	−0.456891	−0.0350419
$171$	0	0
$172$	−1.15353	−0.0879561
$173$	−25.4066	−1.93162	−0.965812	−	0.259242i	$-0.916527\pi$
$173$	−25.4066	−1.93162	−0.965812	+	0.259242i	$0.916527\pi$
$174$	23.2756	1.76452
$175$	−2.19649	−0.166039
$176$	7.12828	0.537314
$177$	−29.5031	−2.21759
$178$	7.83802	0.587484
$179$	0.388799	0.0290602	0.0145301	−	0.999894i	$-0.495375\pi$
$179$	0.388799	0.0290602	0.0145301	+	0.999894i	$0.495375\pi$
$180$	1.24444	0.0927550
$181$	−4.78386	−0.355582	−0.177791	−	0.984068i	$-0.556895\pi$
$181$	−4.78386	−0.355582	−0.177791	+	0.984068i	$0.556895\pi$
$182$	10.7041	0.793442
$183$	−13.5844	−1.00419
$184$	9.14735	0.674352
$185$	−10.7694	−0.791784
$186$	−12.7369	−0.933917
$187$	−1.08150	−0.0790869
$188$	6.25720	0.456353
$189$	−4.15748	−0.302412
$190$	0	0
$191$	−23.8516	−1.72584	−0.862921	−	0.505338i	$-0.831368\pi$
$191$	−23.8516	−1.72584	−0.862921	+	0.505338i	$0.831368\pi$
$192$	−19.9783	−1.44181
$193$	11.2260	0.808064	0.404032	−	0.914745i	$-0.367608\pi$
$193$	11.2260	0.808064	0.404032	+	0.914745i	$0.367608\pi$
$194$	−17.2500	−1.23847
$195$	−9.27731	−0.664362
$196$	1.24908	0.0892202
$197$	−16.8728	−1.20214	−0.601068	−	0.799198i	$-0.705258\pi$
$197$	−16.8728	−1.20214	−0.601068	+	0.799198i	$0.705258\pi$
$198$	−7.31486	−0.519844
$199$	−15.7225	−1.11454	−0.557268	−	0.830333i	$-0.688150\pi$
$199$	−15.7225	−1.11454	−0.557268	+	0.830333i	$0.688150\pi$
$200$	−3.07377	−0.217348
$201$	2.38553	0.168262
$202$	5.07531	0.357097
$203$	18.8349	1.32195
$204$	0.499412	0.0349659
$205$	3.13533	0.218981
$206$	17.5178	1.22052
$207$	−6.44988	−0.448297
$208$	10.2927	0.713668
$209$	0	0
$210$	−5.96205	−0.411421
$211$	9.28875	0.639464	0.319732	−	0.947508i	$-0.396407\pi$
$211$	9.28875	0.639464	0.319732	+	0.947508i	$0.396407\pi$
$212$	4.29241	0.294804
$213$	−17.7934	−1.21919
$214$	7.37995	0.504483
$215$	−2.00902	−0.137014
$216$	−5.81797	−0.395863
$217$	−10.3069	−0.699677
$218$	−0.900172	−0.0609674
$219$	32.0282	2.16426
$220$	−1.62290	−0.109416
$221$	−1.56159	−0.105044
$222$	−29.2320	−1.96193
$223$	2.79095	0.186896	0.0934478	−	0.995624i	$-0.470211\pi$
$223$	2.79095	0.186896	0.0934478	+	0.995624i	$0.470211\pi$
$224$	−6.88844	−0.460254
$225$	2.16734	0.144489
$226$	−1.03885	−0.0691034
$227$	0.844086	0.0560240	0.0280120	−	0.999608i	$-0.491082\pi$
$227$	0.844086	0.0560240	0.0280120	+	0.999608i	$0.491082\pi$
$228$	0	0
$229$	21.9559	1.45089	0.725444	−	0.688282i	$-0.241635\pi$
$229$	21.9559	1.45089	0.725444	+	0.688282i	$0.241635\pi$
$230$	3.55350	0.234311
$231$	−14.1127	−0.928544
$232$	26.3576	1.73046
$233$	−4.41544	−0.289265	−0.144633	−	0.989485i	$-0.546200\pi$
$233$	−4.41544	−0.289265	−0.144633	+	0.989485i	$0.546200\pi$
$234$	−10.5621	−0.690464
$235$	10.8977	0.710886
$236$	−7.45212	−0.485092
$237$	−30.5479	−1.98430
$238$	−1.00356	−0.0650509
$239$	19.8272	1.28251	0.641256	−	0.767327i	$-0.278414\pi$
$239$	19.8272	1.28251	0.641256	+	0.767327i	$0.278414\pi$
$240$	−5.73288	−0.370056
$241$	20.8843	1.34527	0.672637	−	0.739973i	$-0.265162\pi$
$241$	20.8843	1.34527	0.672637	+	0.739973i	$0.265162\pi$
$242$	−3.59539	−0.231120
$243$	18.8826	1.21132
$244$	−3.43125	−0.219663
$245$	2.17543	0.138983
$246$	8.51040	0.542603
$247$	0	0
$248$	−14.4235	−0.915891
$249$	12.6301	0.800399
$250$	−1.19408	−0.0755201
$251$	5.55450	0.350597	0.175299	−	0.984515i	$-0.443911\pi$
$251$	5.55450	0.350597	0.175299	+	0.984515i	$0.443911\pi$
$252$	2.73340	0.172188
$253$	8.41143	0.528822
$254$	4.11290	0.258066
$255$	0.869788	0.0544682
$256$	−12.5358	−0.783488
$257$	−20.1168	−1.25485	−0.627427	−	0.778676i	$-0.715892\pi$
$257$	−20.1168	−1.25485	−0.627427	+	0.778676i	$0.715892\pi$
$258$	−5.45319	−0.339501
$259$	−23.6550	−1.46985
$260$	−2.34334	−0.145328
$261$	−18.5850	−1.15038
$262$	12.2999	0.759891
$263$	11.7083	0.721963	0.360982	−	0.932573i	$-0.382442\pi$
$263$	11.7083	0.721963	0.360982	+	0.932573i	$0.382442\pi$
$264$	−19.7492	−1.21548
$265$	7.47576	0.459232
$266$	0	0
$267$	−14.9213	−0.913169
$268$	0.602557	0.0368070
$269$	12.8856	0.785648	0.392824	−	0.919614i	$-0.371498\pi$
$269$	12.8856	0.785648	0.392824	+	0.919614i	$0.371498\pi$
$270$	−2.26013	−0.137547
$271$	−15.4165	−0.936485	−0.468243	−	0.883600i	$-0.655113\pi$
$271$	−15.4165	−0.936485	−0.468243	+	0.883600i	$0.655113\pi$
$272$	−0.964981	−0.0585106
$273$	−20.3775	−1.23330
$274$	1.75281	0.105891
$275$	−2.82648	−0.170443
$276$	−3.88422	−0.233803
$277$	5.29710	0.318272	0.159136	−	0.987257i	$-0.449129\pi$
$277$	5.29710	0.318272	0.159136	+	0.987257i	$0.449129\pi$
$278$	−8.74975	−0.524775
$279$	10.1701	0.608869
$280$	−6.75150	−0.403480
$281$	5.38329	0.321140	0.160570	−	0.987024i	$-0.448667\pi$
$281$	5.38329	0.321140	0.160570	+	0.987024i	$0.448667\pi$
$282$	29.5801	1.76147
$283$	17.6766	1.05077	0.525383	−	0.850866i	$-0.323922\pi$
$283$	17.6766	1.05077	0.525383	+	0.850866i	$0.323922\pi$
$284$	−4.49441	−0.266694
$285$	0	0
$286$	13.7742	0.814487
$287$	6.88673	0.406511
$288$	6.79703	0.400519
$289$	−16.8536	−0.991388
$290$	10.2392	0.601268
$291$	32.8389	1.92505
$292$	8.08993	0.473427
$293$	−4.71047	−0.275189	−0.137594	−	0.990489i	$-0.543937\pi$
$293$	−4.71047	−0.275189	−0.137594	+	0.990489i	$0.543937\pi$
$294$	5.90488	0.344380
$295$	−12.9788	−0.755654
$296$	−33.1027	−1.92406
$297$	−5.34991	−0.310433
$298$	11.9311	0.691148
$299$	12.1454	0.702388
$300$	1.30521	0.0753562
$301$	−4.41279	−0.254349
$302$	−17.9934	−1.03540
$303$	−9.66191	−0.555062
$304$	0	0
$305$	−5.97594	−0.342181
$306$	0.990238	0.0566082
$307$	−11.8058	−0.673793	−0.336897	−	0.941542i	$-0.609377\pi$
$307$	−11.8058	−0.673793	−0.336897	+	0.941542i	$0.609377\pi$
$308$	−3.56468	−0.203117
$309$	−33.3488	−1.89715
$310$	−5.60313	−0.318237
$311$	−8.94011	−0.506947	−0.253474	−	0.967342i	$-0.581573\pi$
$311$	−8.94011	−0.506947	−0.253474	+	0.967342i	$0.581573\pi$
$312$	−28.5163	−1.61442
$313$	−13.4305	−0.759135	−0.379567	−	0.925164i	$-0.623927\pi$
$313$	−13.4305	−0.759135	−0.379567	+	0.925164i	$0.623927\pi$
$314$	12.3522	0.697075
$315$	4.76054	0.268226
$316$	−7.71603	−0.434060
$317$	11.0576	0.621057	0.310529	−	0.950564i	$-0.399494\pi$
$317$	11.0576	0.621057	0.310529	+	0.950564i	$0.399494\pi$
$318$	20.2918	1.13791
$319$	24.2371	1.35702
$320$	−8.78870	−0.491303
$321$	−14.0493	−0.784155
$322$	7.80524	0.434969
$323$	0	0
$324$	6.20379	0.344655
$325$	−4.08121	−0.226385
$326$	−8.23925	−0.456330
$327$	1.71367	0.0947660
$328$	9.63729	0.532130
$329$	23.9366	1.31967
$330$	−7.67206	−0.422333
$331$	2.84546	0.156401	0.0782003	−	0.996938i	$-0.475083\pi$
$331$	2.84546	0.156401	0.0782003	+	0.996938i	$0.475083\pi$
$332$	3.19021	0.175085
$333$	23.3410	1.27908
$334$	−14.1642	−0.775029
$335$	1.04943	0.0573363
$336$	−12.5922	−0.686961
$337$	−6.40586	−0.348949	−0.174475	−	0.984662i	$-0.555823\pi$
$337$	−6.40586	−0.348949	−0.174475	+	0.984662i	$0.555823\pi$
$338$	4.36585	0.237471
$339$	1.97767	0.107412
$340$	0.219698	0.0119148
$341$	−13.2631	−0.718235
$342$	0	0
$343$	20.1537	1.08820
$344$	−6.17526	−0.332948
$345$	−6.76484	−0.364207
$346$	−30.3374	−1.63095
$347$	15.8029	0.848344	0.424172	−	0.905582i	$-0.360565\pi$
$347$	15.8029	0.848344	0.424172	+	0.905582i	$0.360565\pi$
$348$	−11.1922	−0.599963
$349$	−27.5651	−1.47553	−0.737763	−	0.675060i	$-0.764118\pi$
$349$	−27.5651	−1.47553	−0.737763	+	0.675060i	$0.764118\pi$
$350$	−2.62278	−0.140194
$351$	−7.72484	−0.412321
$352$	−8.86416	−0.472461
$353$	−4.22884	−0.225078	−0.112539	−	0.993647i	$-0.535898\pi$
$353$	−4.22884	−0.225078	−0.112539	+	0.993647i	$0.535898\pi$
$354$	−35.2290	−1.87240
$355$	−7.82756	−0.415444
$356$	−3.76894	−0.199754
$357$	1.91048	0.101113
$358$	0.464257	0.0245367
$359$	5.73116	0.302479	0.151239	−	0.988497i	$-0.451674\pi$
$359$	5.73116	0.302479	0.151239	+	0.988497i	$0.451674\pi$
$360$	6.66191	0.351113
$361$	0	0
$362$	−5.71231	−0.300232
$363$	6.84458	0.359247
$364$	−5.14712	−0.269782
$365$	14.0896	0.737483
$366$	−16.2208	−0.847875
$367$	−0.945619	−0.0493609	−0.0246804	−	0.999695i	$-0.507857\pi$
$367$	−0.945619	−0.0493609	−0.0246804	+	0.999695i	$0.507857\pi$
$368$	7.50522	0.391237
$369$	−6.79533	−0.353751
$370$	−12.8595	−0.668536
$371$	16.4204	0.852506
$372$	6.12460	0.317546
$373$	−0.673299	−0.0348621	−0.0174310	−	0.999848i	$-0.505549\pi$
$373$	−0.673299	−0.0348621	−0.0174310	+	0.999848i	$0.505549\pi$
$374$	−1.29139	−0.0667763
$375$	2.27318	0.117386
$376$	33.4969	1.72747
$377$	34.9964	1.80240
$378$	−4.96435	−0.255339
$379$	34.7701	1.78602	0.893010	−	0.450037i	$-0.148589\pi$
$379$	34.7701	1.78602	0.893010	+	0.450037i	$0.148589\pi$
$380$	0	0
$381$	−7.82977	−0.401131
$382$	−28.4807	−1.45720
$383$	−27.2567	−1.39275	−0.696377	−	0.717677i	$-0.745206\pi$
$383$	−27.2567	−1.39275	−0.696377	+	0.717677i	$0.745206\pi$
$384$	−9.59773	−0.489782
$385$	−6.20833	−0.316406
$386$	13.4047	0.682281
$387$	4.35423	0.221338
$388$	8.29471	0.421100
$389$	36.5011	1.85068	0.925339	−	0.379141i	$-0.123780\pi$
$389$	36.5011	1.85068	0.925339	+	0.379141i	$0.123780\pi$
$390$	−11.0778	−0.560948
$391$	−1.13869	−0.0575858
$392$	6.68677	0.337733
$393$	−23.4155	−1.18115
$394$	−20.1474	−1.01501
$395$	−13.4384	−0.676159
$396$	3.51738	0.176755
$397$	−13.8357	−0.694394	−0.347197	−	0.937792i	$-0.612866\pi$
$397$	−13.8357	−0.694394	−0.347197	+	0.937792i	$0.612866\pi$
$398$	−18.7739	−0.941048
$399$	0	0
$400$	−2.52197	−0.126098
$401$	−24.2734	−1.21216	−0.606078	−	0.795405i	$-0.707258\pi$
$401$	−24.2734	−1.21216	−0.606078	+	0.795405i	$0.707258\pi$
$402$	2.84851	0.142071
$403$	−19.1508	−0.953969
$404$	−2.44048	−0.121419
$405$	10.8047	0.536888
$406$	22.4904	1.11618
$407$	−30.4396	−1.50883
$408$	2.67353	0.132359
$409$	33.9340	1.67793	0.838964	−	0.544187i	$-0.183162\pi$
$409$	33.9340	1.67793	0.838964	+	0.544187i	$0.183162\pi$
$410$	3.74383	0.184895
$411$	−3.33685	−0.164595
$412$	−8.42351	−0.414997
$413$	−28.5078	−1.40278
$414$	−7.70166	−0.378516
$415$	5.55613	0.272740
$416$	−12.7991	−0.627529
$417$	16.6570	0.815696
$418$	0	0
$419$	21.4325	1.04705	0.523523	−	0.852012i	$-0.324618\pi$
$419$	21.4325	1.04705	0.523523	+	0.852012i	$0.324618\pi$
$420$	2.86688	0.139889
$421$	7.34404	0.357927	0.178963	−	0.983856i	$-0.442726\pi$
$421$	7.34404	0.357927	0.178963	+	0.983856i	$0.442726\pi$
$422$	11.0915	0.539925
$423$	−23.6190	−1.14839
$424$	22.9788	1.11595
$425$	0.382631	0.0185603
$426$	−21.2468	−1.02941
$427$	−13.1261	−0.635216
$428$	−3.54868	−0.171532
$429$	−26.2221	−1.26602
$430$	−2.39893	−0.115687
$431$	−0.126372	−0.00608714	−0.00304357	−	0.999995i	$-0.500969\pi$
$431$	−0.126372	−0.00608714	−0.00304357	+	0.999995i	$0.500969\pi$
$432$	−4.77353	−0.229667
$433$	−5.81812	−0.279601	−0.139801	−	0.990180i	$-0.544646\pi$
$433$	−5.81812	−0.279601	−0.139801	+	0.990180i	$0.544646\pi$
$434$	−12.3072	−0.590766
$435$	−19.4925	−0.934595
$436$	0.432852	0.0207298
$437$	0	0
$438$	38.2441	1.82738
$439$	−18.5030	−0.883102	−0.441551	−	0.897236i	$-0.645572\pi$
$439$	−18.5030	−0.883102	−0.441551	+	0.897236i	$0.645572\pi$
$440$	−8.68794	−0.414181
$441$	−4.71490	−0.224519
$442$	−1.86467	−0.0886931
$443$	22.1253	1.05120	0.525601	−	0.850731i	$-0.323840\pi$
$443$	22.1253	1.05120	0.525601	+	0.850731i	$0.323840\pi$
$444$	14.0563	0.667085
$445$	−6.56407	−0.311167
$446$	3.33261	0.157804
$447$	−22.7133	−1.07430
$448$	−19.3043	−0.912042
$449$	20.5679	0.970661	0.485331	−	0.874331i	$-0.338699\pi$
$449$	20.5679	0.970661	0.485331	+	0.874331i	$0.338699\pi$
$450$	2.58797	0.121998
$451$	8.86195	0.417293
$452$	0.499536	0.0234962
$453$	34.2542	1.60941
$454$	1.00790	0.0473033
$455$	−8.96433	−0.420254
$456$	0	0
$457$	20.3583	0.952323	0.476161	−	0.879358i	$-0.342028\pi$
$457$	20.3583	0.952323	0.476161	+	0.879358i	$0.342028\pi$
$458$	26.2171	1.22504
$459$	0.724236	0.0338045
$460$	−1.70872	−0.0796694
$461$	−5.54265	−0.258147	−0.129073	−	0.991635i	$-0.541200\pi$
$461$	−5.54265	−0.258147	−0.129073	+	0.991635i	$0.541200\pi$
$462$	−16.8516	−0.784008
$463$	32.6500	1.51737	0.758686	−	0.651457i	$-0.225842\pi$
$463$	32.6500	1.51737	0.758686	+	0.651457i	$0.225842\pi$
$464$	21.6259	1.00396
$465$	10.6667	0.494658
$466$	−5.27238	−0.244238
$467$	28.6612	1.32628	0.663142	−	0.748494i	$-0.269223\pi$
$467$	28.6612	1.32628	0.663142	+	0.748494i	$0.269223\pi$
$468$	5.07881	0.234768
$469$	2.30505	0.106437
$470$	13.0127	0.600230
$471$	−23.5150	−1.08351
$472$	−39.8938	−1.83626
$473$	−5.67845	−0.261095
$474$	−36.4766	−1.67542
$475$	0	0
$476$	0.482564	0.0221183
$477$	−16.2025	−0.741862
$478$	23.6752	1.08288
$479$	10.2725	0.469364	0.234682	−	0.972072i	$-0.424595\pi$
$479$	10.2725	0.469364	0.234682	+	0.972072i	$0.424595\pi$
$480$	7.12895	0.325390
$481$	−43.9523	−2.00405
$482$	24.9374	1.13587
$483$	−14.8589	−0.676104
$484$	1.72886	0.0785845
$485$	14.4463	0.655971
$486$	22.5473	1.02276
$487$	−11.1245	−0.504097	−0.252049	−	0.967715i	$-0.581104\pi$
$487$	−11.1245	−0.504097	−0.252049	+	0.967715i	$0.581104\pi$
$488$	−18.3687	−0.831510
$489$	15.6851	0.709307
$490$	2.59763	0.117349
$491$	13.8847	0.626608	0.313304	−	0.949653i	$-0.398564\pi$
$491$	13.8847	0.626608	0.313304	+	0.949653i	$0.398564\pi$
$492$	−4.09226	−0.184493
$493$	−3.28106	−0.147771
$494$	0	0
$495$	6.12594	0.275341
$496$	−11.8342	−0.531369
$497$	−17.1932	−0.771219
$498$	15.0813	0.675809
$499$	12.7879	0.572464	0.286232	−	0.958160i	$-0.407597\pi$
$499$	12.7879	0.572464	0.286232	+	0.958160i	$0.407597\pi$
$500$	0.574177	0.0256780
$501$	26.9645	1.20468
$502$	6.63251	0.296023
$503$	10.4645	0.466587	0.233294	−	0.972406i	$-0.425050\pi$
$503$	10.4645	0.466587	0.233294	+	0.972406i	$0.425050\pi$
$504$	14.6328	0.651797
$505$	−4.25040	−0.189140
$506$	10.0439	0.446506
$507$	−8.31132	−0.369118
$508$	−1.97771	−0.0877465
$509$	−27.9357	−1.23823	−0.619115	−	0.785300i	$-0.712509\pi$
$509$	−27.9357	−1.23823	−0.619115	+	0.785300i	$0.712509\pi$
$510$	1.03859	0.0459897
$511$	30.9477	1.36904
$512$	−23.4130	−1.03472
$513$	0	0
$514$	−24.0211	−1.05952
$515$	−14.6706	−0.646463
$516$	2.62219	0.115435
$517$	30.8020	1.35467
$518$	−28.2459	−1.24105
$519$	57.7536	2.53510
$520$	−12.5447	−0.550121
$521$	8.06277	0.353236	0.176618	−	0.984279i	$-0.443484\pi$
$521$	8.06277	0.353236	0.176618	+	0.984279i	$0.443484\pi$
$522$	−22.1919	−0.971313
$523$	11.5417	0.504685	0.252342	−	0.967638i	$-0.418799\pi$
$523$	11.5417	0.504685	0.252342	+	0.967638i	$0.418799\pi$
$524$	−5.91446	−0.258374
$525$	4.99302	0.217913
$526$	13.9806	0.609583
$527$	1.79547	0.0782119
$528$	−16.2039	−0.705182
$529$	−14.1438	−0.614947
$530$	8.92664	0.387748
$531$	28.1294	1.22071
$532$	0	0
$533$	12.7959	0.554254
$534$	−17.8172	−0.771026
$535$	−6.18046	−0.267205
$536$	3.22569	0.139329
$537$	−0.883811	−0.0381392
$538$	15.3864	0.663355
$539$	6.14881	0.264848
$540$	1.08679	0.0467681
$541$	34.2473	1.47241	0.736203	−	0.676761i	$-0.236617\pi$
$541$	34.2473	1.47241	0.736203	+	0.676761i	$0.236617\pi$
$542$	−18.4085	−0.790713
$543$	10.8746	0.466673
$544$	1.19997	0.0514484
$545$	0.753864	0.0322920
$546$	−24.3324	−1.04133
$547$	27.6945	1.18413	0.592066	−	0.805889i	$-0.298312\pi$
$547$	27.6945	1.18413	0.592066	+	0.805889i	$0.298312\pi$
$548$	−0.842848	−0.0360047
$549$	12.9519	0.552774
$550$	−3.37504	−0.143912
$551$	0	0
$552$	−20.7936	−0.885033
$553$	−29.5173	−1.25520
$554$	6.32515	0.268730
$555$	24.4808	1.03915
$556$	4.20735	0.178431
$557$	13.6357	0.577762	0.288881	−	0.957365i	$-0.406717\pi$
$557$	13.6357	0.577762	0.288881	+	0.957365i	$0.406717\pi$
$558$	12.1439	0.514092
$559$	−8.19923	−0.346790
$560$	−5.53947	−0.234085
$561$	2.45844	0.103795
$562$	6.42807	0.271152
$563$	−39.0185	−1.64443	−0.822217	−	0.569174i	$-0.807263\pi$
$563$	−39.0185	−1.64443	−0.822217	+	0.569174i	$0.807263\pi$
$564$	−14.2237	−0.598927
$565$	0.870003	0.0366013
$566$	21.1073	0.887204
$567$	23.7323	0.996664
$568$	−24.0601	−1.00954
$569$	−8.86810	−0.371770	−0.185885	−	0.982572i	$-0.559515\pi$
$569$	−8.86810	−0.371770	−0.185885	+	0.982572i	$0.559515\pi$
$570$	0	0
$571$	35.4054	1.48167	0.740834	−	0.671688i	$-0.234431\pi$
$571$	35.4054	1.48167	0.740834	+	0.671688i	$0.234431\pi$
$572$	−6.62339	−0.276938
$573$	54.2190	2.26503
$574$	8.22329	0.343234
$575$	−2.97594	−0.124105
$576$	19.0481	0.793671
$577$	−26.0082	−1.08274	−0.541368	−	0.840786i	$-0.682093\pi$
$577$	−26.0082	−1.08274	−0.541368	+	0.840786i	$0.682093\pi$
$578$	−20.1245	−0.837069
$579$	−25.5187	−1.06052
$580$	−4.92357	−0.204440
$581$	12.2040	0.506307
$582$	39.2122	1.62540
$583$	21.1301	0.875118
$584$	43.3082	1.79210
$585$	8.84537	0.365711
$586$	−5.62467	−0.232353
$587$	10.5407	0.435060	0.217530	−	0.976054i	$-0.430200\pi$
$587$	10.5407	0.435060	0.217530	+	0.976054i	$0.430200\pi$
$588$	−2.83939	−0.117094
$589$	0	0
$590$	−15.4977	−0.638029
$591$	38.3548	1.57771
$592$	−27.1601	−1.11627
$593$	−13.2247	−0.543071	−0.271536	−	0.962428i	$-0.587532\pi$
$593$	−13.2247	−0.543071	−0.271536	+	0.962428i	$0.587532\pi$
$594$	−6.38821	−0.262111
$595$	0.840444	0.0344549
$596$	−5.73710	−0.235001
$597$	35.7400	1.46274
$598$	14.5026	0.593055
$599$	3.71961	0.151979	0.0759896	−	0.997109i	$-0.475788\pi$
$599$	3.71961	0.151979	0.0759896	+	0.997109i	$0.475788\pi$
$600$	6.98723	0.285252
$601$	42.1344	1.71870	0.859349	−	0.511389i	$-0.170869\pi$
$601$	42.1344	1.71870	0.859349	+	0.511389i	$0.170869\pi$
$602$	−5.26922	−0.214757
$603$	−2.27446	−0.0926233
$604$	8.65221	0.352053
$605$	3.01102	0.122415
$606$	−11.5371	−0.468662
$607$	27.1082	1.10029	0.550144	−	0.835070i	$-0.314573\pi$
$607$	27.1082	1.10029	0.550144	+	0.835070i	$0.314573\pi$
$608$	0	0
$609$	−42.8151	−1.73496
$610$	−7.13574	−0.288918
$611$	44.4756	1.79929
$612$	−0.476160	−0.0192476
$613$	−11.2475	−0.454283	−0.227142	−	0.973862i	$-0.572938\pi$
$613$	−11.2475	−0.454283	−0.227142	+	0.973862i	$0.572938\pi$
$614$	−14.0971	−0.568911
$615$	−7.12717	−0.287395
$616$	−19.0830	−0.768875
$617$	30.6559	1.23416	0.617080	−	0.786900i	$-0.288315\pi$
$617$	30.6559	1.23416	0.617080	+	0.786900i	$0.288315\pi$
$618$	−39.8211	−1.60184
$619$	−40.2768	−1.61886	−0.809431	−	0.587215i	$-0.800224\pi$
$619$	−40.2768	−1.61886	−0.809431	+	0.587215i	$0.800224\pi$
$620$	2.69429	0.108205
$621$	−5.63281	−0.226037
$622$	−10.6752	−0.428036
$623$	−14.4179	−0.577642
$624$	−23.3971	−0.936632
$625$	1.00000	0.0400000
$626$	−16.0370	−0.640968
$627$	0	0
$628$	−5.93960	−0.237016
$629$	4.12071	0.164304
$630$	5.68446	0.226474
$631$	38.6765	1.53969	0.769844	−	0.638232i	$-0.220334\pi$
$631$	38.6765	1.53969	0.769844	+	0.638232i	$0.220334\pi$
$632$	−41.3065	−1.64309
$633$	−21.1150	−0.839245
$634$	13.2037	0.524384
$635$	−3.44442	−0.136687
$636$	−9.75742	−0.386907
$637$	8.87838	0.351774
$638$	28.9410	1.14578
$639$	16.9650	0.671125
$640$	−4.22216	−0.166896
$641$	43.1730	1.70523	0.852616	−	0.522537i	$-0.175015\pi$
$641$	43.1730	1.70523	0.852616	+	0.522537i	$0.175015\pi$
$642$	−16.7760	−0.662094
$643$	4.37891	0.172687	0.0863436	−	0.996265i	$-0.472482\pi$
$643$	4.37891	0.172687	0.0863436	+	0.996265i	$0.472482\pi$
$644$	−3.75318	−0.147896
$645$	4.56686	0.179820
$646$	0	0
$647$	−16.4916	−0.648351	−0.324176	−	0.945997i	$-0.605087\pi$
$647$	−16.4916	−0.648351	−0.324176	+	0.945997i	$0.605087\pi$
$648$	33.2110	1.30465
$649$	−36.6842	−1.43998
$650$	−4.87328	−0.191146
$651$	23.4294	0.918271
$652$	3.96188	0.155159
$653$	1.62612	0.0636349	0.0318175	−	0.999494i	$-0.489870\pi$
$653$	1.62612	0.0636349	0.0318175	+	0.999494i	$0.489870\pi$
$654$	2.04625	0.0800148
$655$	−10.3008	−0.402484
$656$	7.90720	0.308724
$657$	−30.5370	−1.19136
$658$	28.5822	1.11425
$659$	1.90693	0.0742833	0.0371416	−	0.999310i	$-0.488175\pi$
$659$	1.90693	0.0742833	0.0371416	+	0.999310i	$0.488175\pi$
$660$	3.68914	0.143600
$661$	−6.62019	−0.257496	−0.128748	−	0.991677i	$-0.541096\pi$
$661$	−6.62019	−0.257496	−0.128748	+	0.991677i	$0.541096\pi$
$662$	3.39770	0.132055
$663$	3.54978	0.137862
$664$	17.0783	0.662765
$665$	0	0
$666$	27.8710	1.07998
$667$	25.5187	0.988088
$668$	6.81090	0.263522
$669$	−6.34432	−0.245286
$670$	1.25310	0.0484113
$671$	−16.8909	−0.652065
$672$	15.6587	0.604046
$673$	12.4460	0.479757	0.239878	−	0.970803i	$-0.422892\pi$
$673$	12.4460	0.479757	0.239878	+	0.970803i	$0.422892\pi$
$674$	−7.64909	−0.294632
$675$	1.89278	0.0728532
$676$	−2.09934	−0.0807438
$677$	−4.70606	−0.180868	−0.0904342	−	0.995902i	$-0.528825\pi$
$677$	−4.70606	−0.180868	−0.0904342	+	0.995902i	$0.528825\pi$
$678$	2.36150	0.0906927
$679$	31.7311	1.21773
$680$	1.17612	0.0451021
$681$	−1.91876	−0.0735270
$682$	−15.8371	−0.606435
$683$	−17.6914	−0.676942	−0.338471	−	0.940977i	$-0.609910\pi$
$683$	−17.6914	−0.676942	−0.338471	+	0.940977i	$0.609910\pi$
$684$	0	0
$685$	−1.46792	−0.0560864
$686$	24.0651	0.918811
$687$	−49.9097	−1.90417
$688$	−5.06668	−0.193165
$689$	30.5101	1.16234
$690$	−8.07775	−0.307515
$691$	26.1278	0.993947	0.496974	−	0.867766i	$-0.334445\pi$
$691$	26.1278	0.993947	0.496974	+	0.867766i	$0.334445\pi$
$692$	14.5879	0.554548
$693$	13.4556	0.511135
$694$	18.8699	0.716291
$695$	7.32762	0.277952
$696$	−59.9155	−2.27109
$697$	−1.19967	−0.0454409
$698$	−32.9149	−1.24585
$699$	10.0371	0.379637
$700$	1.26118	0.0476679
$701$	−21.2694	−0.803336	−0.401668	−	0.915785i	$-0.631569\pi$
$701$	−21.2694	−0.803336	−0.401668	+	0.915785i	$0.631569\pi$
$702$	−9.22406	−0.348140
$703$	0	0
$704$	−24.8411	−0.936233
$705$	−24.7723	−0.932981
$706$	−5.04956	−0.190043
$707$	−9.33596	−0.351115
$708$	16.9400	0.636644
$709$	10.6415	0.399650	0.199825	−	0.979832i	$-0.435963\pi$
$709$	10.6415	0.399650	0.199825	+	0.979832i	$0.435963\pi$
$710$	−9.34672	−0.350776
$711$	29.1256	1.09230
$712$	−20.1764	−0.756144
$713$	−13.9644	−0.522971
$714$	2.28126	0.0853741
$715$	−11.5354	−0.431401
$716$	−0.223240	−0.00834287
$717$	−45.0707	−1.68320
$718$	6.84345	0.255395
$719$	−38.3404	−1.42986	−0.714928	−	0.699198i	$-0.753541\pi$
$719$	−38.3404	−1.42986	−0.714928	+	0.699198i	$0.753541\pi$
$720$	5.46596	0.203704
$721$	−32.2238	−1.20008
$722$	0	0
$723$	−47.4736	−1.76556
$724$	2.74679	0.102083
$725$	−8.57501	−0.318468
$726$	8.17297	0.303327
$727$	7.70633	0.285812	0.142906	−	0.989736i	$-0.454355\pi$
$727$	7.70633	0.285812	0.142906	+	0.989736i	$0.454355\pi$
$728$	−27.5543	−1.02123
$729$	−10.5095	−0.389240
$730$	16.8241	0.622687
$731$	0.768712	0.0284319
$732$	7.79985	0.288291
$733$	4.08527	0.150893	0.0754464	−	0.997150i	$-0.475962\pi$
$733$	4.08527	0.150893	0.0754464	+	0.997150i	$0.475962\pi$
$734$	−1.12914	−0.0416774
$735$	−4.94514	−0.182404
$736$	−9.33289	−0.344015
$737$	2.96618	0.109261
$738$	−8.11416	−0.298686
$739$	−24.6380	−0.906323	−0.453162	−	0.891428i	$-0.649704\pi$
$739$	−24.6380	−0.906323	−0.453162	+	0.891428i	$0.649704\pi$
$740$	6.18356	0.227312
$741$	0	0
$742$	19.6073	0.719806
$743$	25.7762	0.945639	0.472819	−	0.881159i	$-0.343236\pi$
$743$	25.7762	0.945639	0.472819	+	0.881159i	$0.343236\pi$
$744$	32.7871	1.20203
$745$	−9.99186	−0.366073
$746$	−0.803971	−0.0294355
$747$	−12.0420	−0.440595
$748$	0.620971	0.0227050
$749$	−13.5753	−0.496031
$750$	2.71435	0.0991142
$751$	15.5253	0.566527	0.283264	−	0.959042i	$-0.408583\pi$
$751$	15.5253	0.566527	0.283264	+	0.959042i	$0.408583\pi$
$752$	27.4835	1.00222
$753$	−12.6264	−0.460131
$754$	41.7884	1.52184
$755$	15.0689	0.548413
$756$	2.38713	0.0868191
$757$	−21.6732	−0.787726	−0.393863	−	0.919169i	$-0.628862\pi$
$757$	−21.6732	−0.787726	−0.393863	+	0.919169i	$0.628862\pi$
$758$	41.5182	1.50801
$759$	−19.1207	−0.694037
$760$	0	0
$761$	1.91229	0.0693204	0.0346602	−	0.999399i	$-0.488965\pi$
$761$	1.91229	0.0693204	0.0346602	+	0.999399i	$0.488965\pi$
$762$	−9.34936	−0.338692
$763$	1.65585	0.0599460
$764$	13.6951	0.495470
$765$	−0.829291	−0.0299831
$766$	−32.5466	−1.17596
$767$	−52.9691	−1.91260
$768$	28.4961	1.02827
$769$	24.9508	0.899750	0.449875	−	0.893091i	$-0.351468\pi$
$769$	24.9508	0.899750	0.449875	+	0.893091i	$0.351468\pi$
$770$	−7.41324	−0.267154
$771$	45.7292	1.64690
$772$	−6.44570	−0.231986
$773$	17.4627	0.628089	0.314044	−	0.949408i	$-0.398316\pi$
$773$	17.4627	0.628089	0.314044	+	0.949408i	$0.398316\pi$
$774$	5.19929	0.186885
$775$	4.69244	0.168557
$776$	44.4045	1.59403
$777$	53.7719	1.92906
$778$	43.5851	1.56260
$779$	0	0
$780$	5.32682	0.190731
$781$	−22.1244	−0.791674
$782$	−1.35968	−0.0486220
$783$	−16.2306	−0.580035
$784$	5.48636	0.195941
$785$	−10.3445	−0.369213
$786$	−27.9599	−0.997296
$787$	49.1608	1.75239	0.876196	−	0.481955i	$-0.160073\pi$
$787$	49.1608	1.75239	0.876196	+	0.481955i	$0.160073\pi$
$788$	9.68796	0.345119
$789$	−26.6150	−0.947519
$790$	−16.0465	−0.570909
$791$	1.91095	0.0679457
$792$	18.8297	0.669086
$793$	−24.3891	−0.866081
$794$	−16.5209	−0.586305
$795$	−16.9937	−0.602706
$796$	9.02749	0.319971
$797$	35.4304	1.25501	0.627505	−	0.778613i	$-0.284076\pi$
$797$	35.4304	1.25501	0.627505	+	0.778613i	$0.284076\pi$
$798$	0	0
$799$	−4.16978	−0.147516
$800$	3.13611	0.110878
$801$	14.2266	0.502672
$802$	−28.9843	−1.02347
$803$	39.8239	1.40536
$804$	−1.36972	−0.0483063
$805$	−6.53662	−0.230386
$806$	−22.8676	−0.805475
$807$	−29.2912	−1.03110
$808$	−13.0647	−0.459616
$809$	−36.3006	−1.27626	−0.638131	−	0.769928i	$-0.720292\pi$
$809$	−36.3006	−1.27626	−0.638131	+	0.769928i	$0.720292\pi$
$810$	12.9016	0.453316
$811$	6.02560	0.211587	0.105794	−	0.994388i	$-0.466262\pi$
$811$	6.02560	0.211587	0.105794	+	0.994388i	$0.466262\pi$
$812$	−10.8146	−0.379518
$813$	35.0444	1.22906
$814$	−36.3472	−1.27397
$815$	6.90009	0.241700
$816$	2.19357	0.0767905
$817$	0	0
$818$	40.5198	1.41674
$819$	19.4288	0.678896
$820$	−1.80024	−0.0628670
$821$	−36.6258	−1.27825	−0.639125	−	0.769103i	$-0.720703\pi$
$821$	−36.6258	−1.27825	−0.639125	+	0.769103i	$0.720703\pi$
$822$	−3.98446	−0.138974
$823$	−15.3080	−0.533602	−0.266801	−	0.963752i	$-0.585967\pi$
$823$	−15.3080	−0.533602	−0.266801	+	0.963752i	$0.585967\pi$
$824$	−45.0939	−1.57092
$825$	6.42509	0.223693
$826$	−34.0405	−1.18442
$827$	−21.0944	−0.733525	−0.366763	−	0.930315i	$-0.619534\pi$
$827$	−21.0944	−0.733525	−0.366763	+	0.930315i	$0.619534\pi$
$828$	3.70337	0.128701
$829$	−40.1934	−1.39597	−0.697987	−	0.716111i	$-0.745921\pi$
$829$	−40.1934	−1.39597	−0.697987	+	0.716111i	$0.745921\pi$
$830$	6.63446	0.230285
$831$	−12.0413	−0.417707
$832$	−35.8685	−1.24352
$833$	−0.832386	−0.0288405
$834$	19.8897	0.688725
$835$	11.8620	0.410502
$836$	0	0
$837$	8.88176	0.306998
$838$	25.5921	0.884063
$839$	−27.8807	−0.962549	−0.481274	−	0.876570i	$-0.659826\pi$
$839$	−27.8807	−0.962549	−0.481274	+	0.876570i	$0.659826\pi$
$840$	15.3474	0.529535
$841$	44.5307	1.53554
$842$	8.76936	0.302212
$843$	−12.2372	−0.421471
$844$	−5.33339	−0.183583
$845$	−3.65625	−0.125779
$846$	−28.2029	−0.969635
$847$	6.61367	0.227248
$848$	18.8536	0.647435
$849$	−40.1821	−1.37905
$850$	0.456891	0.0156712
$851$	−32.0492	−1.09863
$852$	10.2166	0.350015
$853$	20.1162	0.688766	0.344383	−	0.938829i	$-0.388088\pi$
$853$	20.1162	0.688766	0.344383	+	0.938829i	$0.388088\pi$
$854$	−15.6736	−0.536339
$855$	0	0
$856$	−18.9973	−0.649315
$857$	4.35223	0.148669	0.0743347	−	0.997233i	$-0.476317\pi$
$857$	4.35223	0.148669	0.0743347	+	0.997233i	$0.476317\pi$
$858$	−31.3113	−1.06895
$859$	−5.52121	−0.188381	−0.0941906	−	0.995554i	$-0.530026\pi$
$859$	−5.52121	−0.188381	−0.0941906	+	0.995554i	$0.530026\pi$
$860$	1.15353	0.0393352
$861$	−15.6548	−0.533513
$862$	−0.150898	−0.00513962
$863$	−35.8065	−1.21887	−0.609433	−	0.792837i	$-0.708603\pi$
$863$	−35.8065	−1.21887	−0.609433	+	0.792837i	$0.708603\pi$
$864$	5.93598	0.201946
$865$	25.4066	0.863849
$866$	−6.94729	−0.236079
$867$	38.3112	1.30112
$868$	5.91798	0.200869
$869$	−37.9834	−1.28850
$870$	−23.2756	−0.789116
$871$	4.28292	0.145121
$872$	2.31720	0.0784704
$873$	−31.3100	−1.05968
$874$	0	0
$875$	2.19649	0.0742549
$876$	−18.3898	−0.621335
$877$	24.5187	0.827938	0.413969	−	0.910291i	$-0.364142\pi$
$877$	24.5187	0.827938	0.413969	+	0.910291i	$0.364142\pi$
$878$	−22.0941	−0.745639
$879$	10.7077	0.361163
$880$	−7.12828	−0.240294
$881$	−29.4843	−0.993350	−0.496675	−	0.867937i	$-0.665446\pi$
$881$	−29.4843	−0.993350	−0.496675	+	0.867937i	$0.665446\pi$
$882$	−5.62996	−0.189571
$883$	−8.02859	−0.270184	−0.135092	−	0.990833i	$-0.543133\pi$
$883$	−8.02859	−0.270184	−0.135092	+	0.990833i	$0.543133\pi$
$884$	0.896632	0.0301570
$885$	29.5031	0.991735
$886$	26.4193	0.887573
$887$	−20.9165	−0.702308	−0.351154	−	0.936318i	$-0.614211\pi$
$887$	−20.9165	−0.702308	−0.351154	+	0.936318i	$0.614211\pi$
$888$	75.2485	2.52517
$889$	−7.56563	−0.253743
$890$	−7.83802	−0.262731
$891$	30.5391	1.02310
$892$	−1.60250	−0.0536556
$893$	0	0
$894$	−27.1214	−0.907077
$895$	−0.388799	−0.0129961
$896$	−9.27394	−0.309821
$897$	−27.6087	−0.921829
$898$	24.5597	0.819569
$899$	−40.2377	−1.34200
$900$	−1.24444	−0.0414813
$901$	−2.86045	−0.0952955
$902$	10.5819	0.352337
$903$	10.0311	0.333813
$904$	2.67419	0.0889422
$905$	4.78386	0.159021
$906$	40.9023	1.35889
$907$	0.293120	0.00973290	0.00486645	−	0.999988i	$-0.498451\pi$
$907$	0.293120	0.00973290	0.00486645	+	0.999988i	$0.498451\pi$
$908$	−0.484655	−0.0160838
$909$	9.21206	0.305545
$910$	−10.7041	−0.354838
$911$	22.0356	0.730073	0.365037	−	0.930993i	$-0.381056\pi$
$911$	22.0356	0.730073	0.365037	+	0.930993i	$0.381056\pi$
$912$	0	0
$913$	15.7043	0.519736
$914$	24.3094	0.804085
$915$	13.5844	0.449086
$916$	−12.6066	−0.416533
$917$	−22.6255	−0.747160
$918$	0.864795	0.0285425
$919$	−0.921513	−0.0303979	−0.0151990	−	0.999884i	$-0.504838\pi$
$919$	−0.921513	−0.0303979	−0.0151990	+	0.999884i	$0.504838\pi$
$920$	−9.14735	−0.301579
$921$	26.8367	0.884300
$922$	−6.61836	−0.217964
$923$	−31.9459	−1.05151
$924$	8.10317	0.266575
$925$	10.7694	0.354097
$926$	38.9866	1.28118
$927$	31.7961	1.04432
$928$	−26.8922	−0.882780
$929$	−23.4997	−0.771000	−0.385500	−	0.922708i	$-0.625971\pi$
$929$	−23.4997	−0.771000	−0.385500	+	0.922708i	$0.625971\pi$
$930$	12.7369	0.417660
$931$	0	0
$932$	2.53525	0.0830448
$933$	20.3225	0.665328
$934$	34.2238	1.11984
$935$	1.08150	0.0353687
$936$	27.1886	0.888688
$937$	−53.3229	−1.74198	−0.870991	−	0.491299i	$-0.836522\pi$
$937$	−53.3229	−1.74198	−0.870991	+	0.491299i	$0.836522\pi$
$938$	2.75241	0.0898695
$939$	30.5298	0.996304
$940$	−6.25720	−0.204087
$941$	4.12948	0.134617	0.0673087	−	0.997732i	$-0.478559\pi$
$941$	4.12948	0.134617	0.0673087	+	0.997732i	$0.478559\pi$
$942$	−28.0787	−0.914855
$943$	9.33056	0.303845
$944$	−32.7320	−1.06534
$945$	4.15748	0.135243
$946$	−6.78052	−0.220454
$947$	8.42169	0.273668	0.136834	−	0.990594i	$-0.456307\pi$
$947$	8.42169	0.273668	0.136834	+	0.990594i	$0.456307\pi$
$948$	17.5399	0.569670
$949$	57.5025	1.86661
$950$	0	0
$951$	−25.1359	−0.815088
$952$	2.58333	0.0837263
$953$	18.9742	0.614633	0.307317	−	0.951607i	$-0.400569\pi$
$953$	18.9742	0.614633	0.307317	+	0.951607i	$0.400569\pi$
$954$	−19.3471	−0.626385
$955$	23.8516	0.771820
$956$	−11.3843	−0.368195
$957$	−55.0952	−1.78097
$958$	12.2662	0.396303
$959$	−3.22428	−0.104117
$960$	19.9783	0.644796
$961$	−8.98105	−0.289711
$962$	−52.4825	−1.69210
$963$	13.3952	0.431653
$964$	−11.9913	−0.386213
$965$	−11.2260	−0.361377
$966$	−17.7427	−0.570862
$967$	−3.75873	−0.120873	−0.0604363	−	0.998172i	$-0.519249\pi$
$967$	−3.75873	−0.120873	−0.0604363	+	0.998172i	$0.519249\pi$
$968$	9.25517	0.297473
$969$	0	0
$970$	17.2500	0.553863
$971$	−12.8337	−0.411854	−0.205927	−	0.978567i	$-0.566021\pi$
$971$	−12.8337	−0.411854	−0.205927	+	0.978567i	$0.566021\pi$
$972$	−10.8419	−0.347755
$973$	16.0950	0.515983
$974$	−13.2835	−0.425630
$975$	9.27731	0.297112
$976$	−15.0711	−0.482415
$977$	27.5345	0.880906	0.440453	−	0.897776i	$-0.354818\pi$
$977$	27.5345	0.880906	0.440453	+	0.897776i	$0.354818\pi$
$978$	18.7293	0.598896
$979$	−18.5532	−0.592963
$980$	−1.24908	−0.0399005
$981$	−1.63388	−0.0521658
$982$	16.5794	0.529071
$983$	−48.2635	−1.53937	−0.769683	−	0.638426i	$-0.779586\pi$
$983$	−48.2635	−1.53937	−0.769683	+	0.638426i	$0.779586\pi$
$984$	−21.9073	−0.698378
$985$	16.8728	0.537611
$986$	−3.91784	−0.124769
$987$	−54.4122	−1.73196
$988$	0	0
$989$	−5.97872	−0.190112
$990$	7.31486	0.232481
$991$	43.6279	1.38589	0.692944	−	0.720992i	$-0.256314\pi$
$991$	43.6279	1.38589	0.692944	+	0.720992i	$0.256314\pi$
$992$	14.7160	0.467234
$993$	−6.46823	−0.205263
$994$	−20.5300	−0.651171
$995$	15.7225	0.498436
$996$	−7.25191	−0.229786
$997$	30.1978	0.956375	0.478187	−	0.878258i	$-0.341294\pi$
$997$	30.1978	0.956375	0.478187	+	0.878258i	$0.341294\pi$
$998$	15.2697	0.483355
$999$	20.3842	0.644927

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.u.1.6		9
5.4	even	2		9025.2.a.cd.1.4		9
19.2	odd	18		95.2.k.b.61.2	✓	18
19.10	odd	18		95.2.k.b.81.2	yes	18
19.18	odd	2		1805.2.a.t.1.4		9
57.2	even	18		855.2.bs.b.631.2		18
57.29	even	18		855.2.bs.b.271.2		18
95.2	even	36		475.2.u.c.99.3		36
95.29	odd	18		475.2.l.b.176.2		18
95.48	even	36		475.2.u.c.24.3		36
95.59	odd	18		475.2.l.b.251.2		18
95.67	even	36		475.2.u.c.24.4		36
95.78	even	36		475.2.u.c.99.4		36
95.94	odd	2		9025.2.a.ce.1.6		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.61.2	✓	18	19.2	odd	18
95.2.k.b.81.2	yes	18	19.10	odd	18
475.2.l.b.176.2		18	95.29	odd	18
475.2.l.b.251.2		18	95.59	odd	18
475.2.u.c.24.3		36	95.48	even	36
475.2.u.c.24.4		36	95.67	even	36
475.2.u.c.99.3		36	95.2	even	36
475.2.u.c.99.4		36	95.78	even	36
855.2.bs.b.271.2		18	57.29	even	18
855.2.bs.b.631.2		18	57.2	even	18
1805.2.a.t.1.4		9	19.18	odd	2
1805.2.a.u.1.6		9	1.1	even	1	trivial
9025.2.a.cd.1.4		9	5.4	even	2
9025.2.a.ce.1.6		9	95.94	odd	2

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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q+1.19408 q^{2} -2.27318 q^{3} -0.574177 q^{4} -1.00000 q^{5} -2.71435 q^{6} -2.19649 q^{7} -3.07377 q^{8} +2.16734 q^{9} +O(q^{10})\)	\(q+1.19408 q^{2} -2.27318 q^{3} -0.574177 q^{4} -1.00000 q^{5} -2.71435 q^{6} -2.19649 q^{7} -3.07377 q^{8} +2.16734 q^{9} -1.19408 q^{10} -2.82648 q^{11} +1.30521 q^{12} -4.08121 q^{13} -2.62278 q^{14} +2.27318 q^{15} -2.52197 q^{16} +0.382631 q^{17} +2.58797 q^{18} +0.574177 q^{20} +4.99302 q^{21} -3.37504 q^{22} -2.97594 q^{23} +6.98723 q^{24} +1.00000 q^{25} -4.87328 q^{26} +1.89278 q^{27} +1.26118 q^{28} -8.57501 q^{29} +2.71435 q^{30} +4.69244 q^{31} +3.13611 q^{32} +6.42509 q^{33} +0.456891 q^{34} +2.19649 q^{35} -1.24444 q^{36} +10.7694 q^{37} +9.27731 q^{39} +3.07377 q^{40} -3.13533 q^{41} +5.96205 q^{42} +2.00902 q^{43} +1.62290 q^{44} -2.16734 q^{45} -3.55350 q^{46} -10.8977 q^{47} +5.73288 q^{48} -2.17543 q^{49} +1.19408 q^{50} -0.869788 q^{51} +2.34334 q^{52} -7.47576 q^{53} +2.26013 q^{54} +2.82648 q^{55} +6.75150 q^{56} -10.2392 q^{58} +12.9788 q^{59} -1.30521 q^{60} +5.97594 q^{61} +5.60313 q^{62} -4.76054 q^{63} +8.78870 q^{64} +4.08121 q^{65} +7.67206 q^{66} -1.04943 q^{67} -0.219698 q^{68} +6.76484 q^{69} +2.62278 q^{70} +7.82756 q^{71} -6.66191 q^{72} -14.0896 q^{73} +12.8595 q^{74} -2.27318 q^{75} +6.20833 q^{77} +11.0778 q^{78} +13.4384 q^{79} +2.52197 q^{80} -10.8047 q^{81} -3.74383 q^{82} -5.55613 q^{83} -2.86688 q^{84} -0.382631 q^{85} +2.39893 q^{86} +19.4925 q^{87} +8.68794 q^{88} +6.56407 q^{89} -2.58797 q^{90} +8.96433 q^{91} +1.70872 q^{92} -10.6667 q^{93} -13.0127 q^{94} -7.12895 q^{96} -14.4463 q^{97} -2.59763 q^{98} -6.12594 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} - 12 q^{8} + 6 q^{9}+O(q^{10}) \) 9 * q + 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 - 12 * q^8 + 6 * q^9	\( 9 q + 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} - 12 q^{8} + 6 q^{9} + 6 q^{12} - 3 q^{13} + 12 q^{14} - 3 q^{15} - 12 q^{16} - 9 q^{17} + 6 q^{18} - 6 q^{20} + 12 q^{21} + 12 q^{22} + 15 q^{24} + 9 q^{25} + 21 q^{26} + 6 q^{27} - 15 q^{28} + 15 q^{29} + 12 q^{30} + 30 q^{31} - 9 q^{32} + 9 q^{33} - 6 q^{36} + 30 q^{37} + 6 q^{39} + 12 q^{40} + 18 q^{41} + 36 q^{42} - 6 q^{43} - 24 q^{44} - 6 q^{45} + 21 q^{46} + 21 q^{47} + 15 q^{48} + 3 q^{49} + 18 q^{51} - 3 q^{52} - 9 q^{53} - 9 q^{54} + 36 q^{56} + 18 q^{58} + 27 q^{59} - 6 q^{60} + 12 q^{61} - 6 q^{62} - 15 q^{63} + 24 q^{64} + 3 q^{65} + 3 q^{66} + 36 q^{67} + 3 q^{68} + 27 q^{69} - 12 q^{70} - 6 q^{71} + 12 q^{72} - 9 q^{73} - 9 q^{74} + 3 q^{75} + 12 q^{77} + 54 q^{78} + 45 q^{79} + 12 q^{80} - 15 q^{81} - 48 q^{82} - 12 q^{84} + 9 q^{85} - 9 q^{86} + 45 q^{87} + 39 q^{88} - 9 q^{89} - 6 q^{90} + 51 q^{91} - 54 q^{92} + 9 q^{93} + 33 q^{94} - 9 q^{96} + 45 q^{97} + 33 q^{98} + 12 q^{99}+O(q^{100}) \) 9 * q + 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 - 12 * q^8 + 6 * q^9 + 6 * q^12 - 3 * q^13 + 12 * q^14 - 3 * q^15 - 12 * q^16 - 9 * q^17 + 6 * q^18 - 6 * q^20 + 12 * q^21 + 12 * q^22 + 15 * q^24 + 9 * q^25 + 21 * q^26 + 6 * q^27 - 15 * q^28 + 15 * q^29 + 12 * q^30 + 30 * q^31 - 9 * q^32 + 9 * q^33 - 6 * q^36 + 30 * q^37 + 6 * q^39 + 12 * q^40 + 18 * q^41 + 36 * q^42 - 6 * q^43 - 24 * q^44 - 6 * q^45 + 21 * q^46 + 21 * q^47 + 15 * q^48 + 3 * q^49 + 18 * q^51 - 3 * q^52 - 9 * q^53 - 9 * q^54 + 36 * q^56 + 18 * q^58 + 27 * q^59 - 6 * q^60 + 12 * q^61 - 6 * q^62 - 15 * q^63 + 24 * q^64 + 3 * q^65 + 3 * q^66 + 36 * q^67 + 3 * q^68 + 27 * q^69 - 12 * q^70 - 6 * q^71 + 12 * q^72 - 9 * q^73 - 9 * q^74 + 3 * q^75 + 12 * q^77 + 54 * q^78 + 45 * q^79 + 12 * q^80 - 15 * q^81 - 48 * q^82 - 12 * q^84 + 9 * q^85 - 9 * q^86 + 45 * q^87 + 39 * q^88 - 9 * q^89 - 6 * q^90 + 51 * q^91 - 54 * q^92 + 9 * q^93 + 33 * q^94 - 9 * q^96 + 45 * q^97 + 33 * q^98 + 12 * q^99

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