LMFDB - Embedded newform 2001.2.a.i.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.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:	$15.9780654445$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 5x^{5} + 18x^{4} + 4x^{3} - 26x^{2} + x + 8 $ x^7 - 3x^6 - 5x^5 + 18x^4 + 4x^3 - 26*x^2 + x + 8
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			1.6
Root			$-1.21072$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.21072 q^{2} +1.00000 q^{3} -0.534159 q^{4} +3.03795 q^{5} +1.21072 q^{6} -3.40847 q^{7} -3.06816 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.21072 q^{2} +1.00000 q^{3} -0.534159 q^{4} +3.03795 q^{5} +1.21072 q^{6} -3.40847 q^{7} -3.06816 q^{8} +1.00000 q^{9} +3.67810 q^{10} -3.85707 q^{11} -0.534159 q^{12} -5.15691 q^{13} -4.12670 q^{14} +3.03795 q^{15} -2.64635 q^{16} -2.07488 q^{17} +1.21072 q^{18} -0.0953170 q^{19} -1.62275 q^{20} -3.40847 q^{21} -4.66983 q^{22} +1.00000 q^{23} -3.06816 q^{24} +4.22914 q^{25} -6.24357 q^{26} +1.00000 q^{27} +1.82067 q^{28} -1.00000 q^{29} +3.67810 q^{30} -3.70527 q^{31} +2.93232 q^{32} -3.85707 q^{33} -2.51210 q^{34} -10.3548 q^{35} -0.534159 q^{36} -8.24097 q^{37} -0.115402 q^{38} -5.15691 q^{39} -9.32090 q^{40} +4.31059 q^{41} -4.12670 q^{42} +2.81904 q^{43} +2.06029 q^{44} +3.03795 q^{45} +1.21072 q^{46} -2.48043 q^{47} -2.64635 q^{48} +4.61770 q^{49} +5.12030 q^{50} -2.07488 q^{51} +2.75461 q^{52} -6.40448 q^{53} +1.21072 q^{54} -11.7176 q^{55} +10.4577 q^{56} -0.0953170 q^{57} -1.21072 q^{58} -10.8564 q^{59} -1.62275 q^{60} +5.67822 q^{61} -4.48604 q^{62} -3.40847 q^{63} +8.84292 q^{64} -15.6664 q^{65} -4.66983 q^{66} +12.8177 q^{67} +1.10832 q^{68} +1.00000 q^{69} -12.5367 q^{70} -2.25971 q^{71} -3.06816 q^{72} +14.0533 q^{73} -9.97750 q^{74} +4.22914 q^{75} +0.0509145 q^{76} +13.1467 q^{77} -6.24357 q^{78} +0.679730 q^{79} -8.03950 q^{80} +1.00000 q^{81} +5.21891 q^{82} +4.99221 q^{83} +1.82067 q^{84} -6.30339 q^{85} +3.41307 q^{86} -1.00000 q^{87} +11.8341 q^{88} +8.87404 q^{89} +3.67810 q^{90} +17.5772 q^{91} -0.534159 q^{92} -3.70527 q^{93} -3.00310 q^{94} -0.289568 q^{95} +2.93232 q^{96} +12.0257 q^{97} +5.59073 q^{98} -3.85707 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 3 q^{2} + 7 q^{3} + 5 q^{4} - 3 q^{5} - 3 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 3 * q^2 + 7 * q^3 + 5 * q^4 - 3 * q^5 - 3 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9	\( 7 q - 3 q^{2} + 7 q^{3} + 5 q^{4} - 3 q^{5} - 3 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9} + 3 q^{10} - 4 q^{11} + 5 q^{12} - 18 q^{13} - 2 q^{14} - 3 q^{15} - 7 q^{16} - 3 q^{17} - 3 q^{18} - 4 q^{19} - 2 q^{20} - 5 q^{21} - 26 q^{22} + 7 q^{23} - 6 q^{24} - 8 q^{25} - 7 q^{26} + 7 q^{27} - 6 q^{28} - 7 q^{29} + 3 q^{30} - 22 q^{31} + 5 q^{32} - 4 q^{33} + 9 q^{34} + 3 q^{35} + 5 q^{36} - 25 q^{37} + 14 q^{38} - 18 q^{39} - 10 q^{40} - 13 q^{41} - 2 q^{42} - 2 q^{43} + 4 q^{44} - 3 q^{45} - 3 q^{46} - 25 q^{47} - 7 q^{48} - 8 q^{49} + 19 q^{50} - 3 q^{51} - 12 q^{52} - 5 q^{53} - 3 q^{54} - 15 q^{55} + 18 q^{56} - 4 q^{57} + 3 q^{58} + 11 q^{59} - 2 q^{60} - 33 q^{61} + 28 q^{62} - 5 q^{63} - 14 q^{64} - 2 q^{65} - 26 q^{66} + 8 q^{67} + 12 q^{68} + 7 q^{69} - 22 q^{70} - 6 q^{71} - 6 q^{72} + 15 q^{73} + 34 q^{74} - 8 q^{75} - 28 q^{76} - q^{77} - 7 q^{78} - 15 q^{79} - 12 q^{80} + 7 q^{81} - 14 q^{82} + 21 q^{83} - 6 q^{84} - 28 q^{85} - 12 q^{86} - 7 q^{87} - 13 q^{88} + 8 q^{89} + 3 q^{90} + 6 q^{91} + 5 q^{92} - 22 q^{93} - 35 q^{94} - 25 q^{95} + 5 q^{96} + 13 q^{97} + q^{98} - 4 q^{99}+O(q^{100}) \) 7 * q - 3 * q^2 + 7 * q^3 + 5 * q^4 - 3 * q^5 - 3 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9 + 3 * q^10 - 4 * q^11 + 5 * q^12 - 18 * q^13 - 2 * q^14 - 3 * q^15 - 7 * q^16 - 3 * q^17 - 3 * q^18 - 4 * q^19 - 2 * q^20 - 5 * q^21 - 26 * q^22 + 7 * q^23 - 6 * q^24 - 8 * q^25 - 7 * q^26 + 7 * q^27 - 6 * q^28 - 7 * q^29 + 3 * q^30 - 22 * q^31 + 5 * q^32 - 4 * q^33 + 9 * q^34 + 3 * q^35 + 5 * q^36 - 25 * q^37 + 14 * q^38 - 18 * q^39 - 10 * q^40 - 13 * q^41 - 2 * q^42 - 2 * q^43 + 4 * q^44 - 3 * q^45 - 3 * q^46 - 25 * q^47 - 7 * q^48 - 8 * q^49 + 19 * q^50 - 3 * q^51 - 12 * q^52 - 5 * q^53 - 3 * q^54 - 15 * q^55 + 18 * q^56 - 4 * q^57 + 3 * q^58 + 11 * q^59 - 2 * q^60 - 33 * q^61 + 28 * q^62 - 5 * q^63 - 14 * q^64 - 2 * q^65 - 26 * q^66 + 8 * q^67 + 12 * q^68 + 7 * q^69 - 22 * q^70 - 6 * q^71 - 6 * q^72 + 15 * q^73 + 34 * q^74 - 8 * q^75 - 28 * q^76 - q^77 - 7 * q^78 - 15 * q^79 - 12 * q^80 + 7 * q^81 - 14 * q^82 + 21 * q^83 - 6 * q^84 - 28 * q^85 - 12 * q^86 - 7 * q^87 - 13 * q^88 + 8 * q^89 + 3 * q^90 + 6 * q^91 + 5 * q^92 - 22 * q^93 - 35 * q^94 - 25 * q^95 + 5 * q^96 + 13 * q^97 + q^98 - 4 * 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 $

$2$	1.21072	0.856108	0.428054	−	0.903753i	$-0.359199\pi$
$2$	1.21072	0.856108	0.428054	+	0.903753i	$0.359199\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.534159	−0.267080
$5$	3.03795	1.35861	0.679306	−	0.733855i	$-0.262281\pi$
$5$	3.03795	1.35861	0.679306	+	0.733855i	$0.262281\pi$
$6$	1.21072	0.494274
$7$	−3.40847	−1.28828	−0.644141	−	0.764907i	$-0.722785\pi$
$7$	−3.40847	−1.28828	−0.644141	+	0.764907i	$0.722785\pi$
$8$	−3.06816	−1.08476
$9$	1.00000	0.333333
$10$	3.67810	1.16312
$11$	−3.85707	−1.16295	−0.581476	−	0.813564i	$-0.697524\pi$
$11$	−3.85707	−1.16295	−0.581476	+	0.813564i	$0.697524\pi$
$12$	−0.534159	−0.154199
$13$	−5.15691	−1.43027	−0.715135	−	0.698987i	$-0.753635\pi$
$13$	−5.15691	−1.43027	−0.715135	+	0.698987i	$0.753635\pi$
$14$	−4.12670	−1.10291
$15$	3.03795	0.784395
$16$	−2.64635	−0.661589
$17$	−2.07488	−0.503233	−0.251616	−	0.967827i	$-0.580962\pi$
$17$	−2.07488	−0.503233	−0.251616	+	0.967827i	$0.580962\pi$
$18$	1.21072	0.285369
$19$	−0.0953170	−0.0218672	−0.0109336	−	0.999940i	$-0.503480\pi$
$19$	−0.0953170	−0.0218672	−0.0109336	+	0.999940i	$0.503480\pi$
$20$	−1.62275	−0.362858
$21$	−3.40847	−0.743790
$22$	−4.66983	−0.995612
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−3.06816	−0.626285
$25$	4.22914	0.845828
$26$	−6.24357	−1.22446
$27$	1.00000	0.192450
$28$	1.82067	0.344074
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	3.67810	0.671527
$31$	−3.70527	−0.665485	−0.332743	−	0.943018i	$-0.607974\pi$
$31$	−3.70527	−0.665485	−0.332743	+	0.943018i	$0.607974\pi$
$32$	2.93232	0.518365
$33$	−3.85707	−0.671430
$34$	−2.51210	−0.430821
$35$	−10.3548	−1.75028
$36$	−0.534159	−0.0890266
$37$	−8.24097	−1.35481	−0.677404	−	0.735612i	$-0.736895\pi$
$37$	−8.24097	−1.35481	−0.677404	+	0.735612i	$0.736895\pi$
$38$	−0.115402	−0.0187207
$39$	−5.15691	−0.825766
$40$	−9.32090	−1.47376
$41$	4.31059	0.673201	0.336600	−	0.941648i	$-0.390723\pi$
$41$	4.31059	0.673201	0.336600	+	0.941648i	$0.390723\pi$
$42$	−4.12670	−0.636764
$43$	2.81904	0.429900	0.214950	−	0.976625i	$-0.431041\pi$
$43$	2.81904	0.429900	0.214950	+	0.976625i	$0.431041\pi$
$44$	2.06029	0.310601
$45$	3.03795	0.452871
$46$	1.21072	0.178511
$47$	−2.48043	−0.361808	−0.180904	−	0.983501i	$-0.557902\pi$
$47$	−2.48043	−0.361808	−0.180904	+	0.983501i	$0.557902\pi$
$48$	−2.64635	−0.381968
$49$	4.61770	0.659671
$50$	5.12030	0.724120
$51$	−2.07488	−0.290542
$52$	2.75461	0.381996
$53$	−6.40448	−0.879723	−0.439861	−	0.898066i	$-0.644972\pi$
$53$	−6.40448	−0.879723	−0.439861	+	0.898066i	$0.644972\pi$
$54$	1.21072	0.164758
$55$	−11.7176	−1.58000
$56$	10.4577	1.39747
$57$	−0.0953170	−0.0126250
$58$	−1.21072	−0.158975
$59$	−10.8564	−1.41338	−0.706692	−	0.707521i	$-0.749813\pi$
$59$	−10.8564	−1.41338	−0.706692	+	0.707521i	$0.749813\pi$
$60$	−1.62275	−0.209496
$61$	5.67822	0.727021	0.363510	−	0.931590i	$-0.381578\pi$
$61$	5.67822	0.727021	0.363510	+	0.931590i	$0.381578\pi$
$62$	−4.48604	−0.569727
$63$	−3.40847	−0.429427
$64$	8.84292	1.10537
$65$	−15.6664	−1.94318
$66$	−4.66983	−0.574817
$67$	12.8177	1.56593	0.782963	−	0.622068i	$-0.213707\pi$
$67$	12.8177	1.56593	0.782963	+	0.622068i	$0.213707\pi$
$68$	1.10832	0.134403
$69$	1.00000	0.120386
$70$	−12.5367	−1.49843
$71$	−2.25971	−0.268178	−0.134089	−	0.990969i	$-0.542811\pi$
$71$	−2.25971	−0.268178	−0.134089	+	0.990969i	$0.542811\pi$
$72$	−3.06816	−0.361586
$73$	14.0533	1.64482	0.822408	−	0.568898i	$-0.192630\pi$
$73$	14.0533	1.64482	0.822408	+	0.568898i	$0.192630\pi$
$74$	−9.97750	−1.15986
$75$	4.22914	0.488339
$76$	0.0509145	0.00584029
$77$	13.1467	1.49821
$78$	−6.24357	−0.706945
$79$	0.679730	0.0764756	0.0382378	−	0.999269i	$-0.487826\pi$
$79$	0.679730	0.0764756	0.0382378	+	0.999269i	$0.487826\pi$
$80$	−8.03950	−0.898843
$81$	1.00000	0.111111
$82$	5.21891	0.576332
$83$	4.99221	0.547967	0.273983	−	0.961734i	$-0.411659\pi$
$83$	4.99221	0.547967	0.273983	+	0.961734i	$0.411659\pi$
$84$	1.82067	0.198651
$85$	−6.30339	−0.683698
$86$	3.41307	0.368041
$87$	−1.00000	−0.107211
$88$	11.8341	1.26152
$89$	8.87404	0.940646	0.470323	−	0.882494i	$-0.344137\pi$
$89$	8.87404	0.940646	0.470323	+	0.882494i	$0.344137\pi$
$90$	3.67810	0.387706
$91$	17.5772	1.84259
$92$	−0.534159	−0.0556900
$93$	−3.70527	−0.384218
$94$	−3.00310	−0.309747
$95$	−0.289568	−0.0297091
$96$	2.93232	0.299278
$97$	12.0257	1.22102	0.610511	−	0.792007i	$-0.290964\pi$
$97$	12.0257	1.22102	0.610511	+	0.792007i	$0.290964\pi$
$98$	5.59073	0.564749
$99$	−3.85707	−0.387651
$100$	−2.25904	−0.225904
$101$	−12.8874	−1.28234	−0.641172	−	0.767397i	$-0.721552\pi$
$101$	−12.8874	−1.28234	−0.641172	+	0.767397i	$0.721552\pi$
$102$	−2.51210	−0.248735
$103$	−16.6608	−1.64164	−0.820818	−	0.571190i	$-0.806482\pi$
$103$	−16.6608	−1.64164	−0.820818	+	0.571190i	$0.806482\pi$
$104$	15.8222	1.55149
$105$	−10.3548	−1.01052
$106$	−7.75402	−0.753137
$107$	−3.34894	−0.323754	−0.161877	−	0.986811i	$-0.551755\pi$
$107$	−3.34894	−0.323754	−0.161877	+	0.986811i	$0.551755\pi$
$108$	−0.534159	−0.0513995
$109$	1.99607	0.191189	0.0955944	−	0.995420i	$-0.469525\pi$
$109$	1.99607	0.191189	0.0955944	+	0.995420i	$0.469525\pi$
$110$	−14.1867	−1.35265
$111$	−8.24097	−0.782198
$112$	9.02003	0.852313
$113$	−7.18948	−0.676330	−0.338165	−	0.941087i	$-0.609806\pi$
$113$	−7.18948	−0.676330	−0.338165	+	0.941087i	$0.609806\pi$
$114$	−0.115402	−0.0108084
$115$	3.03795	0.283290
$116$	0.534159	0.0495955
$117$	−5.15691	−0.476756
$118$	−13.1441	−1.21001
$119$	7.07218	0.648306
$120$	−9.32090	−0.850878
$121$	3.87702	0.352456
$122$	6.87472	0.622408
$123$	4.31059	0.388673
$124$	1.97920	0.177738
$125$	−2.34183	−0.209459
$126$	−4.12670	−0.367636
$127$	3.54176	0.314280	0.157140	−	0.987576i	$-0.449773\pi$
$127$	3.54176	0.314280	0.157140	+	0.987576i	$0.449773\pi$
$128$	4.84166	0.427946
$129$	2.81904	0.248203
$130$	−18.9676	−1.66357
$131$	−4.63906	−0.405316	−0.202658	−	0.979250i	$-0.564958\pi$
$131$	−4.63906	−0.405316	−0.202658	+	0.979250i	$0.564958\pi$
$132$	2.06029	0.179325
$133$	0.324885	0.0281711
$134$	15.5186	1.34060
$135$	3.03795	0.261465
$136$	6.36606	0.545885
$137$	−16.9239	−1.44591	−0.722954	−	0.690897i	$-0.757216\pi$
$137$	−16.9239	−1.44591	−0.722954	+	0.690897i	$0.757216\pi$
$138$	1.21072	0.103063
$139$	6.59644	0.559503	0.279751	−	0.960072i	$-0.409748\pi$
$139$	6.59644	0.559503	0.279751	+	0.960072i	$0.409748\pi$
$140$	5.53110	0.467463
$141$	−2.48043	−0.208890
$142$	−2.73587	−0.229589
$143$	19.8906	1.66333
$144$	−2.64635	−0.220530
$145$	−3.03795	−0.252288
$146$	17.0146	1.40814
$147$	4.61770	0.380861
$148$	4.40199	0.361841
$149$	3.08255	0.252532	0.126266	−	0.991996i	$-0.459701\pi$
$149$	3.08255	0.252532	0.126266	+	0.991996i	$0.459701\pi$
$150$	5.12030	0.418071
$151$	−11.3917	−0.927046	−0.463523	−	0.886085i	$-0.653415\pi$
$151$	−11.3917	−0.927046	−0.463523	+	0.886085i	$0.653415\pi$
$152$	0.292447	0.0237206
$153$	−2.07488	−0.167744
$154$	15.9170	1.28263
$155$	−11.2564	−0.904137
$156$	2.75461	0.220545
$157$	−7.45670	−0.595109	−0.297555	−	0.954705i	$-0.596171\pi$
$157$	−7.45670	−0.595109	−0.297555	+	0.954705i	$0.596171\pi$
$158$	0.822962	0.0654713
$159$	−6.40448	−0.507908
$160$	8.90824	0.704258
$161$	−3.40847	−0.268625
$162$	1.21072	0.0951231
$163$	−16.9258	−1.32573	−0.662865	−	0.748739i	$-0.730660\pi$
$163$	−16.9258	−1.32573	−0.662865	+	0.748739i	$0.730660\pi$
$164$	−2.30254	−0.179798
$165$	−11.7176	−0.912214
$166$	6.04417	0.469118
$167$	5.32428	0.412005	0.206002	−	0.978551i	$-0.433955\pi$
$167$	5.32428	0.412005	0.206002	+	0.978551i	$0.433955\pi$
$168$	10.4577	0.806831
$169$	13.5937	1.04567
$170$	−7.63163	−0.585319
$171$	−0.0953170	−0.00728907
$172$	−1.50582	−0.114818
$173$	24.7597	1.88244	0.941222	−	0.337789i	$-0.109679\pi$
$173$	24.7597	1.88244	0.941222	+	0.337789i	$0.109679\pi$
$174$	−1.21072	−0.0917844
$175$	−14.4149	−1.08967
$176$	10.2072	0.769396
$177$	−10.8564	−0.816017
$178$	10.7440	0.805294
$179$	−6.67712	−0.499071	−0.249536	−	0.968366i	$-0.580278\pi$
$179$	−6.67712	−0.499071	−0.249536	+	0.968366i	$0.580278\pi$
$180$	−1.62275	−0.120953
$181$	10.7524	0.799219	0.399609	−	0.916686i	$-0.369146\pi$
$181$	10.7524	0.799219	0.399609	+	0.916686i	$0.369146\pi$
$182$	21.2810	1.57746
$183$	5.67822	0.419746
$184$	−3.06816	−0.226187
$185$	−25.0357	−1.84066
$186$	−4.48604	−0.328932
$187$	8.00297	0.585235
$188$	1.32494	0.0966315
$189$	−3.40847	−0.247930
$190$	−0.350586	−0.0254342
$191$	−9.96489	−0.721034	−0.360517	−	0.932753i	$-0.617400\pi$
$191$	−9.96489	−0.721034	−0.360517	+	0.932753i	$0.617400\pi$
$192$	8.84292	0.638183
$193$	5.72373	0.412003	0.206002	−	0.978552i	$-0.433955\pi$
$193$	5.72373	0.412003	0.206002	+	0.978552i	$0.433955\pi$
$194$	14.5597	1.04533
$195$	−15.6664	−1.12190
$196$	−2.46659	−0.176185
$197$	−7.92245	−0.564451	−0.282226	−	0.959348i	$-0.591073\pi$
$197$	−7.92245	−0.564451	−0.282226	+	0.959348i	$0.591073\pi$
$198$	−4.66983	−0.331871
$199$	−16.2857	−1.15446	−0.577230	−	0.816581i	$-0.695866\pi$
$199$	−16.2857	−1.15446	−0.577230	+	0.816581i	$0.695866\pi$
$200$	−12.9757	−0.917518
$201$	12.8177	0.904088
$202$	−15.6030	−1.09782
$203$	3.40847	0.239228
$204$	1.10832	0.0775977
$205$	13.0953	0.914619
$206$	−20.1715	−1.40542
$207$	1.00000	0.0695048
$208$	13.6470	0.946250
$209$	0.367645	0.0254305
$210$	−12.5367	−0.865116
$211$	−8.49660	−0.584930	−0.292465	−	0.956276i	$-0.594476\pi$
$211$	−8.49660	−0.584930	−0.292465	+	0.956276i	$0.594476\pi$
$212$	3.42101	0.234956
$213$	−2.25971	−0.154833
$214$	−4.05462	−0.277168
$215$	8.56411	0.584068
$216$	−3.06816	−0.208762
$217$	12.6293	0.857333
$218$	2.41668	0.163678
$219$	14.0533	0.949635
$220$	6.25907	0.421986
$221$	10.7000	0.719758
$222$	−9.97750	−0.669646
$223$	−22.8578	−1.53067	−0.765334	−	0.643633i	$-0.777426\pi$
$223$	−22.8578	−1.53067	−0.765334	+	0.643633i	$0.777426\pi$
$224$	−9.99473	−0.667801
$225$	4.22914	0.281943
$226$	−8.70444	−0.579011
$227$	−7.74967	−0.514363	−0.257182	−	0.966363i	$-0.582794\pi$
$227$	−7.74967	−0.514363	−0.257182	+	0.966363i	$0.582794\pi$
$228$	0.0509145	0.00337189
$229$	−22.2253	−1.46869	−0.734344	−	0.678778i	$-0.762510\pi$
$229$	−22.2253	−1.46869	−0.734344	+	0.678778i	$0.762510\pi$
$230$	3.67810	0.242527
$231$	13.1467	0.864992
$232$	3.06816	0.201434
$233$	10.7454	0.703954	0.351977	−	0.936009i	$-0.385510\pi$
$233$	10.7454	0.703954	0.351977	+	0.936009i	$0.385510\pi$
$234$	−6.24357	−0.408155
$235$	−7.53542	−0.491557
$236$	5.79905	0.377486
$237$	0.679730	0.0441532
$238$	8.56242	0.555019
$239$	−13.8541	−0.896146	−0.448073	−	0.893997i	$-0.647890\pi$
$239$	−13.8541	−0.896146	−0.448073	+	0.893997i	$0.647890\pi$
$240$	−8.03950	−0.518947
$241$	10.4272	0.671676	0.335838	−	0.941920i	$-0.390980\pi$
$241$	10.4272	0.671676	0.335838	+	0.941920i	$0.390980\pi$
$242$	4.69398	0.301741
$243$	1.00000	0.0641500
$244$	−3.03307	−0.194173
$245$	14.0283	0.896237
$246$	5.21891	0.332746
$247$	0.491541	0.0312760
$248$	11.3683	0.721890
$249$	4.99221	0.316369
$250$	−2.83529	−0.179320
$251$	1.35842	0.0857428	0.0428714	−	0.999081i	$-0.486349\pi$
$251$	1.35842	0.0857428	0.0428714	+	0.999081i	$0.486349\pi$
$252$	1.82067	0.114691
$253$	−3.85707	−0.242492
$254$	4.28807	0.269058
$255$	−6.30339	−0.394733
$256$	−11.8240	−0.738997
$257$	5.57472	0.347741	0.173871	−	0.984768i	$-0.444373\pi$
$257$	5.57472	0.347741	0.173871	+	0.984768i	$0.444373\pi$
$258$	3.41307	0.212488
$259$	28.0891	1.74537
$260$	8.36837	0.518984
$261$	−1.00000	−0.0618984
$262$	−5.61660	−0.346994
$263$	31.2075	1.92433	0.962167	−	0.272460i	$-0.0878374\pi$
$263$	31.2075	1.92433	0.962167	+	0.272460i	$0.0878374\pi$
$264$	11.8341	0.728339
$265$	−19.4565	−1.19520
$266$	0.393345	0.0241175
$267$	8.87404	0.543082
$268$	−6.84667	−0.418227
$269$	15.0114	0.915259	0.457629	−	0.889143i	$-0.348699\pi$
$269$	15.0114	0.915259	0.457629	+	0.889143i	$0.348699\pi$
$270$	3.67810	0.223842
$271$	−16.3564	−0.993584	−0.496792	−	0.867870i	$-0.665489\pi$
$271$	−16.3564	−0.993584	−0.496792	+	0.867870i	$0.665489\pi$
$272$	5.49087	0.332933
$273$	17.5772	1.06382
$274$	−20.4901	−1.23785
$275$	−16.3121	−0.983658
$276$	−0.534159	−0.0321526
$277$	21.8350	1.31194	0.655969	−	0.754788i	$-0.272260\pi$
$277$	21.8350	1.31194	0.655969	+	0.754788i	$0.272260\pi$
$278$	7.98644	0.478995
$279$	−3.70527	−0.221828
$280$	31.7701	1.89862
$281$	24.1432	1.44026	0.720130	−	0.693839i	$-0.244082\pi$
$281$	24.1432	1.44026	0.720130	+	0.693839i	$0.244082\pi$
$282$	−3.00310	−0.178832
$283$	−26.8035	−1.59330	−0.796651	−	0.604439i	$-0.793397\pi$
$283$	−26.8035	−1.59330	−0.796651	+	0.604439i	$0.793397\pi$
$284$	1.20704	0.0716249
$285$	−0.289568	−0.0171525
$286$	24.0819	1.42399
$287$	−14.6925	−0.867272
$288$	2.93232	0.172788
$289$	−12.6949	−0.746757
$290$	−3.67810	−0.215986
$291$	12.0257	0.704958
$292$	−7.50671	−0.439297
$293$	13.5767	0.793156	0.396578	−	0.918001i	$-0.370198\pi$
$293$	13.5767	0.793156	0.396578	+	0.918001i	$0.370198\pi$
$294$	5.59073	0.326058
$295$	−32.9812	−1.92024
$296$	25.2846	1.46964
$297$	−3.85707	−0.223810
$298$	3.73210	0.216195
$299$	−5.15691	−0.298232
$300$	−2.25904	−0.130426
$301$	−9.60863	−0.553833
$302$	−13.7922	−0.793651
$303$	−12.8874	−0.740362
$304$	0.252243	0.0144671
$305$	17.2501	0.987740
$306$	−2.51210	−0.143607
$307$	−19.6964	−1.12414	−0.562068	−	0.827091i	$-0.689994\pi$
$307$	−19.6964	−1.12414	−0.562068	+	0.827091i	$0.689994\pi$
$308$	−7.02245	−0.400141
$309$	−16.6608	−0.947799
$310$	−13.6284	−0.774039
$311$	−29.6322	−1.68029	−0.840143	−	0.542364i	$-0.817529\pi$
$311$	−29.6322	−1.68029	−0.840143	+	0.542364i	$0.817529\pi$
$312$	15.8222	0.895755
$313$	−23.8630	−1.34882	−0.674408	−	0.738359i	$-0.735601\pi$
$313$	−23.8630	−1.34882	−0.674408	+	0.738359i	$0.735601\pi$
$314$	−9.02797	−0.509478
$315$	−10.3548	−0.583425
$316$	−0.363084	−0.0204251
$317$	27.3388	1.53550	0.767751	−	0.640748i	$-0.221376\pi$
$317$	27.3388	1.53550	0.767751	+	0.640748i	$0.221376\pi$
$318$	−7.75402	−0.434824
$319$	3.85707	0.215955
$320$	26.8644	1.50176
$321$	−3.34894	−0.186919
$322$	−4.12670	−0.229972
$323$	0.197771	0.0110043
$324$	−0.534159	−0.0296755
$325$	−21.8093	−1.20976
$326$	−20.4924	−1.13497
$327$	1.99607	0.110383
$328$	−13.2255	−0.730259
$329$	8.45448	0.466111
$330$	−14.1867	−0.780953
$331$	33.9104	1.86388	0.931942	−	0.362607i	$-0.118113\pi$
$331$	33.9104	1.86388	0.931942	+	0.362607i	$0.118113\pi$
$332$	−2.66664	−0.146351
$333$	−8.24097	−0.451602
$334$	6.44620	0.352721
$335$	38.9394	2.12749
$336$	9.02003	0.492083
$337$	7.35469	0.400636	0.200318	−	0.979731i	$-0.435803\pi$
$337$	7.35469	0.400636	0.200318	+	0.979731i	$0.435803\pi$
$338$	16.4582	0.895206
$339$	−7.18948	−0.390479
$340$	3.36701	0.182602
$341$	14.2915	0.773927
$342$	−0.115402	−0.00624023
$343$	8.12002	0.438440
$344$	−8.64926	−0.466337
$345$	3.03795	0.163558
$346$	29.9770	1.61157
$347$	11.9665	0.642394	0.321197	−	0.947012i	$-0.395915\pi$
$347$	11.9665	0.642394	0.321197	+	0.947012i	$0.395915\pi$
$348$	0.534159	0.0286339
$349$	21.1613	1.13274	0.566368	−	0.824152i	$-0.308348\pi$
$349$	21.1613	1.13274	0.566368	+	0.824152i	$0.308348\pi$
$350$	−17.4524	−0.932871
$351$	−5.15691	−0.275255
$352$	−11.3102	−0.602834
$353$	−29.9515	−1.59416	−0.797080	−	0.603874i	$-0.793623\pi$
$353$	−29.9515	−1.59416	−0.797080	+	0.603874i	$0.793623\pi$
$354$	−13.1441	−0.698599
$355$	−6.86488	−0.364350
$356$	−4.74015	−0.251227
$357$	7.07218	0.374299
$358$	−8.08411	−0.427259
$359$	−33.8970	−1.78901	−0.894507	−	0.447053i	$-0.852473\pi$
$359$	−33.8970	−1.78901	−0.894507	+	0.447053i	$0.852473\pi$
$360$	−9.32090	−0.491255
$361$	−18.9909	−0.999522
$362$	13.0181	0.684217
$363$	3.87702	0.203491
$364$	−9.38902	−0.492118
$365$	42.6933	2.23467
$366$	6.87472	0.359348
$367$	−1.12298	−0.0586189	−0.0293094	−	0.999570i	$-0.509331\pi$
$367$	−1.12298	−0.0586189	−0.0293094	+	0.999570i	$0.509331\pi$
$368$	−2.64635	−0.137951
$369$	4.31059	0.224400
$370$	−30.3111	−1.57580
$371$	21.8295	1.13333
$372$	1.97920	0.102617
$373$	11.0715	0.573261	0.286630	−	0.958041i	$-0.407465\pi$
$373$	11.0715	0.573261	0.286630	+	0.958041i	$0.407465\pi$
$374$	9.68935	0.501024
$375$	−2.34183	−0.120931
$376$	7.61034	0.392474
$377$	5.15691	0.265594
$378$	−4.12670	−0.212255
$379$	13.9430	0.716203	0.358101	−	0.933683i	$-0.383424\pi$
$379$	13.9430	0.716203	0.358101	+	0.933683i	$0.383424\pi$
$380$	0.154676	0.00793469
$381$	3.54176	0.181450
$382$	−12.0647	−0.617283
$383$	15.0622	0.769644	0.384822	−	0.922991i	$-0.374263\pi$
$383$	15.0622	0.769644	0.384822	+	0.922991i	$0.374263\pi$
$384$	4.84166	0.247075
$385$	39.9391	2.03549
$386$	6.92983	0.352719
$387$	2.81904	0.143300
$388$	−6.42363	−0.326110
$389$	10.4235	0.528491	0.264245	−	0.964456i	$-0.414877\pi$
$389$	10.4235	0.528491	0.264245	+	0.964456i	$0.414877\pi$
$390$	−18.9676	−0.960464
$391$	−2.07488	−0.104931
$392$	−14.1678	−0.715582
$393$	−4.63906	−0.234010
$394$	−9.59186	−0.483231
$395$	2.06499	0.103901
$396$	2.06029	0.103534
$397$	26.3518	1.32256	0.661280	−	0.750139i	$-0.270013\pi$
$397$	26.3518	1.32256	0.661280	+	0.750139i	$0.270013\pi$
$398$	−19.7174	−0.988342
$399$	0.324885	0.0162646
$400$	−11.1918	−0.559591
$401$	16.3597	0.816964	0.408482	−	0.912766i	$-0.366058\pi$
$401$	16.3597	0.816964	0.408482	+	0.912766i	$0.366058\pi$
$402$	15.5186	0.773996
$403$	19.1077	0.951823
$404$	6.88393	0.342488
$405$	3.03795	0.150957
$406$	4.12670	0.204805
$407$	31.7860	1.57558
$408$	6.36606	0.315167
$409$	−16.8579	−0.833568	−0.416784	−	0.909005i	$-0.636843\pi$
$409$	−16.8579	−0.833568	−0.416784	+	0.909005i	$0.636843\pi$
$410$	15.8548	0.783012
$411$	−16.9239	−0.834795
$412$	8.89951	0.438447
$413$	37.0038	1.82084
$414$	1.21072	0.0595036
$415$	15.1661	0.744474
$416$	−15.1217	−0.741402
$417$	6.59644	0.323029
$418$	0.445114	0.0217713
$419$	−0.578582	−0.0282656	−0.0141328	−	0.999900i	$-0.504499\pi$
$419$	−0.578582	−0.0282656	−0.0141328	+	0.999900i	$0.504499\pi$
$420$	5.53110	0.269890
$421$	21.3261	1.03937	0.519686	−	0.854357i	$-0.326049\pi$
$421$	21.3261	1.03937	0.519686	+	0.854357i	$0.326049\pi$
$422$	−10.2870	−0.500763
$423$	−2.48043	−0.120603
$424$	19.6499	0.954285
$425$	−8.77497	−0.425649
$426$	−2.73587	−0.132553
$427$	−19.3540	−0.936608
$428$	1.78887	0.0864681
$429$	19.8906	0.960326
$430$	10.3687	0.500025
$431$	−1.62870	−0.0784518	−0.0392259	−	0.999230i	$-0.512489\pi$
$431$	−1.62870	−0.0784518	−0.0392259	+	0.999230i	$0.512489\pi$
$432$	−2.64635	−0.127323
$433$	6.74749	0.324264	0.162132	−	0.986769i	$-0.448163\pi$
$433$	6.74749	0.324264	0.162132	+	0.986769i	$0.448163\pi$
$434$	15.2905	0.733969
$435$	−3.03795	−0.145659
$436$	−1.06622	−0.0510626
$437$	−0.0953170	−0.00455963
$438$	17.0146	0.812990
$439$	−7.43797	−0.354995	−0.177498	−	0.984121i	$-0.556800\pi$
$439$	−7.43797	−0.354995	−0.177498	+	0.984121i	$0.556800\pi$
$440$	35.9514	1.71392
$441$	4.61770	0.219890
$442$	12.9547	0.616191
$443$	2.20485	0.104755	0.0523777	−	0.998627i	$-0.483320\pi$
$443$	2.20485	0.104755	0.0523777	+	0.998627i	$0.483320\pi$
$444$	4.40199	0.208909
$445$	26.9589	1.27797
$446$	−27.6743	−1.31042
$447$	3.08255	0.145799
$448$	−30.1409	−1.42402
$449$	−37.0431	−1.74817	−0.874087	−	0.485770i	$-0.838539\pi$
$449$	−37.0431	−1.74817	−0.874087	+	0.485770i	$0.838539\pi$
$450$	5.12030	0.241373
$451$	−16.6263	−0.782900
$452$	3.84033	0.180634
$453$	−11.3917	−0.535230
$454$	−9.38267	−0.440351
$455$	53.3986	2.50337
$456$	0.292447	0.0136951
$457$	28.8088	1.34762	0.673810	−	0.738904i	$-0.264657\pi$
$457$	28.8088	1.34762	0.673810	+	0.738904i	$0.264657\pi$
$458$	−26.9086	−1.25735
$459$	−2.07488	−0.0968472
$460$	−1.62275	−0.0756611
$461$	−22.4332	−1.04482	−0.522409	−	0.852695i	$-0.674966\pi$
$461$	−22.4332	−1.04482	−0.522409	+	0.852695i	$0.674966\pi$
$462$	15.9170	0.740526
$463$	−0.887793	−0.0412593	−0.0206296	−	0.999787i	$-0.506567\pi$
$463$	−0.887793	−0.0412593	−0.0206296	+	0.999787i	$0.506567\pi$
$464$	2.64635	0.122854
$465$	−11.2564	−0.522004
$466$	13.0096	0.602660
$467$	21.3965	0.990113	0.495056	−	0.868861i	$-0.335147\pi$
$467$	21.3965	0.990113	0.495056	+	0.868861i	$0.335147\pi$
$468$	2.75461	0.127332
$469$	−43.6886	−2.01735
$470$	−9.12328	−0.420826
$471$	−7.45670	−0.343586
$472$	33.3091	1.53318
$473$	−10.8733	−0.499953
$474$	0.822962	0.0377999
$475$	−0.403109	−0.0184959
$476$	−3.77767	−0.173149
$477$	−6.40448	−0.293241
$478$	−16.7734	−0.767198
$479$	−27.8301	−1.27159	−0.635795	−	0.771858i	$-0.719327\pi$
$479$	−27.8301	−1.27159	−0.635795	+	0.771858i	$0.719327\pi$
$480$	8.90824	0.406603
$481$	42.4979	1.93774
$482$	12.6244	0.575027
$483$	−3.40847	−0.155091
$484$	−2.07095	−0.0941339
$485$	36.5334	1.65890
$486$	1.21072	0.0549193
$487$	−6.27093	−0.284163	−0.142081	−	0.989855i	$-0.545379\pi$
$487$	−6.27093	−0.284163	−0.142081	+	0.989855i	$0.545379\pi$
$488$	−17.4216	−0.788641
$489$	−16.9258	−0.765410
$490$	16.9844	0.767275
$491$	−23.6758	−1.06847	−0.534236	−	0.845335i	$-0.679401\pi$
$491$	−23.6758	−1.06847	−0.534236	+	0.845335i	$0.679401\pi$
$492$	−2.30254	−0.103807
$493$	2.07488	0.0934480
$494$	0.595118	0.0267756
$495$	−11.7176	−0.526667
$496$	9.80545	0.440278
$497$	7.70216	0.345489
$498$	6.04417	0.270846
$499$	−16.9094	−0.756969	−0.378484	−	0.925608i	$-0.623555\pi$
$499$	−16.9094	−0.756969	−0.378484	+	0.925608i	$0.623555\pi$
$500$	1.25091	0.0559424
$501$	5.32428	0.237871
$502$	1.64467	0.0734050
$503$	4.36684	0.194708	0.0973539	−	0.995250i	$-0.468962\pi$
$503$	4.36684	0.194708	0.0973539	+	0.995250i	$0.468962\pi$
$504$	10.4577	0.465824
$505$	−39.1513	−1.74221
$506$	−4.66983	−0.207599
$507$	13.5937	0.603718
$508$	−1.89186	−0.0839378
$509$	−23.8848	−1.05868	−0.529338	−	0.848411i	$-0.677559\pi$
$509$	−23.8848	−1.05868	−0.529338	+	0.848411i	$0.677559\pi$
$510$	−7.63163	−0.337934
$511$	−47.9004	−2.11899
$512$	−23.9988	−1.06061
$513$	−0.0953170	−0.00420835
$514$	6.74942	0.297704
$515$	−50.6146	−2.23035
$516$	−1.50582	−0.0662900
$517$	9.56720	0.420765
$518$	34.0080	1.49423
$519$	24.7597	1.08683
$520$	48.0670	2.10788
$521$	11.2081	0.491037	0.245519	−	0.969392i	$-0.421042\pi$
$521$	11.2081	0.491037	0.245519	+	0.969392i	$0.421042\pi$
$522$	−1.21072	−0.0529917
$523$	2.67524	0.116980	0.0584901	−	0.998288i	$-0.481371\pi$
$523$	2.67524	0.116980	0.0584901	+	0.998288i	$0.481371\pi$
$524$	2.47800	0.108252
$525$	−14.4149	−0.629119
$526$	37.7835	1.64744
$527$	7.68799	0.334894
$528$	10.2072	0.444211
$529$	1.00000	0.0434783
$530$	−23.5563	−1.02322
$531$	−10.8564	−0.471128
$532$	−0.173541	−0.00752394
$533$	−22.2293	−0.962858
$534$	10.7440	0.464937
$535$	−10.1739	−0.439856
$536$	−39.3266	−1.69865
$537$	−6.67712	−0.288139
$538$	18.1745	0.783560
$539$	−17.8108	−0.767165
$540$	−1.62275	−0.0698320
$541$	−4.28908	−0.184402	−0.0922010	−	0.995740i	$-0.529390\pi$
$541$	−4.28908	−0.184402	−0.0922010	+	0.995740i	$0.529390\pi$
$542$	−19.8031	−0.850614
$543$	10.7524	0.461429
$544$	−6.08421	−0.260858
$545$	6.06396	0.259752
$546$	21.2810	0.910744
$547$	−35.7338	−1.52787	−0.763933	−	0.645296i	$-0.776734\pi$
$547$	−35.7338	−1.52787	−0.763933	+	0.645296i	$0.776734\pi$
$548$	9.04006	0.386172
$549$	5.67822	0.242340
$550$	−19.7494	−0.842117
$551$	0.0953170	0.00406064
$552$	−3.06816	−0.130589
$553$	−2.31684	−0.0985221
$554$	26.4361	1.12316
$555$	−25.0357	−1.06270
$556$	−3.52355	−0.149432
$557$	−3.81954	−0.161839	−0.0809195	−	0.996721i	$-0.525786\pi$
$557$	−3.81954	−0.161839	−0.0809195	+	0.996721i	$0.525786\pi$
$558$	−4.48604	−0.189909
$559$	−14.5375	−0.614873
$560$	27.4024	1.15796
$561$	8.00297	0.337886
$562$	29.2306	1.23302
$563$	−20.4663	−0.862554	−0.431277	−	0.902220i	$-0.641937\pi$
$563$	−20.4663	−0.862554	−0.431277	+	0.902220i	$0.641937\pi$
$564$	1.32494	0.0557902
$565$	−21.8413	−0.918870
$566$	−32.4515	−1.36404
$567$	−3.40847	−0.143142
$568$	6.93314	0.290908
$569$	10.7702	0.451510	0.225755	−	0.974184i	$-0.427515\pi$
$569$	10.7702	0.451510	0.225755	+	0.974184i	$0.427515\pi$
$570$	−0.350586	−0.0146844
$571$	−19.2253	−0.804556	−0.402278	−	0.915518i	$-0.631781\pi$
$571$	−19.2253	−0.804556	−0.402278	+	0.915518i	$0.631781\pi$
$572$	−10.6247	−0.444243
$573$	−9.96489	−0.416289
$574$	−17.7885	−0.742478
$575$	4.22914	0.176367
$576$	8.84292	0.368455
$577$	−16.6266	−0.692174	−0.346087	−	0.938203i	$-0.612490\pi$
$577$	−16.6266	−0.692174	−0.346087	+	0.938203i	$0.612490\pi$
$578$	−15.3699	−0.639304
$579$	5.72373	0.237870
$580$	1.62275	0.0673810
$581$	−17.0158	−0.705936
$582$	14.5597	0.603520
$583$	24.7025	1.02308
$584$	−43.1177	−1.78423
$585$	−15.6664	−0.647727
$586$	16.4375	0.679027
$587$	38.1799	1.57585	0.787926	−	0.615769i	$-0.211155\pi$
$587$	38.1799	1.57585	0.787926	+	0.615769i	$0.211155\pi$
$588$	−2.46659	−0.101720
$589$	0.353175	0.0145523
$590$	−39.9310	−1.64393
$591$	−7.92245	−0.325886
$592$	21.8085	0.896325
$593$	24.9127	1.02304	0.511522	−	0.859270i	$-0.329082\pi$
$593$	24.9127	1.02304	0.511522	+	0.859270i	$0.329082\pi$
$594$	−4.66983	−0.191606
$595$	21.4849	0.880796
$596$	−1.64657	−0.0674462
$597$	−16.2857	−0.666528
$598$	−6.24357	−0.255318
$599$	−41.2275	−1.68451	−0.842255	−	0.539079i	$-0.818772\pi$
$599$	−41.2275	−1.68451	−0.842255	+	0.539079i	$0.818772\pi$
$600$	−12.9757	−0.529729
$601$	20.1084	0.820241	0.410120	−	0.912031i	$-0.365487\pi$
$601$	20.1084	0.820241	0.410120	+	0.912031i	$0.365487\pi$
$602$	−11.6334	−0.474140
$603$	12.8177	0.521975
$604$	6.08500	0.247595
$605$	11.7782	0.478852
$606$	−15.6030	−0.633829
$607$	−15.0972	−0.612776	−0.306388	−	0.951907i	$-0.599121\pi$
$607$	−15.0972	−0.612776	−0.306388	+	0.951907i	$0.599121\pi$
$608$	−0.279500	−0.0113352
$609$	3.40847	0.138118
$610$	20.8851	0.845612
$611$	12.7914	0.517483
$612$	1.10832	0.0448011
$613$	−26.9957	−1.09035	−0.545174	−	0.838323i	$-0.683536\pi$
$613$	−26.9957	−1.09035	−0.545174	+	0.838323i	$0.683536\pi$
$614$	−23.8469	−0.962381
$615$	13.0953	0.528055
$616$	−40.3362	−1.62519
$617$	8.06126	0.324534	0.162267	−	0.986747i	$-0.448119\pi$
$617$	8.06126	0.324534	0.162267	+	0.986747i	$0.448119\pi$
$618$	−20.1715	−0.811418
$619$	−38.6945	−1.55526	−0.777631	−	0.628721i	$-0.783579\pi$
$619$	−38.6945	−1.55526	−0.777631	+	0.628721i	$0.783579\pi$
$620$	6.01272	0.241477
$621$	1.00000	0.0401286
$622$	−35.8762	−1.43851
$623$	−30.2469	−1.21182
$624$	13.6470	0.546318
$625$	−28.2601	−1.13040
$626$	−28.8914	−1.15473
$627$	0.367645	0.0146823
$628$	3.98306	0.158942
$629$	17.0990	0.681783
$630$	−12.5367	−0.499475
$631$	18.5647	0.739048	0.369524	−	0.929221i	$-0.379521\pi$
$631$	18.5647	0.739048	0.369524	+	0.929221i	$0.379521\pi$
$632$	−2.08552	−0.0829574
$633$	−8.49660	−0.337710
$634$	33.0997	1.31456
$635$	10.7597	0.426985
$636$	3.42101	0.135652
$637$	−23.8130	−0.943507
$638$	4.66983	0.184880
$639$	−2.25971	−0.0893927
$640$	14.7087	0.581413
$641$	−3.84832	−0.151999	−0.0759997	−	0.997108i	$-0.524215\pi$
$641$	−3.84832	−0.151999	−0.0759997	+	0.997108i	$0.524215\pi$
$642$	−4.05462	−0.160023
$643$	19.0776	0.752348	0.376174	−	0.926549i	$-0.377239\pi$
$643$	19.0776	0.752348	0.376174	+	0.926549i	$0.377239\pi$
$644$	1.82067	0.0717444
$645$	8.56411	0.337212
$646$	0.239446	0.00942086
$647$	35.1122	1.38040	0.690202	−	0.723617i	$-0.257522\pi$
$647$	35.1122	1.38040	0.690202	+	0.723617i	$0.257522\pi$
$648$	−3.06816	−0.120529
$649$	41.8740	1.64370
$650$	−26.4049	−1.03569
$651$	12.6293	0.494981
$652$	9.04106	0.354075
$653$	−12.2338	−0.478745	−0.239372	−	0.970928i	$-0.576942\pi$
$653$	−12.2338	−0.478745	−0.239372	+	0.970928i	$0.576942\pi$
$654$	2.41668	0.0944996
$655$	−14.0932	−0.550668
$656$	−11.4073	−0.445382
$657$	14.0533	0.548272
$658$	10.2360	0.399041
$659$	−2.80788	−0.109380	−0.0546898	−	0.998503i	$-0.517417\pi$
$659$	−2.80788	−0.109380	−0.0546898	+	0.998503i	$0.517417\pi$
$660$	6.25907	0.243634
$661$	−37.6385	−1.46397	−0.731984	−	0.681322i	$-0.761405\pi$
$661$	−37.6385	−1.46397	−0.731984	+	0.681322i	$0.761405\pi$
$662$	41.0560	1.59569
$663$	10.7000	0.415553
$664$	−15.3169	−0.594410
$665$	0.986986	0.0382737
$666$	−9.97750	−0.386620
$667$	−1.00000	−0.0387202
$668$	−2.84401	−0.110038
$669$	−22.8578	−0.883732
$670$	47.1447	1.82136
$671$	−21.9013	−0.845490
$672$	−9.99473	−0.385555
$673$	−50.4621	−1.94517	−0.972586	−	0.232543i	$-0.925295\pi$
$673$	−50.4621	−1.94517	−0.972586	+	0.232543i	$0.925295\pi$
$674$	8.90447	0.342987
$675$	4.22914	0.162780
$676$	−7.26121	−0.279277
$677$	18.5792	0.714055	0.357028	−	0.934094i	$-0.383790\pi$
$677$	18.5792	0.714055	0.357028	+	0.934094i	$0.383790\pi$
$678$	−8.70444	−0.334292
$679$	−40.9892	−1.57302
$680$	19.3398	0.741646
$681$	−7.74967	−0.296968
$682$	17.3030	0.662565
$683$	49.7804	1.90480	0.952398	−	0.304858i	$-0.0986089\pi$
$683$	49.7804	1.90480	0.952398	+	0.304858i	$0.0986089\pi$
$684$	0.0509145	0.00194676
$685$	−51.4140	−1.96443
$686$	9.83107	0.375352
$687$	−22.2253	−0.847947
$688$	−7.46019	−0.284417
$689$	33.0273	1.25824
$690$	3.67810	0.140023
$691$	45.4174	1.72776	0.863880	−	0.503698i	$-0.168027\pi$
$691$	45.4174	1.72776	0.863880	+	0.503698i	$0.168027\pi$
$692$	−13.2256	−0.502763
$693$	13.1467	0.499403
$694$	14.4880	0.549959
$695$	20.0397	0.760148
$696$	3.06816	0.116298
$697$	−8.94396	−0.338777
$698$	25.6203	0.969744
$699$	10.7454	0.406428
$700$	7.69987	0.291028
$701$	16.6480	0.628788	0.314394	−	0.949293i	$-0.398199\pi$
$701$	16.6480	0.628788	0.314394	+	0.949293i	$0.398199\pi$
$702$	−6.24357	−0.235648
$703$	0.785504	0.0296259
$704$	−34.1078	−1.28549
$705$	−7.53542	−0.283800
$706$	−36.2629	−1.36477
$707$	43.9264	1.65202
$708$	5.79905	0.217942
$709$	−8.65867	−0.325183	−0.162592	−	0.986693i	$-0.551985\pi$
$709$	−8.65867	−0.325183	−0.162592	+	0.986693i	$0.551985\pi$
$710$	−8.31145	−0.311923
$711$	0.679730	0.0254919
$712$	−27.2269	−1.02037
$713$	−3.70527	−0.138763
$714$	8.56242	0.320441
$715$	60.4266	2.25983
$716$	3.56664	0.133292
$717$	−13.8541	−0.517390
$718$	−41.0397	−1.53159
$719$	−19.1222	−0.713138	−0.356569	−	0.934269i	$-0.616054\pi$
$719$	−19.1222	−0.713138	−0.356569	+	0.934269i	$0.616054\pi$
$720$	−8.03950	−0.299614
$721$	56.7878	2.11489
$722$	−22.9927	−0.855698
$723$	10.4272	0.387792
$724$	−5.74349	−0.213455
$725$	−4.22914	−0.157066
$726$	4.69398	0.174210
$727$	−9.85298	−0.365427	−0.182713	−	0.983166i	$-0.558488\pi$
$727$	−9.85298	−0.365427	−0.182713	+	0.983166i	$0.558488\pi$
$728$	−53.9295	−1.99876
$729$	1.00000	0.0370370
$730$	51.6896	1.91312
$731$	−5.84918	−0.216340
$732$	−3.03307	−0.112106
$733$	29.0623	1.07344	0.536721	−	0.843760i	$-0.319663\pi$
$733$	29.0623	1.07344	0.536721	+	0.843760i	$0.319663\pi$
$734$	−1.35961	−0.0501841
$735$	14.0283	0.517443
$736$	2.93232	0.108087
$737$	−49.4386	−1.82110
$738$	5.21891	0.192111
$739$	−18.5216	−0.681327	−0.340663	−	0.940185i	$-0.610652\pi$
$739$	−18.5216	−0.681327	−0.340663	+	0.940185i	$0.610652\pi$
$740$	13.3730	0.491602
$741$	0.491541	0.0180572
$742$	26.4294	0.970253
$743$	33.6795	1.23558	0.617790	−	0.786343i	$-0.288028\pi$
$743$	33.6795	1.23558	0.617790	+	0.786343i	$0.288028\pi$
$744$	11.3683	0.416783
$745$	9.36462	0.343093
$746$	13.4045	0.490773
$747$	4.99221	0.182656
$748$	−4.27486	−0.156304
$749$	11.4148	0.417086
$750$	−2.83529	−0.103530
$751$	51.9526	1.89578	0.947889	−	0.318600i	$-0.103213\pi$
$751$	51.9526	1.89578	0.947889	+	0.318600i	$0.103213\pi$
$752$	6.56410	0.239368
$753$	1.35842	0.0495036
$754$	6.24357	0.227377
$755$	−34.6075	−1.25950
$756$	1.82067	0.0662171
$757$	33.8994	1.23210	0.616048	−	0.787709i	$-0.288733\pi$
$757$	33.8994	1.23210	0.616048	+	0.787709i	$0.288733\pi$
$758$	16.8810	0.613147
$759$	−3.85707	−0.140003
$760$	0.888440	0.0322271
$761$	47.1104	1.70775	0.853875	−	0.520478i	$-0.174246\pi$
$761$	47.1104	1.70775	0.853875	+	0.520478i	$0.174246\pi$
$762$	4.28807	0.155340
$763$	−6.80355	−0.246305
$764$	5.32284	0.192574
$765$	−6.30339	−0.227899
$766$	18.2361	0.658898
$767$	55.9855	2.02152
$768$	−11.8240	−0.426660
$769$	−23.6926	−0.854377	−0.427188	−	0.904163i	$-0.640496\pi$
$769$	−23.6926	−0.854377	−0.427188	+	0.904163i	$0.640496\pi$
$770$	48.3551	1.74260
$771$	5.57472	0.200769
$772$	−3.05738	−0.110038
$773$	−20.8577	−0.750201	−0.375100	−	0.926984i	$-0.622392\pi$
$773$	−20.8577	−0.750201	−0.375100	+	0.926984i	$0.622392\pi$
$774$	3.41307	0.122680
$775$	−15.6701	−0.562887
$776$	−36.8967	−1.32451
$777$	28.0891	1.00769
$778$	12.6199	0.452445
$779$	−0.410872	−0.0147210
$780$	8.36837	0.299636
$781$	8.71586	0.311878
$782$	−2.51210	−0.0898325
$783$	−1.00000	−0.0357371
$784$	−12.2201	−0.436431
$785$	−22.6531	−0.808523
$786$	−5.61660	−0.200337
$787$	15.5046	0.552680	0.276340	−	0.961060i	$-0.410878\pi$
$787$	15.5046	0.552680	0.276340	+	0.961060i	$0.410878\pi$
$788$	4.23185	0.150753
$789$	31.2075	1.11101
$790$	2.50012	0.0889502
$791$	24.5052	0.871303
$792$	11.8341	0.420506
$793$	−29.2820	−1.03984
$794$	31.9047	1.13225
$795$	−19.4565	−0.690051
$796$	8.69914	0.308333
$797$	−18.8889	−0.669080	−0.334540	−	0.942382i	$-0.608581\pi$
$797$	−18.8889	−0.669080	−0.334540	+	0.942382i	$0.608581\pi$
$798$	0.393345	0.0139243
$799$	5.14660	0.182074
$800$	12.4012	0.438448
$801$	8.87404	0.313549
$802$	19.8070	0.699409
$803$	−54.2047	−1.91284
$804$	−6.84667	−0.241463
$805$	−10.3548	−0.364958
$806$	23.1341	0.814863
$807$	15.0114	0.528425
$808$	39.5405	1.39103
$809$	10.3408	0.363563	0.181781	−	0.983339i	$-0.441814\pi$
$809$	10.3408	0.363563	0.181781	+	0.983339i	$0.441814\pi$
$810$	3.67810	0.129235
$811$	−31.1199	−1.09277	−0.546383	−	0.837535i	$-0.683996\pi$
$811$	−31.1199	−1.09277	−0.546383	+	0.837535i	$0.683996\pi$
$812$	−1.82067	−0.0638929
$813$	−16.3564	−0.573646
$814$	38.4840	1.34886
$815$	−51.4197	−1.80115
$816$	5.49087	0.192219
$817$	−0.268703	−0.00940072
$818$	−20.4102	−0.713624
$819$	17.5772	0.614197
$820$	−6.99500	−0.244276
$821$	−20.8286	−0.726922	−0.363461	−	0.931609i	$-0.618405\pi$
$821$	−20.8286	−0.726922	−0.363461	+	0.931609i	$0.618405\pi$
$822$	−20.4901	−0.714674
$823$	23.2091	0.809018	0.404509	−	0.914534i	$-0.367443\pi$
$823$	23.2091	0.809018	0.404509	+	0.914534i	$0.367443\pi$
$824$	51.1179	1.78077
$825$	−16.3121	−0.567915
$826$	44.8012	1.55883
$827$	−18.4758	−0.642468	−0.321234	−	0.947000i	$-0.604098\pi$
$827$	−18.4758	−0.642468	−0.321234	+	0.947000i	$0.604098\pi$
$828$	−0.534159	−0.0185633
$829$	20.8312	0.723497	0.361749	−	0.932276i	$-0.382180\pi$
$829$	20.8312	0.723497	0.361749	+	0.932276i	$0.382180\pi$
$830$	18.3619	0.637350
$831$	21.8350	0.757448
$832$	−45.6021	−1.58097
$833$	−9.58117	−0.331968
$834$	7.98644	0.276548
$835$	16.1749	0.559755
$836$	−0.196381	−0.00679197
$837$	−3.70527	−0.128073
$838$	−0.700501	−0.0241984
$839$	−7.97701	−0.275397	−0.137698	−	0.990474i	$-0.543970\pi$
$839$	−7.97701	−0.275397	−0.137698	+	0.990474i	$0.543970\pi$
$840$	31.7701	1.09617
$841$	1.00000	0.0344828
$842$	25.8200	0.889815
$843$	24.1432	0.831534
$844$	4.53854	0.156223
$845$	41.2970	1.42066
$846$	−3.00310	−0.103249
$847$	−13.2147	−0.454063
$848$	16.9485	0.582015
$849$	−26.8035	−0.919894
$850$	−10.6240	−0.364401
$851$	−8.24097	−0.282497
$852$	1.20704	0.0413527
$853$	−28.3893	−0.972030	−0.486015	−	0.873950i	$-0.661550\pi$
$853$	−28.3893	−0.972030	−0.486015	+	0.873950i	$0.661550\pi$
$854$	−23.4323	−0.801837
$855$	−0.289568	−0.00990302
$856$	10.2751	0.351194
$857$	1.06086	0.0362384	0.0181192	−	0.999836i	$-0.494232\pi$
$857$	1.06086	0.0362384	0.0181192	+	0.999836i	$0.494232\pi$
$858$	24.0819	0.822143
$859$	−34.9191	−1.19142	−0.595711	−	0.803199i	$-0.703130\pi$
$859$	−34.9191	−1.19142	−0.595711	+	0.803199i	$0.703130\pi$
$860$	−4.57460	−0.155993
$861$	−14.6925	−0.500720
$862$	−1.97190	−0.0671632
$863$	−31.8477	−1.08411	−0.542054	−	0.840343i	$-0.682353\pi$
$863$	−31.8477	−1.08411	−0.542054	+	0.840343i	$0.682353\pi$
$864$	2.93232	0.0997595
$865$	75.2187	2.55751
$866$	8.16932	0.277605
$867$	−12.6949	−0.431140
$868$	−6.74606	−0.228976
$869$	−2.62177	−0.0889374
$870$	−3.67810	−0.124699
$871$	−66.0995	−2.23970
$872$	−6.12425	−0.207393
$873$	12.0257	0.407008
$874$	−0.115402	−0.00390353
$875$	7.98206	0.269843
$876$	−7.50671	−0.253628
$877$	−28.7892	−0.972141	−0.486071	−	0.873919i	$-0.661570\pi$
$877$	−28.7892	−0.972141	−0.486071	+	0.873919i	$0.661570\pi$
$878$	−9.00530	−0.303914
$879$	13.5767	0.457929
$880$	31.0089	1.04531
$881$	6.20651	0.209103	0.104551	−	0.994519i	$-0.466659\pi$
$881$	6.20651	0.209103	0.104551	+	0.994519i	$0.466659\pi$
$882$	5.59073	0.188250
$883$	−38.2460	−1.28708	−0.643540	−	0.765413i	$-0.722535\pi$
$883$	−38.2460	−1.28708	−0.643540	+	0.765413i	$0.722535\pi$
$884$	−5.71549	−0.192233
$885$	−32.9812	−1.10865
$886$	2.66945	0.0896819
$887$	−13.5713	−0.455681	−0.227841	−	0.973698i	$-0.573166\pi$
$887$	−13.5713	−0.455681	−0.227841	+	0.973698i	$0.573166\pi$
$888$	25.2846	0.848495
$889$	−12.0720	−0.404881
$890$	32.6396	1.09408
$891$	−3.85707	−0.129217
$892$	12.2097	0.408810
$893$	0.236427	0.00791173
$894$	3.73210	0.124820
$895$	−20.2847	−0.678044
$896$	−16.5027	−0.551316
$897$	−5.15691	−0.172184
$898$	−44.8488	−1.49662
$899$	3.70527	0.123578
$900$	−2.25904	−0.0753012
$901$	13.2885	0.442705
$902$	−20.1297	−0.670246
$903$	−9.60863	−0.319755
$904$	22.0584	0.733653
$905$	32.6652	1.08583
$906$	−13.7922	−0.458215
$907$	−8.32618	−0.276466	−0.138233	−	0.990400i	$-0.544142\pi$
$907$	−8.32618	−0.276466	−0.138233	+	0.990400i	$0.544142\pi$
$908$	4.13956	0.137376
$909$	−12.8874	−0.427448
$910$	64.6507	2.14315
$911$	35.8689	1.18839	0.594194	−	0.804321i	$-0.297471\pi$
$911$	35.8689	1.18839	0.594194	+	0.804321i	$0.297471\pi$
$912$	0.252243	0.00835259
$913$	−19.2553	−0.637259
$914$	34.8794	1.15371
$915$	17.2501	0.570272
$916$	11.8718	0.392256
$917$	15.8121	0.522162
$918$	−2.51210	−0.0829116
$919$	38.8879	1.28279	0.641397	−	0.767209i	$-0.278355\pi$
$919$	38.8879	1.28279	0.641397	+	0.767209i	$0.278355\pi$
$920$	−9.32090	−0.307301
$921$	−19.6964	−0.649020
$922$	−27.1603	−0.894476
$923$	11.6531	0.383567
$924$	−7.02245	−0.231022
$925$	−34.8522	−1.14593
$926$	−1.07487	−0.0353224
$927$	−16.6608	−0.547212
$928$	−2.93232	−0.0962580
$929$	−6.58929	−0.216188	−0.108094	−	0.994141i	$-0.534475\pi$
$929$	−6.58929	−0.216188	−0.108094	+	0.994141i	$0.534475\pi$
$930$	−13.6284	−0.446891
$931$	−0.440145	−0.0144252
$932$	−5.73975	−0.188012
$933$	−29.6322	−0.970114
$934$	25.9052	0.847643
$935$	24.3126	0.795108
$936$	15.8222	0.517165
$937$	4.77562	0.156013	0.0780063	−	0.996953i	$-0.475145\pi$
$937$	4.77562	0.156013	0.0780063	+	0.996953i	$0.475145\pi$
$938$	−52.8947	−1.72707
$939$	−23.8630	−0.778739
$940$	4.02512	0.131285
$941$	−48.1961	−1.57115	−0.785573	−	0.618769i	$-0.787632\pi$
$941$	−48.1961	−1.57115	−0.785573	+	0.618769i	$0.787632\pi$
$942$	−9.02797	−0.294147
$943$	4.31059	0.140372
$944$	28.7299	0.935079
$945$	−10.3548	−0.336841
$946$	−13.1645	−0.428014
$947$	35.1573	1.14246	0.571229	−	0.820790i	$-0.306467\pi$
$947$	35.1573	1.14246	0.571229	+	0.820790i	$0.306467\pi$
$948$	−0.363084	−0.0117924
$949$	−72.4717	−2.35253
$950$	−0.488052	−0.0158345
$951$	27.3388	0.886523
$952$	−21.6985	−0.703254
$953$	−24.9046	−0.806740	−0.403370	−	0.915037i	$-0.632161\pi$
$953$	−24.9046	−0.806740	−0.403370	+	0.915037i	$0.632161\pi$
$954$	−7.75402	−0.251046
$955$	−30.2728	−0.979606
$956$	7.40029	0.239342
$957$	3.85707	0.124681
$958$	−33.6944	−1.08862
$959$	57.6847	1.86274
$960$	26.8644	0.867044
$961$	−17.2710	−0.557129
$962$	51.4531	1.65891
$963$	−3.34894	−0.107918
$964$	−5.56980	−0.179391
$965$	17.3884	0.559753
$966$	−4.12670	−0.132775
$967$	−10.6116	−0.341245	−0.170622	−	0.985337i	$-0.554578\pi$
$967$	−10.6116	−0.341245	−0.170622	+	0.985337i	$0.554578\pi$
$968$	−11.8953	−0.382329
$969$	0.197771	0.00635333
$970$	44.2317	1.42019
$971$	25.5705	0.820595	0.410298	−	0.911952i	$-0.365425\pi$
$971$	25.5705	0.820595	0.410298	+	0.911952i	$0.365425\pi$
$972$	−0.534159	−0.0171332
$973$	−22.4838	−0.720798
$974$	−7.59233	−0.243274
$975$	−21.8093	−0.698457
$976$	−15.0266	−0.480989
$977$	48.7768	1.56051	0.780255	−	0.625462i	$-0.215089\pi$
$977$	48.7768	1.56051	0.780255	+	0.625462i	$0.215089\pi$
$978$	−20.4924	−0.655273
$979$	−34.2278	−1.09393
$980$	−7.49336	−0.239367
$981$	1.99607	0.0637296
$982$	−28.6647	−0.914727
$983$	−42.2885	−1.34879	−0.674397	−	0.738369i	$-0.735596\pi$
$983$	−42.2885	−1.34879	−0.674397	+	0.738369i	$0.735596\pi$
$984$	−13.2255	−0.421615
$985$	−24.0680	−0.766871
$986$	2.51210	0.0800015
$987$	8.45448	0.269109
$988$	−0.262561	−0.00835319
$989$	2.81904	0.0896404
$990$	−14.1867	−0.450884
$991$	−2.03129	−0.0645259	−0.0322630	−	0.999479i	$-0.510271\pi$
$991$	−2.03129	−0.0645259	−0.0322630	+	0.999479i	$0.510271\pi$
$992$	−10.8650	−0.344965
$993$	33.9104	1.07611
$994$	9.32515	0.295776
$995$	−49.4750	−1.56846
$996$	−2.66664	−0.0844957
$997$	4.13490	0.130954	0.0654768	−	0.997854i	$-0.479143\pi$
$997$	4.13490	0.130954	0.0654768	+	0.997854i	$0.479143\pi$
$998$	−20.4725	−0.648047
$999$	−8.24097	−0.260733

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.i.1.6	✓	7
3.2	odd	2		6003.2.a.j.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.i.1.6	✓	7	1.1	even	1	trivial
6003.2.a.j.1.2		7	3.2	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:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q+1.21072 q^{2} +1.00000 q^{3} -0.534159 q^{4} +3.03795 q^{5} +1.21072 q^{6} -3.40847 q^{7} -3.06816 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.21072 q^{2} +1.00000 q^{3} -0.534159 q^{4} +3.03795 q^{5} +1.21072 q^{6} -3.40847 q^{7} -3.06816 q^{8} +1.00000 q^{9} +3.67810 q^{10} -3.85707 q^{11} -0.534159 q^{12} -5.15691 q^{13} -4.12670 q^{14} +3.03795 q^{15} -2.64635 q^{16} -2.07488 q^{17} +1.21072 q^{18} -0.0953170 q^{19} -1.62275 q^{20} -3.40847 q^{21} -4.66983 q^{22} +1.00000 q^{23} -3.06816 q^{24} +4.22914 q^{25} -6.24357 q^{26} +1.00000 q^{27} +1.82067 q^{28} -1.00000 q^{29} +3.67810 q^{30} -3.70527 q^{31} +2.93232 q^{32} -3.85707 q^{33} -2.51210 q^{34} -10.3548 q^{35} -0.534159 q^{36} -8.24097 q^{37} -0.115402 q^{38} -5.15691 q^{39} -9.32090 q^{40} +4.31059 q^{41} -4.12670 q^{42} +2.81904 q^{43} +2.06029 q^{44} +3.03795 q^{45} +1.21072 q^{46} -2.48043 q^{47} -2.64635 q^{48} +4.61770 q^{49} +5.12030 q^{50} -2.07488 q^{51} +2.75461 q^{52} -6.40448 q^{53} +1.21072 q^{54} -11.7176 q^{55} +10.4577 q^{56} -0.0953170 q^{57} -1.21072 q^{58} -10.8564 q^{59} -1.62275 q^{60} +5.67822 q^{61} -4.48604 q^{62} -3.40847 q^{63} +8.84292 q^{64} -15.6664 q^{65} -4.66983 q^{66} +12.8177 q^{67} +1.10832 q^{68} +1.00000 q^{69} -12.5367 q^{70} -2.25971 q^{71} -3.06816 q^{72} +14.0533 q^{73} -9.97750 q^{74} +4.22914 q^{75} +0.0509145 q^{76} +13.1467 q^{77} -6.24357 q^{78} +0.679730 q^{79} -8.03950 q^{80} +1.00000 q^{81} +5.21891 q^{82} +4.99221 q^{83} +1.82067 q^{84} -6.30339 q^{85} +3.41307 q^{86} -1.00000 q^{87} +11.8341 q^{88} +8.87404 q^{89} +3.67810 q^{90} +17.5772 q^{91} -0.534159 q^{92} -3.70527 q^{93} -3.00310 q^{94} -0.289568 q^{95} +2.93232 q^{96} +12.0257 q^{97} +5.59073 q^{98} -3.85707 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 3 q^{2} + 7 q^{3} + 5 q^{4} - 3 q^{5} - 3 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 3 * q^2 + 7 * q^3 + 5 * q^4 - 3 * q^5 - 3 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9	\( 7 q - 3 q^{2} + 7 q^{3} + 5 q^{4} - 3 q^{5} - 3 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9} + 3 q^{10} - 4 q^{11} + 5 q^{12} - 18 q^{13} - 2 q^{14} - 3 q^{15} - 7 q^{16} - 3 q^{17} - 3 q^{18} - 4 q^{19} - 2 q^{20} - 5 q^{21} - 26 q^{22} + 7 q^{23} - 6 q^{24} - 8 q^{25} - 7 q^{26} + 7 q^{27} - 6 q^{28} - 7 q^{29} + 3 q^{30} - 22 q^{31} + 5 q^{32} - 4 q^{33} + 9 q^{34} + 3 q^{35} + 5 q^{36} - 25 q^{37} + 14 q^{38} - 18 q^{39} - 10 q^{40} - 13 q^{41} - 2 q^{42} - 2 q^{43} + 4 q^{44} - 3 q^{45} - 3 q^{46} - 25 q^{47} - 7 q^{48} - 8 q^{49} + 19 q^{50} - 3 q^{51} - 12 q^{52} - 5 q^{53} - 3 q^{54} - 15 q^{55} + 18 q^{56} - 4 q^{57} + 3 q^{58} + 11 q^{59} - 2 q^{60} - 33 q^{61} + 28 q^{62} - 5 q^{63} - 14 q^{64} - 2 q^{65} - 26 q^{66} + 8 q^{67} + 12 q^{68} + 7 q^{69} - 22 q^{70} - 6 q^{71} - 6 q^{72} + 15 q^{73} + 34 q^{74} - 8 q^{75} - 28 q^{76} - q^{77} - 7 q^{78} - 15 q^{79} - 12 q^{80} + 7 q^{81} - 14 q^{82} + 21 q^{83} - 6 q^{84} - 28 q^{85} - 12 q^{86} - 7 q^{87} - 13 q^{88} + 8 q^{89} + 3 q^{90} + 6 q^{91} + 5 q^{92} - 22 q^{93} - 35 q^{94} - 25 q^{95} + 5 q^{96} + 13 q^{97} + q^{98} - 4 q^{99}+O(q^{100}) \) 7 * q - 3 * q^2 + 7 * q^3 + 5 * q^4 - 3 * q^5 - 3 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9 + 3 * q^10 - 4 * q^11 + 5 * q^12 - 18 * q^13 - 2 * q^14 - 3 * q^15 - 7 * q^16 - 3 * q^17 - 3 * q^18 - 4 * q^19 - 2 * q^20 - 5 * q^21 - 26 * q^22 + 7 * q^23 - 6 * q^24 - 8 * q^25 - 7 * q^26 + 7 * q^27 - 6 * q^28 - 7 * q^29 + 3 * q^30 - 22 * q^31 + 5 * q^32 - 4 * q^33 + 9 * q^34 + 3 * q^35 + 5 * q^36 - 25 * q^37 + 14 * q^38 - 18 * q^39 - 10 * q^40 - 13 * q^41 - 2 * q^42 - 2 * q^43 + 4 * q^44 - 3 * q^45 - 3 * q^46 - 25 * q^47 - 7 * q^48 - 8 * q^49 + 19 * q^50 - 3 * q^51 - 12 * q^52 - 5 * q^53 - 3 * q^54 - 15 * q^55 + 18 * q^56 - 4 * q^57 + 3 * q^58 + 11 * q^59 - 2 * q^60 - 33 * q^61 + 28 * q^62 - 5 * q^63 - 14 * q^64 - 2 * q^65 - 26 * q^66 + 8 * q^67 + 12 * q^68 + 7 * q^69 - 22 * q^70 - 6 * q^71 - 6 * q^72 + 15 * q^73 + 34 * q^74 - 8 * q^75 - 28 * q^76 - q^77 - 7 * q^78 - 15 * q^79 - 12 * q^80 + 7 * q^81 - 14 * q^82 + 21 * q^83 - 6 * q^84 - 28 * q^85 - 12 * q^86 - 7 * q^87 - 13 * q^88 + 8 * q^89 + 3 * q^90 + 6 * q^91 + 5 * q^92 - 22 * q^93 - 35 * q^94 - 25 * q^95 + 5 * q^96 + 13 * q^97 + q^98 - 4 * q^99

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