LMFDB - Embedded newform 1859.2.a.r.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,2,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, 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("1859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1859.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:	$14.8441897358$
Analytic rank:	$1$
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} - 10x^{7} - x^{6} + 31x^{5} + 9x^{4} - 31x^{3} - 15x^{2} + 2x + 1 $ x^9 - 10x^7 - x^6 + 31x^5 + 9x^4 - 31x^3 - 15x^2 + 2x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-1.49715$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.49715 q^{2} +0.384176 q^{3} +0.241465 q^{4} +2.16802 q^{5} +0.575170 q^{6} -2.79366 q^{7} -2.63279 q^{8} -2.85241 q^{9} +O(q^{10})$	\(q+1.49715 q^{2} +0.384176 q^{3} +0.241465 q^{4} +2.16802 q^{5} +0.575170 q^{6} -2.79366 q^{7} -2.63279 q^{8} -2.85241 q^{9} +3.24586 q^{10} -1.00000 q^{11} +0.0927650 q^{12} -4.18254 q^{14} +0.832901 q^{15} -4.42462 q^{16} -3.44024 q^{17} -4.27049 q^{18} +0.00264176 q^{19} +0.523501 q^{20} -1.07326 q^{21} -1.49715 q^{22} +7.04056 q^{23} -1.01146 q^{24} -0.299687 q^{25} -2.24835 q^{27} -0.674572 q^{28} -3.93577 q^{29} +1.24698 q^{30} -1.20009 q^{31} -1.35875 q^{32} -0.384176 q^{33} -5.15056 q^{34} -6.05672 q^{35} -0.688757 q^{36} +1.77948 q^{37} +0.00395512 q^{38} -5.70795 q^{40} -11.3500 q^{41} -1.60683 q^{42} -12.3353 q^{43} -0.241465 q^{44} -6.18408 q^{45} +10.5408 q^{46} -11.7456 q^{47} -1.69983 q^{48} +0.804544 q^{49} -0.448677 q^{50} -1.32166 q^{51} +8.73416 q^{53} -3.36613 q^{54} -2.16802 q^{55} +7.35514 q^{56} +0.00101490 q^{57} -5.89245 q^{58} +5.43732 q^{59} +0.201117 q^{60} -4.14058 q^{61} -1.79672 q^{62} +7.96866 q^{63} +6.81500 q^{64} -0.575170 q^{66} +7.31500 q^{67} -0.830697 q^{68} +2.70481 q^{69} -9.06783 q^{70} +0.934852 q^{71} +7.50981 q^{72} +2.93110 q^{73} +2.66416 q^{74} -0.115133 q^{75} +0.000637894 q^{76} +2.79366 q^{77} +2.39640 q^{79} -9.59268 q^{80} +7.69346 q^{81} -16.9926 q^{82} +10.6450 q^{83} -0.259154 q^{84} -7.45850 q^{85} -18.4679 q^{86} -1.51203 q^{87} +2.63279 q^{88} +6.54690 q^{89} -9.25851 q^{90} +1.70005 q^{92} -0.461046 q^{93} -17.5849 q^{94} +0.00572740 q^{95} -0.521998 q^{96} +14.3897 q^{97} +1.20453 q^{98} +2.85241 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 5 q^{3} + 2 q^{4} + 4 q^{5} + 11 q^{6} - q^{7} - 3 q^{8} + 2 q^{9}+O(q^{10}) $ 9 * q - 5 * q^3 + 2 * q^4 + 4 * q^5 + 11 * q^6 - q^7 - 3 * q^8 + 2 * q^9	$ 9 q - 5 q^{3} + 2 q^{4} + 4 q^{5} + 11 q^{6} - q^{7} - 3 q^{8} + 2 q^{9} - 8 q^{10} - 9 q^{11} - 9 q^{12} - 3 q^{15} - 8 q^{16} - 8 q^{17} - 27 q^{18} + q^{19} - 12 q^{20} - 17 q^{21} + 6 q^{24} - 15 q^{25} - 23 q^{27} - 11 q^{28} - 22 q^{29} - 3 q^{30} + 6 q^{31} + 19 q^{32} + 5 q^{33} - 10 q^{34} - 15 q^{35} + 7 q^{36} + 15 q^{37} + q^{38} - 3 q^{40} - 10 q^{41} + 2 q^{42} - 19 q^{43} - 2 q^{44} + 2 q^{45} - 19 q^{46} + 2 q^{47} + 6 q^{48} - 20 q^{49} + 17 q^{50} - 2 q^{51} - 5 q^{53} + 27 q^{54} - 4 q^{55} - 16 q^{56} + 32 q^{57} + 11 q^{58} + 11 q^{59} + 6 q^{60} - 68 q^{61} - 21 q^{62} + 29 q^{63} - 23 q^{64} - 11 q^{66} - 5 q^{67} + 16 q^{68} - 34 q^{69} + 5 q^{70} + 34 q^{71} - 13 q^{72} - 26 q^{73} + q^{74} + 10 q^{75} + 11 q^{76} + q^{77} - 32 q^{79} - 8 q^{80} + 13 q^{81} - 42 q^{82} - 8 q^{83} + 13 q^{84} - 23 q^{85} - 30 q^{86} + 10 q^{87} + 3 q^{88} + 37 q^{89} + 21 q^{90} - 12 q^{92} - 20 q^{93} - 12 q^{94} - 4 q^{95} - 60 q^{96} - 3 q^{97} + 9 q^{98} - 2 q^{99}+O(q^{100}) $ 9 * q - 5 * q^3 + 2 * q^4 + 4 * q^5 + 11 * q^6 - q^7 - 3 * q^8 + 2 * q^9 - 8 * q^10 - 9 * q^11 - 9 * q^12 - 3 * q^15 - 8 * q^16 - 8 * q^17 - 27 * q^18 + q^19 - 12 * q^20 - 17 * q^21 + 6 * q^24 - 15 * q^25 - 23 * q^27 - 11 * q^28 - 22 * q^29 - 3 * q^30 + 6 * q^31 + 19 * q^32 + 5 * q^33 - 10 * q^34 - 15 * q^35 + 7 * q^36 + 15 * q^37 + q^38 - 3 * q^40 - 10 * q^41 + 2 * q^42 - 19 * q^43 - 2 * q^44 + 2 * q^45 - 19 * q^46 + 2 * q^47 + 6 * q^48 - 20 * q^49 + 17 * q^50 - 2 * q^51 - 5 * q^53 + 27 * q^54 - 4 * q^55 - 16 * q^56 + 32 * q^57 + 11 * q^58 + 11 * q^59 + 6 * q^60 - 68 * q^61 - 21 * q^62 + 29 * q^63 - 23 * q^64 - 11 * q^66 - 5 * q^67 + 16 * q^68 - 34 * q^69 + 5 * q^70 + 34 * q^71 - 13 * q^72 - 26 * q^73 + q^74 + 10 * q^75 + 11 * q^76 + q^77 - 32 * q^79 - 8 * q^80 + 13 * q^81 - 42 * q^82 - 8 * q^83 + 13 * q^84 - 23 * q^85 - 30 * q^86 + 10 * q^87 + 3 * q^88 + 37 * q^89 + 21 * q^90 - 12 * q^92 - 20 * q^93 - 12 * q^94 - 4 * q^95 - 60 * q^96 - 3 * q^97 + 9 * q^98 - 2 * 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 $

$2$	1.49715	1.05865	0.529323	−	0.848420i	$-0.322446\pi$
$2$	1.49715	1.05865	0.529323	+	0.848420i	$0.322446\pi$
$3$	0.384176	0.221804	0.110902	−	0.993831i	$-0.464626\pi$
$3$	0.384176	0.221804	0.110902	+	0.993831i	$0.464626\pi$
$4$	0.241465	0.120733
$5$	2.16802	0.969568	0.484784	−	0.874634i	$-0.338898\pi$
$5$	2.16802	0.969568	0.484784	+	0.874634i	$0.338898\pi$
$6$	0.575170	0.234812
$7$	−2.79366	−1.05590	−0.527952	−	0.849274i	$-0.677040\pi$
$7$	−2.79366	−1.05590	−0.527952	+	0.849274i	$0.677040\pi$
$8$	−2.63279	−0.930833
$9$	−2.85241	−0.950803
$10$	3.24586	1.02643
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.0927650	0.0267790
$13$	0	0
$13$	0	0
$14$	−4.18254	−1.11783
$15$	0.832901	0.215054
$16$	−4.42462	−1.10616
$17$	−3.44024	−0.834380	−0.417190	−	0.908819i	$-0.636985\pi$
$17$	−3.44024	−0.834380	−0.417190	+	0.908819i	$0.636985\pi$
$18$	−4.27049	−1.00656
$19$	0.00264176	0.000606062 0	0.000303031	−	1.00000i	$-0.499904\pi$
$19$	0.00264176	0.000606062 0	0.000303031		1.00000i	$0.499904\pi$
$20$	0.523501	0.117058
$21$	−1.07326	−0.234204
$22$	−1.49715	−0.319194
$23$	7.04056	1.46806	0.734029	−	0.679118i	$-0.237638\pi$
$23$	7.04056	1.46806	0.734029	+	0.679118i	$0.237638\pi$
$24$	−1.01146	−0.206463
$25$	−0.299687	−0.0599374
$26$	0	0
$27$	−2.24835	−0.432696
$28$	−0.674572	−0.127482
$29$	−3.93577	−0.730854	−0.365427	−	0.930840i	$-0.619077\pi$
$29$	−3.93577	−0.730854	−0.365427	+	0.930840i	$0.619077\pi$
$30$	1.24698	0.227666
$31$	−1.20009	−0.215543	−0.107771	−	0.994176i	$-0.534371\pi$
$31$	−1.20009	−0.215543	−0.107771	+	0.994176i	$0.534371\pi$
$32$	−1.35875	−0.240195
$33$	−0.384176	−0.0668764
$34$	−5.15056	−0.883313
$35$	−6.05672	−1.02377
$36$	−0.688757	−0.114793
$37$	1.77948	0.292546	0.146273	−	0.989244i	$-0.453272\pi$
$37$	1.77948	0.292546	0.146273	+	0.989244i	$0.453272\pi$
$38$	0.00395512	0.000641605 0
$39$	0	0
$40$	−5.70795	−0.902507
$41$	−11.3500	−1.77257	−0.886283	−	0.463144i	$-0.846721\pi$
$41$	−11.3500	−1.77257	−0.886283	+	0.463144i	$0.846721\pi$
$42$	−1.60683	−0.247939
$43$	−12.3353	−1.88112	−0.940560	−	0.339627i	$-0.889699\pi$
$43$	−12.3353	−1.88112	−0.940560	+	0.339627i	$0.889699\pi$
$44$	−0.241465	−0.0364022
$45$	−6.18408	−0.921868
$46$	10.5408	1.55415
$47$	−11.7456	−1.71327	−0.856636	−	0.515922i	$-0.827449\pi$
$47$	−11.7456	−1.71327	−0.856636	+	0.515922i	$0.827449\pi$
$48$	−1.69983	−0.245350
$49$	0.804544	0.114935
$50$	−0.448677	−0.0634525
$51$	−1.32166	−0.185069
$52$	0	0
$53$	8.73416	1.19973	0.599864	−	0.800102i	$-0.295221\pi$
$53$	8.73416	1.19973	0.599864	+	0.800102i	$0.295221\pi$
$54$	−3.36613	−0.458072
$55$	−2.16802	−0.292336
$56$	7.35514	0.982871
$57$	0.00101490	0.000134427 0
$58$	−5.89245	−0.773716
$59$	5.43732	0.707879	0.353939	−	0.935268i	$-0.384842\pi$
$59$	5.43732	0.707879	0.353939	+	0.935268i	$0.384842\pi$
$60$	0.201117	0.0259640
$61$	−4.14058	−0.530147	−0.265074	−	0.964228i	$-0.585396\pi$
$61$	−4.14058	−0.530147	−0.265074	+	0.964228i	$0.585396\pi$
$62$	−1.79672	−0.228184
$63$	7.96866	1.00396
$64$	6.81500	0.851875
$65$	0	0
$66$	−0.575170	−0.0707985
$67$	7.31500	0.893669	0.446834	−	0.894617i	$-0.352551\pi$
$67$	7.31500	0.893669	0.446834	+	0.894617i	$0.352551\pi$
$68$	−0.830697	−0.100737
$69$	2.70481	0.325621
$70$	−9.06783	−1.08381
$71$	0.934852	0.110946	0.0554732	−	0.998460i	$-0.482333\pi$
$71$	0.934852	0.110946	0.0554732	+	0.998460i	$0.482333\pi$
$72$	7.50981	0.885039
$73$	2.93110	0.343059	0.171529	−	0.985179i	$-0.445129\pi$
$73$	2.93110	0.343059	0.171529	+	0.985179i	$0.445129\pi$
$74$	2.66416	0.309702
$75$	−0.115133	−0.0132944
$76$	0.000637894 0	7.31714e−5 0
$77$	2.79366	0.318367
$78$	0	0
$79$	2.39640	0.269616	0.134808	−	0.990872i	$-0.456958\pi$
$79$	2.39640	0.269616	0.134808	+	0.990872i	$0.456958\pi$
$80$	−9.59268	−1.07249
$81$	7.69346	0.854829
$82$	−16.9926	−1.87652
$83$	10.6450	1.16844	0.584221	−	0.811595i	$-0.301400\pi$
$83$	10.6450	1.16844	0.584221	+	0.811595i	$0.301400\pi$
$84$	−0.259154	−0.0282760
$85$	−7.45850	−0.808988
$86$	−18.4679	−1.99144
$87$	−1.51203	−0.162106
$88$	2.63279	0.280657
$89$	6.54690	0.693970	0.346985	−	0.937871i	$-0.387206\pi$
$89$	6.54690	0.693970	0.346985	+	0.937871i	$0.387206\pi$
$90$	−9.25851	−0.975933
$91$	0	0
$92$	1.70005	0.177242
$93$	−0.461046	−0.0478083
$94$	−17.5849	−1.81375
$95$	0.00572740	0.000587618 0
$96$	−0.521998	−0.0532762
$97$	14.3897	1.46105	0.730526	−	0.682885i	$-0.239275\pi$
$97$	14.3897	1.46105	0.730526	+	0.682885i	$0.239275\pi$
$98$	1.20453	0.121675
$99$	2.85241	0.286678
$100$	−0.0723640	−0.00723640
$101$	9.03560	0.899075	0.449538	−	0.893261i	$-0.351589\pi$
$101$	9.03560	0.899075	0.449538	+	0.893261i	$0.351589\pi$
$102$	−1.97872	−0.195922
$103$	−9.88120	−0.973624	−0.486812	−	0.873507i	$-0.661840\pi$
$103$	−9.88120	−0.973624	−0.486812	+	0.873507i	$0.661840\pi$
$104$	0	0
$105$	−2.32684	−0.227077
$106$	13.0764	1.27009
$107$	−14.5106	−1.40279	−0.701396	−	0.712771i	$-0.747440\pi$
$107$	−14.5106	−1.40279	−0.701396	+	0.712771i	$0.747440\pi$
$108$	−0.542899	−0.0522405
$109$	−0.587808	−0.0563018	−0.0281509	−	0.999604i	$-0.508962\pi$
$109$	−0.587808	−0.0563018	−0.0281509	+	0.999604i	$0.508962\pi$
$110$	−3.24586	−0.309480
$111$	0.683635	0.0648878
$112$	12.3609	1.16800
$113$	−18.8145	−1.76992	−0.884958	−	0.465671i	$-0.845813\pi$
$113$	−18.8145	−1.76992	−0.884958	+	0.465671i	$0.845813\pi$
$114$	0.00151946	0.000142311 0
$115$	15.2641	1.42338
$116$	−0.950351	−0.0882379
$117$	0	0
$118$	8.14049	0.749393
$119$	9.61085	0.881026
$120$	−2.19286	−0.200180
$121$	1.00000	0.0909091
$122$	−6.19908	−0.561239
$123$	−4.36038	−0.393162
$124$	−0.289780	−0.0260230
$125$	−11.4898	−1.02768
$126$	11.9303	1.06284
$127$	−4.63349	−0.411156	−0.205578	−	0.978641i	$-0.565907\pi$
$127$	−4.63349	−0.411156	−0.205578	+	0.978641i	$0.565907\pi$
$128$	12.9206	1.14203
$129$	−4.73893	−0.417240
$130$	0	0
$131$	−6.50889	−0.568685	−0.284342	−	0.958723i	$-0.591775\pi$
$131$	−6.50889	−0.568685	−0.284342	+	0.958723i	$0.591775\pi$
$132$	−0.0927650	−0.00807416
$133$	−0.00738019	−0.000639944 0
$134$	10.9517	0.946080
$135$	−4.87448	−0.419528
$136$	9.05743	0.776669
$137$	−1.63202	−0.139433	−0.0697163	−	0.997567i	$-0.522209\pi$
$137$	−1.63202	−0.139433	−0.0697163	+	0.997567i	$0.522209\pi$
$138$	4.04952	0.344718
$139$	−7.96474	−0.675561	−0.337780	−	0.941225i	$-0.609676\pi$
$139$	−7.96474	−0.675561	−0.337780	+	0.941225i	$0.609676\pi$
$140$	−1.46249	−0.123603
$141$	−4.51237	−0.380010
$142$	1.39962	0.117453
$143$	0	0
$144$	12.6208	1.05174
$145$	−8.53283	−0.708613
$146$	4.38830	0.363178
$147$	0.309086	0.0254930
$148$	0.429684	0.0353198
$149$	16.9948	1.39227	0.696135	−	0.717911i	$-0.254901\pi$
$149$	16.9948	1.39227	0.696135	+	0.717911i	$0.254901\pi$
$150$	−0.172371	−0.0140740
$151$	13.4397	1.09371	0.546854	−	0.837228i	$-0.315825\pi$
$151$	13.4397	1.09371	0.546854	+	0.837228i	$0.315825\pi$
$152$	−0.00695522	−0.000564143 0
$153$	9.81296	0.793331
$154$	4.18254	0.337038
$155$	−2.60182	−0.208984
$156$	0	0
$157$	−4.82728	−0.385259	−0.192629	−	0.981272i	$-0.561702\pi$
$157$	−4.82728	−0.385259	−0.192629	+	0.981272i	$0.561702\pi$
$158$	3.58777	0.285428
$159$	3.35545	0.266105
$160$	−2.94579	−0.232885
$161$	−19.6689	−1.55013
$162$	11.5183	0.904962
$163$	4.82117	0.377623	0.188812	−	0.982013i	$-0.439536\pi$
$163$	4.82117	0.377623	0.188812	+	0.982013i	$0.439536\pi$
$164$	−2.74062	−0.214006
$165$	−0.832901	−0.0648413
$166$	15.9372	1.23697
$167$	−2.50415	−0.193777	−0.0968885	−	0.995295i	$-0.530889\pi$
$167$	−2.50415	−0.193777	−0.0968885	+	0.995295i	$0.530889\pi$
$168$	2.82567	0.218005
$169$	0	0
$170$	−11.1665	−0.856433
$171$	−0.00753539	−0.000576246 0
$172$	−2.97855	−0.227112
$173$	19.9089	1.51364	0.756822	−	0.653621i	$-0.226751\pi$
$173$	19.9089	1.51364	0.756822	+	0.653621i	$0.226751\pi$
$174$	−2.26374	−0.171613
$175$	0.837224	0.0632882
$176$	4.42462	0.333519
$177$	2.08889	0.157010
$178$	9.80170	0.734669
$179$	−13.2927	−0.993539	−0.496770	−	0.867882i	$-0.665481\pi$
$179$	−13.2927	−0.993539	−0.496770	+	0.867882i	$0.665481\pi$
$180$	−1.49324	−0.111300
$181$	−20.0625	−1.49124	−0.745618	−	0.666374i	$-0.767846\pi$
$181$	−20.0625	−1.49124	−0.745618	+	0.666374i	$0.767846\pi$
$182$	0	0
$183$	−1.59071	−0.117589
$184$	−18.5363	−1.36652
$185$	3.85796	0.283643
$186$	−0.690256	−0.0506121
$187$	3.44024	0.251575
$188$	−2.83615	−0.206848
$189$	6.28114	0.456886
$190$	0.00857478	0.000622080 0
$191$	10.1733	0.736113	0.368057	−	0.929803i	$-0.380023\pi$
$191$	10.1733	0.736113	0.368057	+	0.929803i	$0.380023\pi$
$192$	2.61816	0.188949
$193$	−19.5707	−1.40873	−0.704363	−	0.709840i	$-0.748767\pi$
$193$	−19.5707	−1.40873	−0.704363	+	0.709840i	$0.748767\pi$
$194$	21.5436	1.54674
$195$	0	0
$196$	0.194269	0.0138764
$197$	1.22350	0.0871707	0.0435853	−	0.999050i	$-0.486122\pi$
$197$	1.22350	0.0871707	0.0435853	+	0.999050i	$0.486122\pi$
$198$	4.27049	0.303491
$199$	20.3226	1.44063	0.720315	−	0.693647i	$-0.243997\pi$
$199$	20.3226	1.44063	0.720315	+	0.693647i	$0.243997\pi$
$200$	0.789014	0.0557917
$201$	2.81024	0.198219
$202$	13.5277	0.951803
$203$	10.9952	0.771712
$204$	−0.319134	−0.0223438
$205$	−24.6069	−1.71862
$206$	−14.7937	−1.03072
$207$	−20.0826	−1.39583
$208$	0	0
$209$	−0.00264176	−0.000182735 0
$210$	−3.48364	−0.240394
$211$	10.0901	0.694634	0.347317	−	0.937748i	$-0.387093\pi$
$211$	10.0901	0.694634	0.347317	+	0.937748i	$0.387093\pi$
$212$	2.10899	0.144846
$213$	0.359147	0.0246084
$214$	−21.7246	−1.48506
$215$	−26.7432	−1.82387
$216$	5.91945	0.402768
$217$	3.35265	0.227593
$218$	−0.880038	−0.0596037
$219$	1.12606	0.0760918
$220$	−0.523501	−0.0352945
$221$	0	0
$222$	1.02351	0.0686932
$223$	18.7597	1.25624	0.628120	−	0.778116i	$-0.283825\pi$
$223$	18.7597	1.25624	0.628120	+	0.778116i	$0.283825\pi$
$224$	3.79588	0.253623
$225$	0.854830	0.0569887
$226$	−28.1681	−1.87372
$227$	−0.901924	−0.0598628	−0.0299314	−	0.999552i	$-0.509529\pi$
$227$	−0.901924	−0.0598628	−0.0299314	+	0.999552i	$0.509529\pi$
$228$	0.000245063 0	1.62297e−5 0
$229$	17.8795	1.18151	0.590756	−	0.806850i	$-0.298830\pi$
$229$	17.8795	1.18151	0.590756	+	0.806850i	$0.298830\pi$
$230$	22.8527	1.50686
$231$	1.07326	0.0706151
$232$	10.3621	0.680303
$233$	−22.1376	−1.45028	−0.725140	−	0.688602i	$-0.758225\pi$
$233$	−22.1376	−1.45028	−0.725140	+	0.688602i	$0.758225\pi$
$234$	0	0
$235$	−25.4647	−1.66113
$236$	1.31292	0.0854640
$237$	0.920638	0.0598019
$238$	14.3889	0.932695
$239$	20.8597	1.34930	0.674650	−	0.738138i	$-0.264295\pi$
$239$	20.8597	1.34930	0.674650	+	0.738138i	$0.264295\pi$
$240$	−3.68527	−0.237883
$241$	−18.1131	−1.16677	−0.583384	−	0.812196i	$-0.698272\pi$
$241$	−18.1131	−1.16677	−0.583384	+	0.812196i	$0.698272\pi$
$242$	1.49715	0.0962406
$243$	9.70070	0.622300
$244$	−0.999806	−0.0640061
$245$	1.74427	0.111437
$246$	−6.52815	−0.416220
$247$	0	0
$248$	3.15960	0.200635
$249$	4.08956	0.259165
$250$	−17.2020	−1.08795
$251$	−25.0022	−1.57813	−0.789063	−	0.614312i	$-0.789434\pi$
$251$	−25.0022	−1.57813	−0.789063	+	0.614312i	$0.789434\pi$
$252$	1.92415	0.121210
$253$	−7.04056	−0.442636
$254$	−6.93704	−0.435269
$255$	−2.86538	−0.179437
$256$	5.71409	0.357131
$257$	−27.8190	−1.73530	−0.867649	−	0.497177i	$-0.834370\pi$
$257$	−27.8190	−1.73530	−0.867649	+	0.497177i	$0.834370\pi$
$258$	−7.09491	−0.441710
$259$	−4.97128	−0.308900
$260$	0	0
$261$	11.2264	0.694898
$262$	−9.74481	−0.602036
$263$	−19.1493	−1.18080	−0.590398	−	0.807112i	$-0.701029\pi$
$263$	−19.1493	−1.18080	−0.590398	+	0.807112i	$0.701029\pi$
$264$	1.01146	0.0622508
$265$	18.9358	1.16322
$266$	−0.0110493	−0.000677474 0
$267$	2.51516	0.153925
$268$	1.76632	0.107895
$269$	−5.44006	−0.331686	−0.165843	−	0.986152i	$-0.553035\pi$
$269$	−5.44006	−0.331686	−0.165843	+	0.986152i	$0.553035\pi$
$270$	−7.29783	−0.444132
$271$	15.6373	0.949896	0.474948	−	0.880014i	$-0.342467\pi$
$271$	15.6373	0.949896	0.474948	+	0.880014i	$0.342467\pi$
$272$	15.2218	0.922954
$273$	0	0
$274$	−2.44338	−0.147610
$275$	0.299687	0.0180718
$276$	0.653118	0.0393131
$277$	−18.7400	−1.12598	−0.562989	−	0.826464i	$-0.690349\pi$
$277$	−18.7400	−1.12598	−0.562989	+	0.826464i	$0.690349\pi$
$278$	−11.9244	−0.715180
$279$	3.42315	0.204939
$280$	15.9461	0.952961
$281$	−8.45386	−0.504315	−0.252157	−	0.967686i	$-0.581140\pi$
$281$	−8.45386	−0.504315	−0.252157	+	0.967686i	$0.581140\pi$
$282$	−6.75571	−0.402297
$283$	25.6268	1.52335	0.761677	−	0.647957i	$-0.224376\pi$
$283$	25.6268	1.52335	0.761677	+	0.647957i	$0.224376\pi$
$284$	0.225734	0.0133949
$285$	0.00220033	0.000130336 0
$286$	0	0
$287$	31.7079	1.87166
$288$	3.87571	0.228378
$289$	−5.16478	−0.303810
$290$	−12.7749	−0.750171
$291$	5.52817	0.324067
$292$	0.707757	0.0414184
$293$	−14.3194	−0.836547	−0.418274	−	0.908321i	$-0.637365\pi$
$293$	−14.3194	−0.836547	−0.418274	+	0.908321i	$0.637365\pi$
$294$	0.462749	0.0269881
$295$	11.7882	0.686337
$296$	−4.68502	−0.272311
$297$	2.24835	0.130463
$298$	25.4439	1.47392
$299$	0	0
$300$	−0.0278005	−0.00160506
$301$	34.4607	1.98628
$302$	20.1213	1.15785
$303$	3.47126	0.199419
$304$	−0.0116888	−0.000670399 0
$305$	−8.97687	−0.514014
$306$	14.6915	0.839857
$307$	11.0328	0.629673	0.314836	−	0.949146i	$-0.398050\pi$
$307$	11.0328	0.629673	0.314836	+	0.949146i	$0.398050\pi$
$308$	0.674572	0.0384373
$309$	−3.79612	−0.215954
$310$	−3.89533	−0.221240
$311$	15.8710	0.899961	0.449980	−	0.893038i	$-0.351431\pi$
$311$	15.8710	0.899961	0.449980	+	0.893038i	$0.351431\pi$
$312$	0	0
$313$	6.98609	0.394877	0.197439	−	0.980315i	$-0.436738\pi$
$313$	6.98609	0.394877	0.197439	+	0.980315i	$0.436738\pi$
$314$	−7.22717	−0.407853
$315$	17.2762	0.973405
$316$	0.578647	0.0325514
$317$	3.78365	0.212511	0.106255	−	0.994339i	$-0.466114\pi$
$317$	3.78365	0.212511	0.106255	+	0.994339i	$0.466114\pi$
$318$	5.02362	0.281711
$319$	3.93577	0.220361
$320$	14.7751	0.825951
$321$	−5.57462	−0.311145
$322$	−29.4474	−1.64104
$323$	−0.00908829	−0.000505686 0
$324$	1.85770	0.103206
$325$	0	0
$326$	7.21803	0.399770
$327$	−0.225822	−0.0124880
$328$	29.8821	1.64996
$329$	32.8132	1.80905
$330$	−1.24698	−0.0686440
$331$	−16.7953	−0.923154	−0.461577	−	0.887100i	$-0.652716\pi$
$331$	−16.7953	−0.923154	−0.461577	+	0.887100i	$0.652716\pi$
$332$	2.57040	0.141069
$333$	−5.07582	−0.278153
$334$	−3.74909	−0.205141
$335$	15.8591	0.866473
$336$	4.74876	0.259066
$337$	3.95110	0.215230	0.107615	−	0.994193i	$-0.465679\pi$
$337$	3.95110	0.215230	0.107615	+	0.994193i	$0.465679\pi$
$338$	0	0
$339$	−7.22806	−0.392574
$340$	−1.80097	−0.0976712
$341$	1.20009	0.0649886
$342$	−0.0112816	−0.000610040 0
$343$	17.3080	0.934544
$344$	32.4764	1.75101
$345$	5.86409	0.315712
$346$	29.8066	1.60241
$347$	16.9016	0.907327	0.453664	−	0.891173i	$-0.350117\pi$
$347$	16.9016	0.907327	0.453664	+	0.891173i	$0.350117\pi$
$348$	−0.365102	−0.0195715
$349$	9.96087	0.533193	0.266597	−	0.963808i	$-0.414101\pi$
$349$	9.96087	0.533193	0.266597	+	0.963808i	$0.414101\pi$
$350$	1.25345	0.0669998
$351$	0	0
$352$	1.35875	0.0724215
$353$	−36.9367	−1.96594	−0.982971	−	0.183761i	$-0.941173\pi$
$353$	−36.9367	−1.96594	−0.982971	+	0.183761i	$0.941173\pi$
$354$	3.12738	0.166218
$355$	2.02678	0.107570
$356$	1.58085	0.0837847
$357$	3.69226	0.195415
$358$	−19.9011	−1.05181
$359$	−35.3261	−1.86444	−0.932220	−	0.361891i	$-0.882131\pi$
$359$	−35.3261	−1.86444	−0.932220	+	0.361891i	$0.882131\pi$
$360$	16.2814	0.858106
$361$	−19.0000	−1.00000
$362$	−30.0367	−1.57869
$363$	0.384176	0.0201640
$364$	0	0
$365$	6.35467	0.332619
$366$	−2.38154	−0.124485
$367$	27.9017	1.45646	0.728228	−	0.685335i	$-0.240344\pi$
$367$	27.9017	1.45646	0.728228	+	0.685335i	$0.240344\pi$
$368$	−31.1518	−1.62390
$369$	32.3747	1.68536
$370$	5.77595	0.300278
$371$	−24.4003	−1.26680
$372$	−0.111327	−0.00577201
$373$	−19.2400	−0.996208	−0.498104	−	0.867117i	$-0.665970\pi$
$373$	−19.2400	−0.996208	−0.498104	+	0.867117i	$0.665970\pi$
$374$	5.15056	0.266329
$375$	−4.41411	−0.227944
$376$	30.9237	1.59477
$377$	0	0
$378$	9.40382	0.483680
$379$	30.5430	1.56889	0.784445	−	0.620198i	$-0.212948\pi$
$379$	30.5430	1.56889	0.784445	+	0.620198i	$0.212948\pi$
$380$	0.00138297	7.09447e−5 0
$381$	−1.78007	−0.0911960
$382$	15.2310	0.779284
$383$	4.16658	0.212902	0.106451	−	0.994318i	$-0.466051\pi$
$383$	4.16658	0.212902	0.106451	+	0.994318i	$0.466051\pi$
$384$	4.96378	0.253307
$385$	6.05672	0.308679
$386$	−29.3002	−1.49134
$387$	35.1854	1.78857
$388$	3.47461	0.176397
$389$	23.8172	1.20758	0.603790	−	0.797143i	$-0.293656\pi$
$389$	23.8172	1.20758	0.603790	+	0.797143i	$0.293656\pi$
$390$	0	0
$391$	−24.2212	−1.22492
$392$	−2.11820	−0.106985
$393$	−2.50056	−0.126137
$394$	1.83176	0.0922829
$395$	5.19544	0.261411
$396$	0.688757	0.0346114
$397$	−13.2020	−0.662591	−0.331295	−	0.943527i	$-0.607486\pi$
$397$	−13.2020	−0.662591	−0.331295	+	0.943527i	$0.607486\pi$
$398$	30.4260	1.52512
$399$	−0.00283529	−0.000141942 0
$400$	1.32600	0.0663001
$401$	−30.7848	−1.53732	−0.768660	−	0.639658i	$-0.779076\pi$
$401$	−30.7848	−1.53732	−0.768660	+	0.639658i	$0.779076\pi$
$402$	4.20736	0.209844
$403$	0	0
$404$	2.18178	0.108548
$405$	16.6796	0.828815
$406$	16.4615	0.816971
$407$	−1.77948	−0.0882058
$408$	3.47965	0.172268
$409$	−35.4740	−1.75408	−0.877038	−	0.480421i	$-0.840484\pi$
$409$	−35.4740	−1.75408	−0.877038	+	0.480421i	$0.840484\pi$
$410$	−36.8403	−1.81942
$411$	−0.626981	−0.0309267
$412$	−2.38597	−0.117548
$413$	−15.1900	−0.747452
$414$	−30.0666	−1.47770
$415$	23.0786	1.13288
$416$	0	0
$417$	−3.05986	−0.149842
$418$	−0.00395512	−0.000193451 0
$419$	−15.1531	−0.740275	−0.370138	−	0.928977i	$-0.620689\pi$
$419$	−15.1531	−0.740275	−0.370138	+	0.928977i	$0.620689\pi$
$420$	−0.561851	−0.0274155
$421$	−5.47319	−0.266747	−0.133373	−	0.991066i	$-0.542581\pi$
$421$	−5.47319	−0.266747	−0.133373	+	0.991066i	$0.542581\pi$
$422$	15.1065	0.735372
$423$	33.5032	1.62898
$424$	−22.9952	−1.11675
$425$	1.03099	0.0500106
$426$	0.537698	0.0260516
$427$	11.5674	0.559785
$428$	−3.50380	−0.169363
$429$	0	0
$430$	−40.0387	−1.93084
$431$	−1.73218	−0.0834364	−0.0417182	−	0.999129i	$-0.513283\pi$
$431$	−1.73218	−0.0834364	−0.0417182	+	0.999129i	$0.513283\pi$
$432$	9.94812	0.478629
$433$	−27.4592	−1.31960	−0.659802	−	0.751440i	$-0.729360\pi$
$433$	−27.4592	−1.31960	−0.659802	+	0.751440i	$0.729360\pi$
$434$	5.01943	0.240940
$435$	−3.27811	−0.157173
$436$	−0.141935	−0.00679746
$437$	0.0185995	0.000889734 0
$438$	1.68588	0.0805543
$439$	−12.0741	−0.576266	−0.288133	−	0.957590i	$-0.593035\pi$
$439$	−12.0741	−0.576266	−0.288133	+	0.957590i	$0.593035\pi$
$440$	5.70795	0.272116
$441$	−2.29489	−0.109280
$442$	0	0
$443$	29.7599	1.41393	0.706967	−	0.707247i	$-0.250063\pi$
$443$	29.7599	1.41393	0.706967	+	0.707247i	$0.250063\pi$
$444$	0.165074	0.00783407
$445$	14.1938	0.672851
$446$	28.0861	1.32992
$447$	6.52900	0.308811
$448$	−19.0388	−0.899498
$449$	−1.94243	−0.0916689	−0.0458345	−	0.998949i	$-0.514595\pi$
$449$	−1.94243	−0.0916689	−0.0458345	+	0.998949i	$0.514595\pi$
$450$	1.27981	0.0603309
$451$	11.3500	0.534449
$452$	−4.54304	−0.213686
$453$	5.16321	0.242589
$454$	−1.35032	−0.0633735
$455$	0	0
$456$	−0.00267203	−0.000125129 0
$457$	−25.7961	−1.20669	−0.603345	−	0.797480i	$-0.706166\pi$
$457$	−25.7961	−1.20669	−0.603345	+	0.797480i	$0.706166\pi$
$458$	26.7684	1.25080
$459$	7.73487	0.361033
$460$	3.68574	0.171849
$461$	1.49705	0.0697245	0.0348623	−	0.999392i	$-0.488901\pi$
$461$	1.49705	0.0697245	0.0348623	+	0.999392i	$0.488901\pi$
$462$	1.60683	0.0747565
$463$	12.2575	0.569654	0.284827	−	0.958579i	$-0.408064\pi$
$463$	12.2575	0.569654	0.284827	+	0.958579i	$0.408064\pi$
$464$	17.4143	0.808439
$465$	−0.999558	−0.0463534
$466$	−33.1433	−1.53533
$467$	0.436468	0.0201973	0.0100987	−	0.999949i	$-0.496785\pi$
$467$	0.436468	0.0201973	0.0100987	+	0.999949i	$0.496785\pi$
$468$	0	0
$469$	−20.4356	−0.943629
$470$	−38.1245	−1.75855
$471$	−1.85452	−0.0854519
$472$	−14.3153	−0.658917
$473$	12.3353	0.567179
$474$	1.37834	0.0633091
$475$	−0.000791702 0	−3.63258e−5 0
$476$	2.32069	0.106368
$477$	−24.9134	−1.14071
$478$	31.2301	1.42843
$479$	−4.43855	−0.202803	−0.101401	−	0.994846i	$-0.532333\pi$
$479$	−4.43855	−0.202803	−0.101401	+	0.994846i	$0.532333\pi$
$480$	−1.13170	−0.0516549
$481$	0	0
$482$	−27.1181	−1.23520
$483$	−7.55633	−0.343825
$484$	0.241465	0.0109757
$485$	31.1972	1.41659
$486$	14.5234	0.658796
$487$	−1.65436	−0.0749661	−0.0374831	−	0.999297i	$-0.511934\pi$
$487$	−1.65436	−0.0749661	−0.0374831	+	0.999297i	$0.511934\pi$
$488$	10.9013	0.493479
$489$	1.85218	0.0837583
$490$	2.61143	0.117973
$491$	−26.3383	−1.18863	−0.594316	−	0.804232i	$-0.702577\pi$
$491$	−26.3383	−1.18863	−0.594316	+	0.804232i	$0.702577\pi$
$492$	−1.05288	−0.0474675
$493$	13.5400	0.609810
$494$	0	0
$495$	6.18408	0.277954
$496$	5.30996	0.238424
$497$	−2.61166	−0.117149
$498$	6.12269	0.274364
$499$	−7.80216	−0.349273	−0.174636	−	0.984633i	$-0.555875\pi$
$499$	−7.80216	−0.349273	−0.174636	+	0.984633i	$0.555875\pi$
$500$	−2.77439	−0.124075
$501$	−0.962034	−0.0429805
$502$	−37.4321	−1.67068
$503$	−29.7637	−1.32710	−0.663549	−	0.748133i	$-0.730951\pi$
$503$	−29.7637	−1.32710	−0.663549	+	0.748133i	$0.730951\pi$
$504$	−20.9799	−0.934517
$505$	19.5894	0.871715
$506$	−10.5408	−0.468595
$507$	0	0
$508$	−1.11883	−0.0496399
$509$	17.4922	0.775327	0.387663	−	0.921801i	$-0.373282\pi$
$509$	17.4922	0.775327	0.387663	+	0.921801i	$0.373282\pi$
$510$	−4.28990	−0.189960
$511$	−8.18849	−0.362237
$512$	−17.2863	−0.763954
$513$	−0.00593962	−0.000262241 0
$514$	−41.6492	−1.83707
$515$	−21.4227	−0.943995
$516$	−1.14429	−0.0503744
$517$	11.7456	0.516571
$518$	−7.44276	−0.327016
$519$	7.64851	0.335732
$520$	0	0
$521$	−12.2038	−0.534657	−0.267329	−	0.963605i	$-0.586141\pi$
$521$	−12.2038	−0.534657	−0.267329	+	0.963605i	$0.586141\pi$
$522$	16.8077	0.735652
$523$	23.6800	1.03545	0.517726	−	0.855546i	$-0.326779\pi$
$523$	23.6800	1.03545	0.517726	+	0.855546i	$0.326779\pi$
$524$	−1.57167	−0.0686588
$525$	0.321641	0.0140376
$526$	−28.6694	−1.25004
$527$	4.12860	0.179845
$528$	1.69983	0.0739758
$529$	26.5695	1.15519
$530$	28.3498	1.23144
$531$	−15.5095	−0.673053
$532$	−0.00178206	−7.72620e−5 0
$533$	0	0
$534$	3.76558	0.162952
$535$	−31.4593	−1.36010
$536$	−19.2589	−0.831857
$537$	−5.10671	−0.220371
$538$	−8.14460	−0.351138
$539$	−0.804544	−0.0346542
$540$	−1.17702	−0.0506507
$541$	−3.65841	−0.157287	−0.0786436	−	0.996903i	$-0.525059\pi$
$541$	−3.65841	−0.157287	−0.0786436	+	0.996903i	$0.525059\pi$
$542$	23.4114	1.00560
$543$	−7.70754	−0.330762
$544$	4.67441	0.200414
$545$	−1.27438	−0.0545884
$546$	0	0
$547$	36.8837	1.57703	0.788516	−	0.615014i	$-0.210850\pi$
$547$	36.8837	1.57703	0.788516	+	0.615014i	$0.210850\pi$
$548$	−0.394075	−0.0168340
$549$	11.8106	0.504066
$550$	0.448677	0.0191317
$551$	−0.0103974	−0.000442943 0
$552$	−7.12122	−0.303099
$553$	−6.69473	−0.284689
$554$	−28.0567	−1.19201
$555$	1.48213	0.0629131
$556$	−1.92321	−0.0815622
$557$	−46.6666	−1.97733	−0.988663	−	0.150154i	$-0.952023\pi$
$557$	−46.6666	−1.97733	−0.988663	+	0.150154i	$0.952023\pi$
$558$	5.12498	0.216958
$559$	0	0
$560$	26.7987	1.13245
$561$	1.32166	0.0558003
$562$	−12.6567	−0.533891
$563$	−17.2731	−0.727973	−0.363986	−	0.931404i	$-0.618585\pi$
$563$	−17.2731	−0.727973	−0.363986	+	0.931404i	$0.618585\pi$
$564$	−1.08958	−0.0458796
$565$	−40.7901	−1.71605
$566$	38.3672	1.61269
$567$	−21.4929	−0.902618
$568$	−2.46127	−0.103273
$569$	1.53599	0.0643922	0.0321961	−	0.999482i	$-0.489750\pi$
$569$	1.53599	0.0643922	0.0321961	+	0.999482i	$0.489750\pi$
$570$	0.00329422	0.000137980 0
$571$	−18.8410	−0.788470	−0.394235	−	0.919010i	$-0.628990\pi$
$571$	−18.8410	−0.788470	−0.394235	+	0.919010i	$0.628990\pi$
$572$	0	0
$573$	3.90833	0.163273
$574$	47.4716	1.98143
$575$	−2.10996	−0.0879916
$576$	−19.4392	−0.809965
$577$	30.8134	1.28278	0.641390	−	0.767215i	$-0.278358\pi$
$577$	30.8134	1.28278	0.641390	+	0.767215i	$0.278358\pi$
$578$	−7.73246	−0.321628
$579$	−7.51857	−0.312461
$580$	−2.06038	−0.0855527
$581$	−29.7386	−1.23376
$582$	8.27652	0.343073
$583$	−8.73416	−0.361732
$584$	−7.71697	−0.319331
$585$	0	0
$586$	−21.4383	−0.885608
$587$	42.6917	1.76208	0.881038	−	0.473046i	$-0.156846\pi$
$587$	42.6917	1.76208	0.881038	+	0.473046i	$0.156846\pi$
$588$	0.0746336	0.00307784
$589$	−0.00317036	−0.000130632 0
$590$	17.6488	0.726588
$591$	0.470038	0.0193348
$592$	−7.87355	−0.323601
$593$	24.6037	1.01035	0.505177	−	0.863016i	$-0.331427\pi$
$593$	24.6037	1.01035	0.505177	+	0.863016i	$0.331427\pi$
$594$	3.36613	0.138114
$595$	20.8365	0.854214
$596$	4.10366	0.168092
$597$	7.80744	0.319537
$598$	0	0
$599$	32.6438	1.33379	0.666896	−	0.745151i	$-0.267623\pi$
$599$	32.6438	1.33379	0.666896	+	0.745151i	$0.267623\pi$
$600$	0.303120	0.0123748
$601$	−30.9908	−1.26414	−0.632071	−	0.774910i	$-0.717795\pi$
$601$	−30.9908	−1.26414	−0.632071	+	0.774910i	$0.717795\pi$
$602$	51.5930	2.10277
$603$	−20.8654	−0.849703
$604$	3.24522	0.132046
$605$	2.16802	0.0881426
$606$	5.19700	0.211114
$607$	25.0541	1.01691	0.508457	−	0.861087i	$-0.330216\pi$
$607$	25.0541	1.01691	0.508457	+	0.861087i	$0.330216\pi$
$608$	−0.00358949	−0.000145573 0
$609$	4.22409	0.171169
$610$	−13.4397	−0.544159
$611$	0	0
$612$	2.36949	0.0957809
$613$	−33.7979	−1.36508	−0.682541	−	0.730847i	$-0.739125\pi$
$613$	−33.7979	−1.36508	−0.682541	+	0.730847i	$0.739125\pi$
$614$	16.5177	0.666601
$615$	−9.45339	−0.381198
$616$	−7.35514	−0.296347
$617$	−15.0190	−0.604641	−0.302320	−	0.953206i	$-0.597761\pi$
$617$	−15.0190	−0.604641	−0.302320	+	0.953206i	$0.597761\pi$
$618$	−5.68337	−0.228619
$619$	−25.6083	−1.02928	−0.514642	−	0.857405i	$-0.672075\pi$
$619$	−25.6083	−1.02928	−0.514642	+	0.857405i	$0.672075\pi$
$620$	−0.628250	−0.0252311
$621$	−15.8297	−0.635223
$622$	23.7613	0.952740
$623$	−18.2898	−0.732766
$624$	0	0
$625$	−23.4118	−0.936470
$626$	10.4592	0.418035
$627$	−0.00101490	−4.05313e−5 0
$628$	−1.16562	−0.0465133
$629$	−6.12185	−0.244094
$630$	25.8651	1.03049
$631$	−39.0429	−1.55428	−0.777138	−	0.629331i	$-0.783329\pi$
$631$	−39.0429	−1.55428	−0.777138	+	0.629331i	$0.783329\pi$
$632$	−6.30923	−0.250968
$633$	3.87639	0.154073
$634$	5.66470	0.224974
$635$	−10.0455	−0.398643
$636$	0.810225	0.0321275
$637$	0	0
$638$	5.89245	0.233284
$639$	−2.66658	−0.105488
$640$	28.0121	1.10728
$641$	1.75840	0.0694524	0.0347262	−	0.999397i	$-0.488944\pi$
$641$	1.75840	0.0694524	0.0347262	+	0.999397i	$0.488944\pi$
$642$	−8.34606	−0.329393
$643$	−2.16409	−0.0853435	−0.0426718	−	0.999089i	$-0.513587\pi$
$643$	−2.16409	−0.0853435	−0.0426718	+	0.999089i	$0.513587\pi$
$644$	−4.74936	−0.187151
$645$	−10.2741	−0.404543
$646$	−0.0136066	−0.000535343 0
$647$	−16.1248	−0.633933	−0.316966	−	0.948437i	$-0.602664\pi$
$647$	−16.1248	−0.633933	−0.316966	+	0.948437i	$0.602664\pi$
$648$	−20.2553	−0.795704
$649$	−5.43732	−0.213433
$650$	0	0
$651$	1.28801	0.0504810
$652$	1.16414	0.0455914
$653$	15.5530	0.608636	0.304318	−	0.952570i	$-0.401571\pi$
$653$	15.5530	0.608636	0.304318	+	0.952570i	$0.401571\pi$
$654$	−0.338089	−0.0132203
$655$	−14.1114	−0.551379
$656$	50.2193	1.96073
$657$	−8.36068	−0.326181
$658$	49.1264	1.91515
$659$	17.4597	0.680134	0.340067	−	0.940401i	$-0.389550\pi$
$659$	17.4597	0.680134	0.340067	+	0.940401i	$0.389550\pi$
$660$	−0.201117	−0.00782845
$661$	−28.8839	−1.12345	−0.561726	−	0.827323i	$-0.689863\pi$
$661$	−28.8839	−1.12345	−0.561726	+	0.827323i	$0.689863\pi$
$662$	−25.1451	−0.977293
$663$	0	0
$664$	−28.0261	−1.08763
$665$	−0.0160004	−0.000620469 0
$666$	−7.59927	−0.294466
$667$	−27.7100	−1.07294
$668$	−0.604665	−0.0233952
$669$	7.20701	0.278639
$670$	23.7434	0.917289
$671$	4.14058	0.159845
$672$	1.45829	0.0562546
$673$	18.2507	0.703513	0.351756	−	0.936092i	$-0.385585\pi$
$673$	18.2507	0.703513	0.351756	+	0.936092i	$0.385585\pi$
$674$	5.91539	0.227852
$675$	0.673802	0.0259347
$676$	0	0
$677$	33.3938	1.28343	0.641714	−	0.766944i	$-0.278224\pi$
$677$	33.3938	1.28343	0.641714	+	0.766944i	$0.278224\pi$
$678$	−10.8215	−0.415597
$679$	−40.1999	−1.54273
$680$	19.6367	0.753033
$681$	−0.346497	−0.0132778
$682$	1.79672	0.0688000
$683$	17.1675	0.656896	0.328448	−	0.944522i	$-0.393474\pi$
$683$	17.1675	0.656896	0.328448	+	0.944522i	$0.393474\pi$
$684$	−0.00181953	−6.95716e−5 0
$685$	−3.53824	−0.135189
$686$	25.9127	0.989352
$687$	6.86888	0.262064
$688$	54.5792	2.08081
$689$	0	0
$690$	8.77943	0.334227
$691$	−4.44294	−0.169017	−0.0845087	−	0.996423i	$-0.526932\pi$
$691$	−4.44294	−0.169017	−0.0845087	+	0.996423i	$0.526932\pi$
$692$	4.80730	0.182746
$693$	−7.96866	−0.302705
$694$	25.3043	0.960539
$695$	−17.2677	−0.655002
$696$	3.98086	0.150894
$697$	39.0465	1.47899
$698$	14.9129	0.564463
$699$	−8.50471	−0.321678
$700$	0.202160	0.00764095
$701$	46.9475	1.77318	0.886591	−	0.462555i	$-0.153067\pi$
$701$	46.9475	1.77318	0.886591	+	0.462555i	$0.153067\pi$
$702$	0	0
$703$	0.00470098	0.000177301 0
$704$	−6.81500	−0.256850
$705$	−9.78292	−0.368446
$706$	−55.2999	−2.08124
$707$	−25.2424	−0.949338
$708$	0.504393	0.0189563
$709$	41.1605	1.54581	0.772907	−	0.634520i	$-0.218802\pi$
$709$	41.1605	1.54581	0.772907	+	0.634520i	$0.218802\pi$
$710$	3.03439	0.113879
$711$	−6.83551	−0.256352
$712$	−17.2366	−0.645970
$713$	−8.44932	−0.316429
$714$	5.52787	0.206875
$715$	0	0
$716$	−3.20971	−0.119953
$717$	8.01378	0.299280
$718$	−52.8886	−1.97378
$719$	−25.2781	−0.942713	−0.471357	−	0.881943i	$-0.656236\pi$
$719$	−25.2781	−0.942713	−0.471357	+	0.881943i	$0.656236\pi$
$720$	27.3622	1.01973
$721$	27.6047	1.02805
$722$	−28.4459	−1.05865
$723$	−6.95862	−0.258794
$724$	−4.84440	−0.180041
$725$	1.17950	0.0438055
$726$	0.575170	0.0213465
$727$	−22.9344	−0.850589	−0.425294	−	0.905055i	$-0.639829\pi$
$727$	−22.9344	−0.850589	−0.425294	+	0.905055i	$0.639829\pi$
$728$	0	0
$729$	−19.3536	−0.716801
$730$	9.51392	0.352126
$731$	42.4364	1.56957
$732$	−0.384101	−0.0141968
$733$	−31.4075	−1.16006	−0.580031	−	0.814594i	$-0.696960\pi$
$733$	−31.4075	−1.16006	−0.580031	+	0.814594i	$0.696960\pi$
$734$	41.7731	1.54187
$735$	0.670106	0.0247172
$736$	−9.56635	−0.352620
$737$	−7.31500	−0.269451
$738$	48.4699	1.78420
$739$	36.7778	1.35289	0.676446	−	0.736492i	$-0.263519\pi$
$739$	36.7778	1.35289	0.676446	+	0.736492i	$0.263519\pi$
$740$	0.931563	0.0342449
$741$	0	0
$742$	−36.5309	−1.34109
$743$	−0.773833	−0.0283892	−0.0141946	−	0.999899i	$-0.504518\pi$
$743$	−0.773833	−0.0283892	−0.0141946	+	0.999899i	$0.504518\pi$
$744$	1.21384	0.0445015
$745$	36.8451	1.34990
$746$	−28.8052	−1.05463
$747$	−30.3639	−1.11096
$748$	0.830697	0.0303733
$749$	40.5377	1.48122
$750$	−6.60860	−0.241312
$751$	−49.5628	−1.80857	−0.904287	−	0.426926i	$-0.859596\pi$
$751$	−49.5628	−1.80857	−0.904287	+	0.426926i	$0.859596\pi$
$752$	51.9699	1.89515
$753$	−9.60525	−0.350035
$754$	0	0
$755$	29.1376	1.06042
$756$	1.51668	0.0551610
$757$	−38.6273	−1.40393	−0.701966	−	0.712210i	$-0.747694\pi$
$757$	−38.6273	−1.40393	−0.701966	+	0.712210i	$0.747694\pi$
$758$	45.7276	1.66090
$759$	−2.70481	−0.0981785
$760$	−0.0150791	−0.000546975 0
$761$	43.4822	1.57623	0.788114	−	0.615530i	$-0.211058\pi$
$761$	43.4822	1.57623	0.788114	+	0.615530i	$0.211058\pi$
$762$	−2.66504	−0.0965443
$763$	1.64214	0.0594493
$764$	2.45649	0.0888728
$765$	21.2747	0.769188
$766$	6.23800	0.225388
$767$	0	0
$768$	2.19521	0.0792130
$769$	−5.59789	−0.201865	−0.100933	−	0.994893i	$-0.532183\pi$
$769$	−5.59789	−0.201865	−0.100933	+	0.994893i	$0.532183\pi$
$770$	9.06783	0.326782
$771$	−10.6874	−0.384896
$772$	−4.72563	−0.170079
$773$	35.3654	1.27201	0.636003	−	0.771687i	$-0.280587\pi$
$773$	35.3654	1.27201	0.636003	+	0.771687i	$0.280587\pi$
$774$	52.6779	1.89347
$775$	0.359652	0.0129191
$776$	−37.8851	−1.36000
$777$	−1.90984	−0.0685153
$778$	35.6580	1.27840
$779$	−0.0299839	−0.00107428
$780$	0	0
$781$	−0.934852	−0.0334516
$782$	−36.2628	−1.29676
$783$	8.84900	0.316238
$784$	−3.55981	−0.127136
$785$	−10.4656	−0.373535
$786$	−3.74372	−0.133534
$787$	−1.82708	−0.0651284	−0.0325642	−	0.999470i	$-0.510367\pi$
$787$	−1.82708	−0.0651284	−0.0325642	+	0.999470i	$0.510367\pi$
$788$	0.295432	0.0105243
$789$	−7.35669	−0.261905
$790$	7.77837	0.276742
$791$	52.5612	1.86886
$792$	−7.50981	−0.266849
$793$	0	0
$794$	−19.7654	−0.701449
$795$	7.27469	0.258007
$796$	4.90719	0.173931
$797$	14.2533	0.504878	0.252439	−	0.967613i	$-0.418767\pi$
$797$	14.2533	0.504878	0.252439	+	0.967613i	$0.418767\pi$
$798$	−0.00424486	−0.000150266 0
$799$	40.4076	1.42952
$800$	0.407199	0.0143967
$801$	−18.6744	−0.659829
$802$	−46.0895	−1.62748
$803$	−2.93110	−0.103436
$804$	0.678576	0.0239315
$805$	−42.6427	−1.50296
$806$	0	0
$807$	−2.08994	−0.0735693
$808$	−23.7889	−0.836890
$809$	−22.2046	−0.780671	−0.390336	−	0.920673i	$-0.627641\pi$
$809$	−22.2046	−0.780671	−0.390336	+	0.920673i	$0.627641\pi$
$810$	24.9719	0.877423
$811$	6.76128	0.237421	0.118710	−	0.992929i	$-0.462124\pi$
$811$	6.76128	0.237421	0.118710	+	0.992929i	$0.462124\pi$
$812$	2.65496	0.0931708
$813$	6.00746	0.210691
$814$	−2.66416	−0.0933788
$815$	10.4524	0.366131
$816$	5.84783	0.204715
$817$	−0.0325870	−0.00114008
$818$	−53.1100	−1.85695
$819$	0	0
$820$	−5.94172	−0.207494
$821$	20.2315	0.706084	0.353042	−	0.935607i	$-0.385147\pi$
$821$	20.2315	0.706084	0.353042	+	0.935607i	$0.385147\pi$
$822$	−0.938686	−0.0327404
$823$	−10.0598	−0.350664	−0.175332	−	0.984509i	$-0.556100\pi$
$823$	−10.0598	−0.350664	−0.175332	+	0.984509i	$0.556100\pi$
$824$	26.0152	0.906282
$825$	0.115133	0.00400840
$826$	−22.7418	−0.791288
$827$	22.9872	0.799345	0.399672	−	0.916658i	$-0.369124\pi$
$827$	22.9872	0.799345	0.399672	+	0.916658i	$0.369124\pi$
$828$	−4.84924	−0.168523
$829$	−41.5027	−1.44145	−0.720723	−	0.693223i	$-0.756190\pi$
$829$	−41.5027	−1.44145	−0.720723	+	0.693223i	$0.756190\pi$
$830$	34.5522	1.19932
$831$	−7.19946	−0.249747
$832$	0	0
$833$	−2.76782	−0.0958993
$834$	−4.58108	−0.158630
$835$	−5.42905	−0.187880
$836$	−0.000637894 0	−2.20620e−5 0
$837$	2.69823	0.0932645
$838$	−22.6864	−0.783690
$839$	−21.5867	−0.745254	−0.372627	−	0.927981i	$-0.621543\pi$
$839$	−21.5867	−0.745254	−0.372627	+	0.927981i	$0.621543\pi$
$840$	6.12610	0.211371
$841$	−13.5097	−0.465852
$842$	−8.19420	−0.282391
$843$	−3.24777	−0.111859
$844$	2.43642	0.0838649
$845$	0	0
$846$	50.1595	1.72452
$847$	−2.79366	−0.0959913
$848$	−38.6454	−1.32709
$849$	9.84519	0.337886
$850$	1.54356	0.0529435
$851$	12.5286	0.429474
$852$	0.0867216	0.00297103
$853$	11.4330	0.391459	0.195730	−	0.980658i	$-0.437293\pi$
$853$	11.4330	0.391459	0.195730	+	0.980658i	$0.437293\pi$
$854$	17.3181	0.592615
$855$	−0.0163369	−0.000558709 0
$856$	38.2034	1.30577
$857$	−25.1941	−0.860614	−0.430307	−	0.902683i	$-0.641595\pi$
$857$	−25.1941	−0.860614	−0.430307	+	0.902683i	$0.641595\pi$
$858$	0	0
$859$	−15.2249	−0.519465	−0.259733	−	0.965681i	$-0.583634\pi$
$859$	−15.2249	−0.519465	−0.259733	+	0.965681i	$0.583634\pi$
$860$	−6.45756	−0.220201
$861$	12.1814	0.415142
$862$	−2.59334	−0.0883296
$863$	−51.4798	−1.75239	−0.876196	−	0.481954i	$-0.839927\pi$
$863$	−51.4798	−1.75239	−0.876196	+	0.481954i	$0.839927\pi$
$864$	3.05495	0.103931
$865$	43.1628	1.46758
$866$	−41.1106	−1.39699
$867$	−1.98418	−0.0673864
$868$	0.809548	0.0274779
$869$	−2.39640	−0.0812923
$870$	−4.90782	−0.166391
$871$	0	0
$872$	1.54758	0.0524076
$873$	−41.0453	−1.38917
$874$	0.0278463	0.000941914 0
$875$	32.0987	1.08513
$876$	0.271903	0.00918676
$877$	−18.8168	−0.635399	−0.317699	−	0.948191i	$-0.602910\pi$
$877$	−18.8168	−0.635399	−0.317699	+	0.948191i	$0.602910\pi$
$878$	−18.0768	−0.610062
$879$	−5.50116	−0.185550
$880$	9.59268	0.323369
$881$	−21.3990	−0.720951	−0.360476	−	0.932769i	$-0.617386\pi$
$881$	−21.3990	−0.720951	−0.360476	+	0.932769i	$0.617386\pi$
$882$	−3.43580	−0.115689
$883$	−6.84791	−0.230451	−0.115225	−	0.993339i	$-0.536759\pi$
$883$	−6.84791	−0.230451	−0.115225	+	0.993339i	$0.536759\pi$
$884$	0	0
$885$	4.52875	0.152232
$886$	44.5550	1.49686
$887$	−35.6454	−1.19685	−0.598427	−	0.801177i	$-0.704207\pi$
$887$	−35.6454	−1.19685	−0.598427	+	0.801177i	$0.704207\pi$
$888$	−1.79987	−0.0603997
$889$	12.9444	0.434141
$890$	21.2503	0.712311
$891$	−7.69346	−0.257741
$892$	4.52981	0.151669
$893$	−0.0310291	−0.00103835
$894$	9.77491	0.326922
$895$	−28.8187	−0.963304
$896$	−36.0957	−1.20587
$897$	0	0
$898$	−2.90811	−0.0970450
$899$	4.72329	0.157530
$900$	0.206412	0.00688039
$901$	−30.0476	−1.00103
$902$	16.9926	0.565792
$903$	13.2390	0.440566
$904$	49.5346	1.64750
$905$	−43.4960	−1.44586
$906$	7.73011	0.256816
$907$	53.7936	1.78619	0.893094	−	0.449870i	$-0.148530\pi$
$907$	53.7936	1.78619	0.893094	+	0.449870i	$0.148530\pi$
$908$	−0.217783	−0.00722739
$909$	−25.7732	−0.854844
$910$	0	0
$911$	13.8124	0.457626	0.228813	−	0.973470i	$-0.426516\pi$
$911$	13.8124	0.457626	0.228813	+	0.973470i	$0.426516\pi$
$912$	−0.00449056	−0.000148697 0
$913$	−10.6450	−0.352299
$914$	−38.6207	−1.27746
$915$	−3.44870	−0.114010
$916$	4.31728	0.142647
$917$	18.1836	0.600477
$918$	11.5803	0.382206
$919$	3.46200	0.114201	0.0571005	−	0.998368i	$-0.481814\pi$
$919$	3.46200	0.114201	0.0571005	+	0.998368i	$0.481814\pi$
$920$	−40.1872	−1.32493
$921$	4.23852	0.139664
$922$	2.24131	0.0738136
$923$	0	0
$924$	0.259154	0.00852555
$925$	−0.533289	−0.0175344
$926$	18.3513	0.603062
$927$	28.1852	0.925725
$928$	5.34772	0.175548
$929$	−51.2384	−1.68108	−0.840539	−	0.541751i	$-0.817761\pi$
$929$	−51.2384	−1.68108	−0.840539	+	0.541751i	$0.817761\pi$
$930$	−1.49649	−0.0490718
$931$	0.00212541	6.96576e−5 0
$932$	−5.34545	−0.175096
$933$	6.09725	0.199615
$934$	0.653460	0.0213819
$935$	7.45850	0.243919
$936$	0	0
$937$	−27.3145	−0.892327	−0.446163	−	0.894952i	$-0.647210\pi$
$937$	−27.3145	−0.892327	−0.446163	+	0.894952i	$0.647210\pi$
$938$	−30.5952	−0.998970
$939$	2.68389	0.0875853
$940$	−6.14884	−0.200553
$941$	−38.4740	−1.25422	−0.627109	−	0.778932i	$-0.715762\pi$
$941$	−38.4740	−1.25422	−0.627109	+	0.778932i	$0.715762\pi$
$942$	−2.77650	−0.0904634
$943$	−79.9101	−2.60223
$944$	−24.0581	−0.783024
$945$	13.6176	0.442982
$946$	18.4679	0.600442
$947$	22.4650	0.730013	0.365006	−	0.931005i	$-0.381067\pi$
$947$	22.4650	0.730013	0.365006	+	0.931005i	$0.381067\pi$
$948$	0.222302	0.00722003
$949$	0	0
$950$	−0.00118530	−3.84562e−5 0
$951$	1.45359	0.0471357
$952$	−25.3034	−0.820088
$953$	22.6500	0.733706	0.366853	−	0.930279i	$-0.380435\pi$
$953$	22.6500	0.733706	0.366853	+	0.930279i	$0.380435\pi$
$954$	−37.2991	−1.20760
$955$	22.0559	0.713712
$956$	5.03688	0.162904
$957$	1.51203	0.0488769
$958$	−6.64519	−0.214696
$959$	4.55930	0.147227
$960$	5.67622	0.183199
$961$	−29.5598	−0.953541
$962$	0	0
$963$	41.3902	1.33378
$964$	−4.37368	−0.140867
$965$	−42.4296	−1.36586
$966$	−11.3130	−0.363989
$967$	−43.7978	−1.40844	−0.704221	−	0.709980i	$-0.748704\pi$
$967$	−43.7978	−1.40844	−0.704221	+	0.709980i	$0.748704\pi$
$968$	−2.63279	−0.0846212
$969$	−0.00349150	−0.000112163 0
$970$	46.7069	1.49967
$971$	20.8123	0.667898	0.333949	−	0.942591i	$-0.391619\pi$
$971$	20.8123	0.667898	0.333949	+	0.942591i	$0.391619\pi$
$972$	2.34238	0.0751319
$973$	22.2508	0.713328
$974$	−2.47683	−0.0793626
$975$	0	0
$976$	18.3205	0.586426
$977$	47.0331	1.50472	0.752362	−	0.658750i	$-0.228915\pi$
$977$	47.0331	1.50472	0.752362	+	0.658750i	$0.228915\pi$
$978$	2.77299	0.0886705
$979$	−6.54690	−0.209240
$980$	0.421180	0.0134541
$981$	1.67667	0.0535319
$982$	−39.4325	−1.25834
$983$	1.76715	0.0563632	0.0281816	−	0.999603i	$-0.491028\pi$
$983$	1.76715	0.0563632	0.0281816	+	0.999603i	$0.491028\pi$
$984$	11.4800	0.365969
$985$	2.65257	0.0845179
$986$	20.2714	0.645573
$987$	12.6060	0.401255
$988$	0	0
$989$	−86.8476	−2.76159
$990$	9.25851	0.294255
$991$	0.486544	0.0154556	0.00772778	−	0.999970i	$-0.497540\pi$
$991$	0.486544	0.0154556	0.00772778	+	0.999970i	$0.497540\pi$
$992$	1.63062	0.0517723
$993$	−6.45235	−0.204759
$994$	−3.91005	−0.124019
$995$	44.0598	1.39679
$996$	0.987485	0.0312897
$997$	−3.64798	−0.115533	−0.0577663	−	0.998330i	$-0.518398\pi$
$997$	−3.64798	−0.115533	−0.0577663	+	0.998330i	$0.518398\pi$
$998$	−11.6810	−0.369756
$999$	−4.00091	−0.126583

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.r.1.8	yes	9
13.12	even	2		1859.2.a.q.1.2	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.2.a.q.1.2	✓	9	13.12	even	2
1859.2.a.r.1.8	yes	9	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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q+1.49715 q^{2} +0.384176 q^{3} +0.241465 q^{4} +2.16802 q^{5} +0.575170 q^{6} -2.79366 q^{7} -2.63279 q^{8} -2.85241 q^{9} +O(q^{10})\)	\(q+1.49715 q^{2} +0.384176 q^{3} +0.241465 q^{4} +2.16802 q^{5} +0.575170 q^{6} -2.79366 q^{7} -2.63279 q^{8} -2.85241 q^{9} +3.24586 q^{10} -1.00000 q^{11} +0.0927650 q^{12} -4.18254 q^{14} +0.832901 q^{15} -4.42462 q^{16} -3.44024 q^{17} -4.27049 q^{18} +0.00264176 q^{19} +0.523501 q^{20} -1.07326 q^{21} -1.49715 q^{22} +7.04056 q^{23} -1.01146 q^{24} -0.299687 q^{25} -2.24835 q^{27} -0.674572 q^{28} -3.93577 q^{29} +1.24698 q^{30} -1.20009 q^{31} -1.35875 q^{32} -0.384176 q^{33} -5.15056 q^{34} -6.05672 q^{35} -0.688757 q^{36} +1.77948 q^{37} +0.00395512 q^{38} -5.70795 q^{40} -11.3500 q^{41} -1.60683 q^{42} -12.3353 q^{43} -0.241465 q^{44} -6.18408 q^{45} +10.5408 q^{46} -11.7456 q^{47} -1.69983 q^{48} +0.804544 q^{49} -0.448677 q^{50} -1.32166 q^{51} +8.73416 q^{53} -3.36613 q^{54} -2.16802 q^{55} +7.35514 q^{56} +0.00101490 q^{57} -5.89245 q^{58} +5.43732 q^{59} +0.201117 q^{60} -4.14058 q^{61} -1.79672 q^{62} +7.96866 q^{63} +6.81500 q^{64} -0.575170 q^{66} +7.31500 q^{67} -0.830697 q^{68} +2.70481 q^{69} -9.06783 q^{70} +0.934852 q^{71} +7.50981 q^{72} +2.93110 q^{73} +2.66416 q^{74} -0.115133 q^{75} +0.000637894 q^{76} +2.79366 q^{77} +2.39640 q^{79} -9.59268 q^{80} +7.69346 q^{81} -16.9926 q^{82} +10.6450 q^{83} -0.259154 q^{84} -7.45850 q^{85} -18.4679 q^{86} -1.51203 q^{87} +2.63279 q^{88} +6.54690 q^{89} -9.25851 q^{90} +1.70005 q^{92} -0.461046 q^{93} -17.5849 q^{94} +0.00572740 q^{95} -0.521998 q^{96} +14.3897 q^{97} +1.20453 q^{98} +2.85241 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 5 q^{3} + 2 q^{4} + 4 q^{5} + 11 q^{6} - q^{7} - 3 q^{8} + 2 q^{9}+O(q^{10}) \) 9 * q - 5 * q^3 + 2 * q^4 + 4 * q^5 + 11 * q^6 - q^7 - 3 * q^8 + 2 * q^9	\( 9 q - 5 q^{3} + 2 q^{4} + 4 q^{5} + 11 q^{6} - q^{7} - 3 q^{8} + 2 q^{9} - 8 q^{10} - 9 q^{11} - 9 q^{12} - 3 q^{15} - 8 q^{16} - 8 q^{17} - 27 q^{18} + q^{19} - 12 q^{20} - 17 q^{21} + 6 q^{24} - 15 q^{25} - 23 q^{27} - 11 q^{28} - 22 q^{29} - 3 q^{30} + 6 q^{31} + 19 q^{32} + 5 q^{33} - 10 q^{34} - 15 q^{35} + 7 q^{36} + 15 q^{37} + q^{38} - 3 q^{40} - 10 q^{41} + 2 q^{42} - 19 q^{43} - 2 q^{44} + 2 q^{45} - 19 q^{46} + 2 q^{47} + 6 q^{48} - 20 q^{49} + 17 q^{50} - 2 q^{51} - 5 q^{53} + 27 q^{54} - 4 q^{55} - 16 q^{56} + 32 q^{57} + 11 q^{58} + 11 q^{59} + 6 q^{60} - 68 q^{61} - 21 q^{62} + 29 q^{63} - 23 q^{64} - 11 q^{66} - 5 q^{67} + 16 q^{68} - 34 q^{69} + 5 q^{70} + 34 q^{71} - 13 q^{72} - 26 q^{73} + q^{74} + 10 q^{75} + 11 q^{76} + q^{77} - 32 q^{79} - 8 q^{80} + 13 q^{81} - 42 q^{82} - 8 q^{83} + 13 q^{84} - 23 q^{85} - 30 q^{86} + 10 q^{87} + 3 q^{88} + 37 q^{89} + 21 q^{90} - 12 q^{92} - 20 q^{93} - 12 q^{94} - 4 q^{95} - 60 q^{96} - 3 q^{97} + 9 q^{98} - 2 q^{99}+O(q^{100}) \) 9 * q - 5 * q^3 + 2 * q^4 + 4 * q^5 + 11 * q^6 - q^7 - 3 * q^8 + 2 * q^9 - 8 * q^10 - 9 * q^11 - 9 * q^12 - 3 * q^15 - 8 * q^16 - 8 * q^17 - 27 * q^18 + q^19 - 12 * q^20 - 17 * q^21 + 6 * q^24 - 15 * q^25 - 23 * q^27 - 11 * q^28 - 22 * q^29 - 3 * q^30 + 6 * q^31 + 19 * q^32 + 5 * q^33 - 10 * q^34 - 15 * q^35 + 7 * q^36 + 15 * q^37 + q^38 - 3 * q^40 - 10 * q^41 + 2 * q^42 - 19 * q^43 - 2 * q^44 + 2 * q^45 - 19 * q^46 + 2 * q^47 + 6 * q^48 - 20 * q^49 + 17 * q^50 - 2 * q^51 - 5 * q^53 + 27 * q^54 - 4 * q^55 - 16 * q^56 + 32 * q^57 + 11 * q^58 + 11 * q^59 + 6 * q^60 - 68 * q^61 - 21 * q^62 + 29 * q^63 - 23 * q^64 - 11 * q^66 - 5 * q^67 + 16 * q^68 - 34 * q^69 + 5 * q^70 + 34 * q^71 - 13 * q^72 - 26 * q^73 + q^74 + 10 * q^75 + 11 * q^76 + q^77 - 32 * q^79 - 8 * q^80 + 13 * q^81 - 42 * q^82 - 8 * q^83 + 13 * q^84 - 23 * q^85 - 30 * q^86 + 10 * q^87 + 3 * q^88 + 37 * q^89 + 21 * q^90 - 12 * q^92 - 20 * q^93 - 12 * q^94 - 4 * q^95 - 60 * q^96 - 3 * q^97 + 9 * q^98 - 2 * q^99

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