LMFDB - Embedded newform 2001.2.a.o.1.3

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:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 33 x^{18} + 64 x^{17} + 453 x^{16} - 846 x^{15} - 3353 x^{14} + 5985 x^{13} + \cdots - 256 $ x^20 - 2x^19 - 33x^18 + 64x^17 + 453x^16 - 846x^15 - 3353x^14 + 5985x^13 + 14484x^12 - 24566x^11 - 36791x^10 + 59410x^9 + 52109x^8 - 82362x^7 - 34967x^6 + 60661x^5 + 5201x^4 - 19624x^3 + 2768x^2 + 1408*x - 256
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.40422$ 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)

$f(q)$	$=$	$q-2.40422 q^{2} +1.00000 q^{3} +3.78028 q^{4} +2.94625 q^{5} -2.40422 q^{6} +2.89217 q^{7} -4.28018 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.40422 q^{2} +1.00000 q^{3} +3.78028 q^{4} +2.94625 q^{5} -2.40422 q^{6} +2.89217 q^{7} -4.28018 q^{8} +1.00000 q^{9} -7.08343 q^{10} -2.53497 q^{11} +3.78028 q^{12} +5.47922 q^{13} -6.95342 q^{14} +2.94625 q^{15} +2.72995 q^{16} -3.33691 q^{17} -2.40422 q^{18} -5.49162 q^{19} +11.1376 q^{20} +2.89217 q^{21} +6.09464 q^{22} +1.00000 q^{23} -4.28018 q^{24} +3.68037 q^{25} -13.1732 q^{26} +1.00000 q^{27} +10.9332 q^{28} +1.00000 q^{29} -7.08343 q^{30} +5.60055 q^{31} +1.99697 q^{32} -2.53497 q^{33} +8.02267 q^{34} +8.52105 q^{35} +3.78028 q^{36} +4.06631 q^{37} +13.2031 q^{38} +5.47922 q^{39} -12.6105 q^{40} -9.72536 q^{41} -6.95342 q^{42} +2.73471 q^{43} -9.58291 q^{44} +2.94625 q^{45} -2.40422 q^{46} +10.0668 q^{47} +2.72995 q^{48} +1.36466 q^{49} -8.84842 q^{50} -3.33691 q^{51} +20.7130 q^{52} +1.45207 q^{53} -2.40422 q^{54} -7.46866 q^{55} -12.3790 q^{56} -5.49162 q^{57} -2.40422 q^{58} +13.0989 q^{59} +11.1376 q^{60} +14.3608 q^{61} -13.4650 q^{62} +2.89217 q^{63} -10.2610 q^{64} +16.1431 q^{65} +6.09464 q^{66} +5.14596 q^{67} -12.6144 q^{68} +1.00000 q^{69} -20.4865 q^{70} -3.43935 q^{71} -4.28018 q^{72} +6.90003 q^{73} -9.77631 q^{74} +3.68037 q^{75} -20.7598 q^{76} -7.33158 q^{77} -13.1732 q^{78} -5.51601 q^{79} +8.04310 q^{80} +1.00000 q^{81} +23.3819 q^{82} +0.148675 q^{83} +10.9332 q^{84} -9.83136 q^{85} -6.57486 q^{86} +1.00000 q^{87} +10.8502 q^{88} -10.6836 q^{89} -7.08343 q^{90} +15.8468 q^{91} +3.78028 q^{92} +5.60055 q^{93} -24.2028 q^{94} -16.1797 q^{95} +1.99697 q^{96} +7.16615 q^{97} -3.28094 q^{98} -2.53497 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + 20 * q^3 + 30 * q^4 - q^5 + 2 * q^6 + 9 * q^7 + 6 * q^8 + 20 * q^9	\( 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9} + 7 q^{10} + 30 q^{12} + 21 q^{13} - q^{14} - q^{15} + 58 q^{16} - 4 q^{17} + 2 q^{18} + 7 q^{19} - 20 q^{20} + 9 q^{21} + 7 q^{22} + 20 q^{23} + 6 q^{24} + 47 q^{25} + 8 q^{26} + 20 q^{27} + 11 q^{28} + 20 q^{29} + 7 q^{30} + 28 q^{31} + 14 q^{32} + 16 q^{34} + 9 q^{35} + 30 q^{36} + 14 q^{37} - 20 q^{38} + 21 q^{39} + 34 q^{40} + 7 q^{41} - q^{42} + 3 q^{43} - q^{44} - q^{45} + 2 q^{46} + 3 q^{47} + 58 q^{48} + 35 q^{49} - 24 q^{50} - 4 q^{51} + 73 q^{52} - 19 q^{53} + 2 q^{54} + 29 q^{55} - 30 q^{56} + 7 q^{57} + 2 q^{58} + 20 q^{59} - 20 q^{60} + 15 q^{61} + 12 q^{62} + 9 q^{63} + 82 q^{64} - 28 q^{65} + 7 q^{66} + 20 q^{67} - 23 q^{68} + 20 q^{69} - 24 q^{70} + 63 q^{71} + 6 q^{72} + 19 q^{73} + 16 q^{74} + 47 q^{75} - 44 q^{76} - 7 q^{77} + 8 q^{78} + 32 q^{79} - 56 q^{80} + 20 q^{81} - 20 q^{82} - 21 q^{83} + 11 q^{84} + 4 q^{85} - 6 q^{86} + 20 q^{87} + 55 q^{88} - 13 q^{89} + 7 q^{90} + 70 q^{91} + 30 q^{92} + 28 q^{93} - 12 q^{94} + 9 q^{95} + 14 q^{96} - 9 q^{97} + 31 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 + 20 * q^3 + 30 * q^4 - q^5 + 2 * q^6 + 9 * q^7 + 6 * q^8 + 20 * q^9 + 7 * q^10 + 30 * q^12 + 21 * q^13 - q^14 - q^15 + 58 * q^16 - 4 * q^17 + 2 * q^18 + 7 * q^19 - 20 * q^20 + 9 * q^21 + 7 * q^22 + 20 * q^23 + 6 * q^24 + 47 * q^25 + 8 * q^26 + 20 * q^27 + 11 * q^28 + 20 * q^29 + 7 * q^30 + 28 * q^31 + 14 * q^32 + 16 * q^34 + 9 * q^35 + 30 * q^36 + 14 * q^37 - 20 * q^38 + 21 * q^39 + 34 * q^40 + 7 * q^41 - q^42 + 3 * q^43 - q^44 - q^45 + 2 * q^46 + 3 * q^47 + 58 * q^48 + 35 * q^49 - 24 * q^50 - 4 * q^51 + 73 * q^52 - 19 * q^53 + 2 * q^54 + 29 * q^55 - 30 * q^56 + 7 * q^57 + 2 * q^58 + 20 * q^59 - 20 * q^60 + 15 * q^61 + 12 * q^62 + 9 * q^63 + 82 * q^64 - 28 * q^65 + 7 * q^66 + 20 * q^67 - 23 * q^68 + 20 * q^69 - 24 * q^70 + 63 * q^71 + 6 * q^72 + 19 * q^73 + 16 * q^74 + 47 * q^75 - 44 * q^76 - 7 * q^77 + 8 * q^78 + 32 * q^79 - 56 * q^80 + 20 * q^81 - 20 * q^82 - 21 * q^83 + 11 * q^84 + 4 * q^85 - 6 * q^86 + 20 * q^87 + 55 * q^88 - 13 * q^89 + 7 * q^90 + 70 * q^91 + 30 * q^92 + 28 * q^93 - 12 * q^94 + 9 * q^95 + 14 * q^96 - 9 * q^97 + 31 * q^98

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 $

$2$	−2.40422	−1.70004	−0.850020	−	0.526750i	$-0.823411\pi$
$2$	−2.40422	−1.70004	−0.850020	+	0.526750i	$0.823411\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.78028	1.89014
$5$	2.94625	1.31760	0.658801	−	0.752317i	$-0.271064\pi$
$5$	2.94625	1.31760	0.658801	+	0.752317i	$0.271064\pi$
$6$	−2.40422	−0.981519
$7$	2.89217	1.09314	0.546569	−	0.837414i	$-0.315934\pi$
$7$	2.89217	1.09314	0.546569	+	0.837414i	$0.315934\pi$
$8$	−4.28018	−1.51327
$9$	1.00000	0.333333
$10$	−7.08343	−2.23998
$11$	−2.53497	−0.764323	−0.382162	−	0.924095i	$-0.624820\pi$
$11$	−2.53497	−0.764323	−0.382162	+	0.924095i	$0.624820\pi$
$12$	3.78028	1.09127
$13$	5.47922	1.51966	0.759831	−	0.650121i	$-0.225282\pi$
$13$	5.47922	1.51966	0.759831	+	0.650121i	$0.225282\pi$
$14$	−6.95342	−1.85838
$15$	2.94625	0.760718
$16$	2.72995	0.682487
$17$	−3.33691	−0.809319	−0.404660	−	0.914467i	$-0.632610\pi$
$17$	−3.33691	−0.809319	−0.404660	+	0.914467i	$0.632610\pi$
$18$	−2.40422	−0.566680
$19$	−5.49162	−1.25986	−0.629932	−	0.776651i	$-0.716917\pi$
$19$	−5.49162	−1.25986	−0.629932	+	0.776651i	$0.716917\pi$
$20$	11.1376	2.49045
$21$	2.89217	0.631124
$22$	6.09464	1.29938
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−4.28018	−0.873688
$25$	3.68037	0.736074
$26$	−13.1732	−2.58349
$27$	1.00000	0.192450
$28$	10.9332	2.06618
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−7.08343	−1.29325
$31$	5.60055	1.00589	0.502944	−	0.864319i	$-0.332250\pi$
$31$	5.60055	1.00589	0.502944	+	0.864319i	$0.332250\pi$
$32$	1.99697	0.353018
$33$	−2.53497	−0.441282
$34$	8.02267	1.37588
$35$	8.52105	1.44032
$36$	3.78028	0.630046
$37$	4.06631	0.668497	0.334249	−	0.942485i	$-0.391517\pi$
$37$	4.06631	0.668497	0.334249	+	0.942485i	$0.391517\pi$
$38$	13.2031	2.14182
$39$	5.47922	0.877377
$40$	−12.6105	−1.99389
$41$	−9.72536	−1.51885	−0.759423	−	0.650597i	$-0.774519\pi$
$41$	−9.72536	−1.51885	−0.759423	+	0.650597i	$0.774519\pi$
$42$	−6.95342	−1.07294
$43$	2.73471	0.417040	0.208520	−	0.978018i	$-0.433135\pi$
$43$	2.73471	0.417040	0.208520	+	0.978018i	$0.433135\pi$
$44$	−9.58291	−1.44468
$45$	2.94625	0.439201
$46$	−2.40422	−0.354483
$47$	10.0668	1.46839	0.734197	−	0.678937i	$-0.237559\pi$
$47$	10.0668	1.46839	0.734197	+	0.678937i	$0.237559\pi$
$48$	2.72995	0.394034
$49$	1.36466	0.194951
$50$	−8.84842	−1.25136
$51$	−3.33691	−0.467261
$52$	20.7130	2.87237
$53$	1.45207	0.199458	0.0997288	−	0.995015i	$-0.468202\pi$
$53$	1.45207	0.199458	0.0997288	+	0.995015i	$0.468202\pi$
$54$	−2.40422	−0.327173
$55$	−7.46866	−1.00707
$56$	−12.3790	−1.65422
$57$	−5.49162	−0.727382
$58$	−2.40422	−0.315690
$59$	13.0989	1.70534	0.852669	−	0.522452i	$-0.174982\pi$
$59$	13.0989	1.70534	0.852669	+	0.522452i	$0.174982\pi$
$60$	11.1376	1.43786
$61$	14.3608	1.83871	0.919354	−	0.393430i	$-0.128712\pi$
$61$	14.3608	1.83871	0.919354	+	0.393430i	$0.128712\pi$
$62$	−13.4650	−1.71005
$63$	2.89217	0.364379
$64$	−10.2610	−1.28263
$65$	16.1431	2.00231
$66$	6.09464	0.750198
$67$	5.14596	0.628679	0.314339	−	0.949311i	$-0.398217\pi$
$67$	5.14596	0.628679	0.314339	+	0.949311i	$0.398217\pi$
$68$	−12.6144	−1.52973
$69$	1.00000	0.120386
$70$	−20.4865	−2.44860
$71$	−3.43935	−0.408176	−0.204088	−	0.978953i	$-0.565423\pi$
$71$	−3.43935	−0.408176	−0.204088	+	0.978953i	$0.565423\pi$
$72$	−4.28018	−0.504424
$73$	6.90003	0.807587	0.403794	−	0.914850i	$-0.367691\pi$
$73$	6.90003	0.807587	0.403794	+	0.914850i	$0.367691\pi$
$74$	−9.77631	−1.13647
$75$	3.68037	0.424972
$76$	−20.7598	−2.38132
$77$	−7.33158	−0.835511
$78$	−13.1732	−1.49158
$79$	−5.51601	−0.620599	−0.310300	−	0.950639i	$-0.600429\pi$
$79$	−5.51601	−0.620599	−0.310300	+	0.950639i	$0.600429\pi$
$80$	8.04310	0.899245
$81$	1.00000	0.111111
$82$	23.3819	2.58210
$83$	0.148675	0.0163192	0.00815958	−	0.999967i	$-0.497403\pi$
$83$	0.148675	0.0163192	0.00815958	+	0.999967i	$0.497403\pi$
$84$	10.9332	1.19291
$85$	−9.83136	−1.06636
$86$	−6.57486	−0.708985
$87$	1.00000	0.107211
$88$	10.8502	1.15663
$89$	−10.6836	−1.13246	−0.566232	−	0.824246i	$-0.691599\pi$
$89$	−10.6836	−1.13246	−0.566232	+	0.824246i	$0.691599\pi$
$90$	−7.08343	−0.746659
$91$	15.8468	1.66120
$92$	3.78028	0.394121
$93$	5.60055	0.580750
$94$	−24.2028	−2.49633
$95$	−16.1797	−1.66000
$96$	1.99697	0.203815
$97$	7.16615	0.727612	0.363806	−	0.931475i	$-0.381477\pi$
$97$	7.16615	0.727612	0.363806	+	0.931475i	$0.381477\pi$
$98$	−3.28094	−0.331425
$99$	−2.53497	−0.254774
$100$	13.9128	1.39128
$101$	−6.87796	−0.684383	−0.342191	−	0.939630i	$-0.611169\pi$
$101$	−6.87796	−0.684383	−0.342191	+	0.939630i	$0.611169\pi$
$102$	8.02267	0.794362
$103$	−2.72286	−0.268292	−0.134146	−	0.990962i	$-0.542829\pi$
$103$	−2.72286	−0.268292	−0.134146	+	0.990962i	$0.542829\pi$
$104$	−23.4520	−2.29966
$105$	8.52105	0.831570
$106$	−3.49111	−0.339086
$107$	−9.21917	−0.891250	−0.445625	−	0.895220i	$-0.647019\pi$
$107$	−9.21917	−0.891250	−0.445625	+	0.895220i	$0.647019\pi$
$108$	3.78028	0.363757
$109$	−0.964241	−0.0923575	−0.0461788	−	0.998933i	$-0.514704\pi$
$109$	−0.964241	−0.0923575	−0.0461788	+	0.998933i	$0.514704\pi$
$110$	17.9563	1.71207
$111$	4.06631	0.385957
$112$	7.89548	0.746052
$113$	−4.79493	−0.451070	−0.225535	−	0.974235i	$-0.572413\pi$
$113$	−4.79493	−0.451070	−0.225535	+	0.974235i	$0.572413\pi$
$114$	13.2031	1.23658
$115$	2.94625	0.274739
$116$	3.78028	0.350990
$117$	5.47922	0.506554
$118$	−31.4928	−2.89914
$119$	−9.65092	−0.884698
$120$	−12.6105	−1.15117
$121$	−4.57391	−0.415810
$122$	−34.5265	−3.12588
$123$	−9.72536	−0.876906
$124$	21.1716	1.90127
$125$	−3.88796	−0.347749
$126$	−6.95342	−0.619460
$127$	−3.74468	−0.332287	−0.166144	−	0.986102i	$-0.553131\pi$
$127$	−3.74468	−0.332287	−0.166144	+	0.986102i	$0.553131\pi$
$128$	20.6759	1.82751
$129$	2.73471	0.240778
$130$	−38.8116	−3.40401
$131$	16.6236	1.45241	0.726207	−	0.687477i	$-0.241282\pi$
$131$	16.6236	1.45241	0.726207	+	0.687477i	$0.241282\pi$
$132$	−9.58291	−0.834085
$133$	−15.8827	−1.37720
$134$	−12.3720	−1.06878
$135$	2.94625	0.253573
$136$	14.2826	1.22472
$137$	−15.9108	−1.35935	−0.679677	−	0.733511i	$-0.737880\pi$
$137$	−15.9108	−1.35935	−0.679677	+	0.733511i	$0.737880\pi$
$138$	−2.40422	−0.204661
$139$	21.1653	1.79522	0.897610	−	0.440791i	$-0.145302\pi$
$139$	21.1653	1.79522	0.897610	+	0.440791i	$0.145302\pi$
$140$	32.2119	2.72241
$141$	10.0668	0.847777
$142$	8.26896	0.693916
$143$	−13.8897	−1.16151
$144$	2.72995	0.227496
$145$	2.94625	0.244672
$146$	−16.5892	−1.37293
$147$	1.36466	0.112555
$148$	15.3718	1.26355
$149$	−19.8722	−1.62799	−0.813995	−	0.580871i	$-0.802712\pi$
$149$	−19.8722	−1.62799	−0.813995	+	0.580871i	$0.802712\pi$
$150$	−8.84842	−0.722471
$151$	−8.85747	−0.720811	−0.360405	−	0.932796i	$-0.617362\pi$
$151$	−8.85747	−0.720811	−0.360405	+	0.932796i	$0.617362\pi$
$152$	23.5051	1.90652
$153$	−3.33691	−0.269773
$154$	17.6267	1.42040
$155$	16.5006	1.32536
$156$	20.7130	1.65836
$157$	−7.35129	−0.586697	−0.293349	−	0.956006i	$-0.594770\pi$
$157$	−7.35129	−0.586697	−0.293349	+	0.956006i	$0.594770\pi$
$158$	13.2617	1.05504
$159$	1.45207	0.115157
$160$	5.88356	0.465137
$161$	2.89217	0.227935
$162$	−2.40422	−0.188893
$163$	15.3238	1.20025	0.600124	−	0.799907i	$-0.295118\pi$
$163$	15.3238	1.20025	0.600124	+	0.799907i	$0.295118\pi$
$164$	−36.7646	−2.87083
$165$	−7.46866	−0.581434
$166$	−0.357446	−0.0277432
$167$	14.1921	1.09822	0.549111	−	0.835750i	$-0.314967\pi$
$167$	14.1921	1.09822	0.549111	+	0.835750i	$0.314967\pi$
$168$	−12.3790	−0.955062
$169$	17.0218	1.30937
$170$	23.6368	1.81286
$171$	−5.49162	−0.419954
$172$	10.3380	0.788264
$173$	−7.20007	−0.547411	−0.273706	−	0.961814i	$-0.588249\pi$
$173$	−7.20007	−0.547411	−0.273706	+	0.961814i	$0.588249\pi$
$174$	−2.40422	−0.182264
$175$	10.6443	0.804631
$176$	−6.92034	−0.521641
$177$	13.0989	0.984577
$178$	25.6858	1.92523
$179$	25.1099	1.87680	0.938399	−	0.345553i	$-0.112308\pi$
$179$	25.1099	1.87680	0.938399	+	0.345553i	$0.112308\pi$
$180$	11.1376	0.830150
$181$	2.09541	0.155750	0.0778752	−	0.996963i	$-0.475186\pi$
$181$	2.09541	0.155750	0.0778752	+	0.996963i	$0.475186\pi$
$182$	−38.0993	−2.82411
$183$	14.3608	1.06158
$184$	−4.28018	−0.315539
$185$	11.9804	0.880813
$186$	−13.4650	−0.987299
$187$	8.45898	0.618582
$188$	38.0553	2.77547
$189$	2.89217	0.210375
$190$	38.8995	2.82206
$191$	13.3115	0.963183	0.481592	−	0.876396i	$-0.340059\pi$
$191$	13.3115	0.963183	0.481592	+	0.876396i	$0.340059\pi$
$192$	−10.2610	−0.740527
$193$	−11.8471	−0.852772	−0.426386	−	0.904541i	$-0.640213\pi$
$193$	−11.8471	−0.852772	−0.426386	+	0.904541i	$0.640213\pi$
$194$	−17.2290	−1.23697
$195$	16.1431	1.15603
$196$	5.15879	0.368485
$197$	−8.41802	−0.599759	−0.299880	−	0.953977i	$-0.596946\pi$
$197$	−8.41802	−0.599759	−0.299880	+	0.953977i	$0.596946\pi$
$198$	6.09464	0.433127
$199$	−10.0318	−0.711134	−0.355567	−	0.934651i	$-0.615712\pi$
$199$	−10.0318	−0.711134	−0.355567	+	0.934651i	$0.615712\pi$
$200$	−15.7527	−1.11388
$201$	5.14596	0.362968
$202$	16.5361	1.16348
$203$	2.89217	0.202991
$204$	−12.6144	−0.883188
$205$	−28.6533	−2.00123
$206$	6.54637	0.456107
$207$	1.00000	0.0695048
$208$	14.9580	1.03715
$209$	13.9211	0.962943
$210$	−20.4865	−1.41370
$211$	−26.3386	−1.81323	−0.906613	−	0.421963i	$-0.861341\pi$
$211$	−26.3386	−1.81323	−0.906613	+	0.421963i	$0.861341\pi$
$212$	5.48924	0.377003
$213$	−3.43935	−0.235661
$214$	22.1649	1.51516
$215$	8.05714	0.549493
$216$	−4.28018	−0.291229
$217$	16.1978	1.09957
$218$	2.31825	0.157012
$219$	6.90003	0.466261
$220$	−28.2336	−1.90351
$221$	−18.2836	−1.22989
$222$	−9.77631	−0.656143
$223$	−21.2327	−1.42185	−0.710923	−	0.703270i	$-0.751723\pi$
$223$	−21.2327	−1.42185	−0.710923	+	0.703270i	$0.751723\pi$
$224$	5.77558	0.385897
$225$	3.68037	0.245358
$226$	11.5281	0.766837
$227$	23.8417	1.58243	0.791213	−	0.611541i	$-0.209450\pi$
$227$	23.8417	1.58243	0.791213	+	0.611541i	$0.209450\pi$
$228$	−20.7598	−1.37485
$229$	16.4089	1.08433	0.542165	−	0.840272i	$-0.317605\pi$
$229$	16.4089	1.08433	0.542165	+	0.840272i	$0.317605\pi$
$230$	−7.08343	−0.467067
$231$	−7.33158	−0.482383
$232$	−4.28018	−0.281008
$233$	−13.3058	−0.871690	−0.435845	−	0.900022i	$-0.643550\pi$
$233$	−13.3058	−0.871690	−0.435845	+	0.900022i	$0.643550\pi$
$234$	−13.1732	−0.861162
$235$	29.6593	1.93476
$236$	49.5177	3.22333
$237$	−5.51601	−0.358303
$238$	23.2029	1.50402
$239$	14.4324	0.933555	0.466777	−	0.884375i	$-0.345415\pi$
$239$	14.4324	0.933555	0.466777	+	0.884375i	$0.345415\pi$
$240$	8.04310	0.519180
$241$	−5.94893	−0.383204	−0.191602	−	0.981473i	$-0.561368\pi$
$241$	−5.94893	−0.383204	−0.191602	+	0.981473i	$0.561368\pi$
$242$	10.9967	0.706893
$243$	1.00000	0.0641500
$244$	54.2877	3.47542
$245$	4.02062	0.256868
$246$	23.3819	1.49078
$247$	−30.0898	−1.91457
$248$	−23.9714	−1.52218
$249$	0.148675	0.00942187
$250$	9.34751	0.591188
$251$	−15.4453	−0.974901	−0.487451	−	0.873151i	$-0.662073\pi$
$251$	−15.4453	−0.974901	−0.487451	+	0.873151i	$0.662073\pi$
$252$	10.9332	0.688728
$253$	−2.53497	−0.159372
$254$	9.00305	0.564901
$255$	−9.83136	−0.615664
$256$	−29.1873	−1.82421
$257$	23.3758	1.45814	0.729070	−	0.684439i	$-0.239953\pi$
$257$	23.3758	1.45814	0.729070	+	0.684439i	$0.239953\pi$
$258$	−6.57486	−0.409333
$259$	11.7605	0.730760
$260$	61.0255	3.78464
$261$	1.00000	0.0618984
$262$	−39.9669	−2.46916
$263$	3.88612	0.239629	0.119814	−	0.992796i	$-0.461770\pi$
$263$	3.88612	0.239629	0.119814	+	0.992796i	$0.461770\pi$
$264$	10.8502	0.667781
$265$	4.27817	0.262806
$266$	38.1855	2.34130
$267$	−10.6836	−0.653828
$268$	19.4531	1.18829
$269$	−13.4486	−0.819977	−0.409989	−	0.912091i	$-0.634467\pi$
$269$	−13.4486	−0.819977	−0.409989	+	0.912091i	$0.634467\pi$
$270$	−7.08343	−0.431084
$271$	18.2914	1.11113	0.555563	−	0.831475i	$-0.312503\pi$
$271$	18.2914	1.11113	0.555563	+	0.831475i	$0.312503\pi$
$272$	−9.10958	−0.552350
$273$	15.8468	0.959094
$274$	38.2532	2.31096
$275$	−9.32964	−0.562599
$276$	3.78028	0.227546
$277$	24.3837	1.46507	0.732537	−	0.680728i	$-0.238336\pi$
$277$	24.3837	1.46507	0.732537	+	0.680728i	$0.238336\pi$
$278$	−50.8861	−3.05195
$279$	5.60055	0.335296
$280$	−36.4717	−2.17960
$281$	−7.44029	−0.443850	−0.221925	−	0.975064i	$-0.571234\pi$
$281$	−7.44029	−0.443850	−0.221925	+	0.975064i	$0.571234\pi$
$282$	−24.2028	−1.44126
$283$	−27.7217	−1.64788	−0.823942	−	0.566674i	$-0.808230\pi$
$283$	−27.7217	−1.64788	−0.823942	+	0.566674i	$0.808230\pi$
$284$	−13.0017	−0.771510
$285$	−16.1797	−0.958400
$286$	33.3938	1.97462
$287$	−28.1274	−1.66031
$288$	1.99697	0.117673
$289$	−5.86503	−0.345002
$290$	−7.08343	−0.415953
$291$	7.16615	0.420087
$292$	26.0840	1.52645
$293$	−9.91319	−0.579135	−0.289567	−	0.957158i	$-0.593511\pi$
$293$	−9.91319	−0.579135	−0.289567	+	0.957158i	$0.593511\pi$
$294$	−3.28094	−0.191348
$295$	38.5927	2.24696
$296$	−17.4045	−1.01162
$297$	−2.53497	−0.147094
$298$	47.7771	2.76765
$299$	5.47922	0.316871
$300$	13.9128	0.803257
$301$	7.90927	0.455883
$302$	21.2953	1.22541
$303$	−6.87796	−0.395129
$304$	−14.9918	−0.859840
$305$	42.3104	2.42269
$306$	8.02267	0.458625
$307$	11.4819	0.655304	0.327652	−	0.944799i	$-0.393743\pi$
$307$	11.4819	0.655304	0.327652	+	0.944799i	$0.393743\pi$
$308$	−27.7154	−1.57923
$309$	−2.72286	−0.154898
$310$	−39.6711	−2.25317
$311$	−9.92846	−0.562992	−0.281496	−	0.959562i	$-0.590831\pi$
$311$	−9.92846	−0.562992	−0.281496	+	0.959562i	$0.590831\pi$
$312$	−23.4520	−1.32771
$313$	−4.22620	−0.238879	−0.119440	−	0.992841i	$-0.538110\pi$
$313$	−4.22620	−0.238879	−0.119440	+	0.992841i	$0.538110\pi$
$314$	17.6741	0.997409
$315$	8.52105	0.480107
$316$	−20.8520	−1.17302
$317$	0.238908	0.0134184	0.00670919	−	0.999977i	$-0.497864\pi$
$317$	0.238908	0.0134184	0.00670919	+	0.999977i	$0.497864\pi$
$318$	−3.49111	−0.195771
$319$	−2.53497	−0.141931
$320$	−30.2316	−1.69000
$321$	−9.21917	−0.514564
$322$	−6.95342	−0.387499
$323$	18.3250	1.01963
$324$	3.78028	0.210015
$325$	20.1655	1.11858
$326$	−36.8417	−2.04047
$327$	−0.964241	−0.0533226
$328$	41.6263	2.29843
$329$	29.1149	1.60516
$330$	17.9563	0.988462
$331$	15.9383	0.876049	0.438024	−	0.898963i	$-0.355678\pi$
$331$	15.9383	0.876049	0.438024	+	0.898963i	$0.355678\pi$
$332$	0.562031	0.0308455
$333$	4.06631	0.222832
$334$	−34.1210	−1.86702
$335$	15.1613	0.828348
$336$	7.89548	0.430733
$337$	10.3579	0.564231	0.282116	−	0.959380i	$-0.408964\pi$
$337$	10.3579	0.564231	0.282116	+	0.959380i	$0.408964\pi$
$338$	−40.9242	−2.22598
$339$	−4.79493	−0.260425
$340$	−37.1653	−2.01557
$341$	−14.1972	−0.768824
$342$	13.2031	0.713940
$343$	−16.2984	−0.880030
$344$	−11.7051	−0.631095
$345$	2.94625	0.158621
$346$	17.3106	0.930621
$347$	−21.5048	−1.15444	−0.577218	−	0.816590i	$-0.695862\pi$
$347$	−21.5048	−1.15444	−0.577218	+	0.816590i	$0.695862\pi$
$348$	3.78028	0.202644
$349$	−16.9041	−0.904857	−0.452429	−	0.891801i	$-0.649442\pi$
$349$	−16.9041	−0.904857	−0.452429	+	0.891801i	$0.649442\pi$
$350$	−25.5912	−1.36790
$351$	5.47922	0.292459
$352$	−5.06227	−0.269820
$353$	−21.8094	−1.16080	−0.580398	−	0.814333i	$-0.697103\pi$
$353$	−21.8094	−1.16080	−0.580398	+	0.814333i	$0.697103\pi$
$354$	−31.4928	−1.67382
$355$	−10.1332	−0.537814
$356$	−40.3871	−2.14051
$357$	−9.65092	−0.510781
$358$	−60.3696	−3.19063
$359$	−5.95246	−0.314159	−0.157080	−	0.987586i	$-0.550208\pi$
$359$	−5.95246	−0.314159	−0.157080	+	0.987586i	$0.550208\pi$
$360$	−12.6105	−0.664630
$361$	11.1579	0.587256
$362$	−5.03782	−0.264782
$363$	−4.57391	−0.240068
$364$	59.9054	3.13990
$365$	20.3292	1.06408
$366$	−34.5265	−1.80473
$367$	7.76989	0.405585	0.202793	−	0.979222i	$-0.434998\pi$
$367$	7.76989	0.405585	0.202793	+	0.979222i	$0.434998\pi$
$368$	2.72995	0.142308
$369$	−9.72536	−0.506282
$370$	−28.8034	−1.49742
$371$	4.19965	0.218035
$372$	21.1716	1.09770
$373$	−30.8504	−1.59737	−0.798687	−	0.601747i	$-0.794472\pi$
$373$	−30.8504	−1.59737	−0.798687	+	0.601747i	$0.794472\pi$
$374$	−20.3373	−1.05161
$375$	−3.88796	−0.200773
$376$	−43.0877	−2.22208
$377$	5.47922	0.282194
$378$	−6.95342	−0.357645
$379$	−35.0094	−1.79831	−0.899157	−	0.437627i	$-0.855819\pi$
$379$	−35.0094	−1.79831	−0.899157	+	0.437627i	$0.855819\pi$
$380$	−61.1636	−3.13763
$381$	−3.74468	−0.191846
$382$	−32.0037	−1.63745
$383$	−6.69965	−0.342336	−0.171168	−	0.985242i	$-0.554754\pi$
$383$	−6.69965	−0.342336	−0.171168	+	0.985242i	$0.554754\pi$
$384$	20.6759	1.05511
$385$	−21.6006	−1.10087
$386$	28.4830	1.44975
$387$	2.73471	0.139013
$388$	27.0900	1.37529
$389$	29.4790	1.49464	0.747321	−	0.664463i	$-0.231340\pi$
$389$	29.4790	1.49464	0.747321	+	0.664463i	$0.231340\pi$
$390$	−38.8116	−1.96530
$391$	−3.33691	−0.168755
$392$	−5.84099	−0.295015
$393$	16.6236	0.838551
$394$	20.2388	1.01961
$395$	−16.2515	−0.817703
$396$	−9.58291	−0.481559
$397$	0.826533	0.0414825	0.0207413	−	0.999785i	$-0.493397\pi$
$397$	0.826533	0.0414825	0.0207413	+	0.999785i	$0.493397\pi$
$398$	24.1186	1.20896
$399$	−15.8827	−0.795130
$400$	10.0472	0.502361
$401$	36.7446	1.83494	0.917469	−	0.397808i	$-0.130229\pi$
$401$	36.7446	1.83494	0.917469	+	0.397808i	$0.130229\pi$
$402$	−12.3720	−0.617060
$403$	30.6866	1.52861
$404$	−26.0006	−1.29358
$405$	2.94625	0.146400
$406$	−6.95342	−0.345092
$407$	−10.3080	−0.510948
$408$	14.2826	0.707093
$409$	−28.9646	−1.43221	−0.716103	−	0.697995i	$-0.754076\pi$
$409$	−28.9646	−1.43221	−0.716103	+	0.697995i	$0.754076\pi$
$410$	68.8889	3.40218
$411$	−15.9108	−0.784824
$412$	−10.2932	−0.507109
$413$	37.8844	1.86417
$414$	−2.40422	−0.118161
$415$	0.438032	0.0215021
$416$	10.9418	0.536467
$417$	21.1653	1.03647
$418$	−33.4694	−1.63704
$419$	−16.0034	−0.781818	−0.390909	−	0.920429i	$-0.627839\pi$
$419$	−16.0034	−0.781818	−0.390909	+	0.920429i	$0.627839\pi$
$420$	32.2119	1.57178
$421$	−13.3663	−0.651435	−0.325718	−	0.945467i	$-0.605606\pi$
$421$	−13.3663	−0.651435	−0.325718	+	0.945467i	$0.605606\pi$
$422$	63.3239	3.08256
$423$	10.0668	0.489464
$424$	−6.21514	−0.301834
$425$	−12.2811	−0.595719
$426$	8.26896	0.400633
$427$	41.5338	2.00996
$428$	−34.8510	−1.68459
$429$	−13.8897	−0.670600
$430$	−19.3712	−0.934160
$431$	21.6711	1.04386	0.521931	−	0.852988i	$-0.325212\pi$
$431$	21.6711	1.04386	0.521931	+	0.852988i	$0.325212\pi$
$432$	2.72995	0.131345
$433$	−9.86289	−0.473980	−0.236990	−	0.971512i	$-0.576161\pi$
$433$	−9.86289	−0.473980	−0.236990	+	0.971512i	$0.576161\pi$
$434$	−38.9430	−1.86932
$435$	2.94625	0.141262
$436$	−3.64510	−0.174569
$437$	−5.49162	−0.262700
$438$	−16.5892	−0.792663
$439$	−1.77488	−0.0847104	−0.0423552	−	0.999103i	$-0.513486\pi$
$439$	−1.77488	−0.0847104	−0.0423552	+	0.999103i	$0.513486\pi$
$440$	31.9672	1.52398
$441$	1.36466	0.0649838
$442$	43.9579	2.09087
$443$	12.0886	0.574345	0.287173	−	0.957879i	$-0.407285\pi$
$443$	12.0886	0.574345	0.287173	+	0.957879i	$0.407285\pi$
$444$	15.3718	0.729513
$445$	−31.4766	−1.49214
$446$	51.0481	2.41720
$447$	−19.8722	−0.939921
$448$	−29.6767	−1.40209
$449$	36.3803	1.71689	0.858447	−	0.512903i	$-0.171430\pi$
$449$	36.3803	1.71689	0.858447	+	0.512903i	$0.171430\pi$
$450$	−8.84842	−0.417119
$451$	24.6535	1.16089
$452$	−18.1262	−0.852584
$453$	−8.85747	−0.416160
$454$	−57.3206	−2.69019
$455$	46.6887	2.18880
$456$	23.5051	1.10073
$457$	−29.5734	−1.38338	−0.691692	−	0.722193i	$-0.743134\pi$
$457$	−29.5734	−1.38338	−0.691692	+	0.722193i	$0.743134\pi$
$458$	−39.4506	−1.84340
$459$	−3.33691	−0.155754
$460$	11.1376	0.519295
$461$	−8.92222	−0.415549	−0.207775	−	0.978177i	$-0.566622\pi$
$461$	−8.92222	−0.415549	−0.207775	+	0.978177i	$0.566622\pi$
$462$	17.6267	0.820070
$463$	−2.14871	−0.0998593	−0.0499296	−	0.998753i	$-0.515900\pi$
$463$	−2.14871	−0.0998593	−0.0499296	+	0.998753i	$0.515900\pi$
$464$	2.72995	0.126735
$465$	16.5006	0.765197
$466$	31.9900	1.48191
$467$	−4.84533	−0.224215	−0.112108	−	0.993696i	$-0.535760\pi$
$467$	−4.84533	−0.224215	−0.112108	+	0.993696i	$0.535760\pi$
$468$	20.7130	0.957457
$469$	14.8830	0.687233
$470$	−71.3074	−3.28917
$471$	−7.35129	−0.338730
$472$	−56.0659	−2.58064
$473$	−6.93243	−0.318754
$474$	13.2617	0.609130
$475$	−20.2112	−0.927353
$476$	−36.4831	−1.67220
$477$	1.45207	0.0664859
$478$	−34.6987	−1.58708
$479$	−37.4306	−1.71025	−0.855124	−	0.518424i	$-0.826519\pi$
$479$	−37.4306	−1.71025	−0.855124	+	0.518424i	$0.826519\pi$
$480$	5.88356	0.268547
$481$	22.2802	1.01589
$482$	14.3025	0.651462
$483$	2.89217	0.131598
$484$	−17.2906	−0.785938
$485$	21.1132	0.958703
$486$	−2.40422	−0.109058
$487$	−39.3534	−1.78327	−0.891636	−	0.452753i	$-0.850442\pi$
$487$	−39.3534	−1.78327	−0.891636	+	0.452753i	$0.850442\pi$
$488$	−61.4667	−2.78247
$489$	15.3238	0.692964
$490$	−9.66646	−0.436686
$491$	−6.74588	−0.304437	−0.152219	−	0.988347i	$-0.548642\pi$
$491$	−6.74588	−0.304437	−0.152219	+	0.988347i	$0.548642\pi$
$492$	−36.7646	−1.65747
$493$	−3.33691	−0.150287
$494$	72.3424	3.25484
$495$	−7.46866	−0.335691
$496$	15.2892	0.686505
$497$	−9.94720	−0.446193
$498$	−0.357446	−0.0160176
$499$	−41.1634	−1.84273	−0.921364	−	0.388701i	$-0.872924\pi$
$499$	−41.1634	−1.84273	−0.921364	+	0.388701i	$0.872924\pi$
$500$	−14.6976	−0.657295
$501$	14.1921	0.634058
$502$	37.1340	1.65737
$503$	16.1315	0.719267	0.359634	−	0.933094i	$-0.382902\pi$
$503$	16.1315	0.719267	0.359634	+	0.933094i	$0.382902\pi$
$504$	−12.3790	−0.551405
$505$	−20.2642	−0.901744
$506$	6.09464	0.270940
$507$	17.0218	0.755965
$508$	−14.1559	−0.628069
$509$	25.5786	1.13375	0.566875	−	0.823804i	$-0.308152\pi$
$509$	25.5786	1.13375	0.566875	+	0.823804i	$0.308152\pi$
$510$	23.6368	1.04665
$511$	19.9561	0.882805
$512$	28.8210	1.27372
$513$	−5.49162	−0.242461
$514$	−56.2005	−2.47890
$515$	−8.02223	−0.353502
$516$	10.3380	0.455104
$517$	−25.5191	−1.12233
$518$	−28.2748	−1.24232
$519$	−7.20007	−0.316048
$520$	−69.0955	−3.03004
$521$	1.33903	0.0586639	0.0293319	−	0.999570i	$-0.490662\pi$
$521$	1.33903	0.0586639	0.0293319	+	0.999570i	$0.490662\pi$
$522$	−2.40422	−0.105230
$523$	−13.3703	−0.584644	−0.292322	−	0.956320i	$-0.594428\pi$
$523$	−13.3703	−0.584644	−0.292322	+	0.956320i	$0.594428\pi$
$524$	62.8419	2.74526
$525$	10.6443	0.464554
$526$	−9.34310	−0.407378
$527$	−18.6885	−0.814085
$528$	−6.92034	−0.301169
$529$	1.00000	0.0434783
$530$	−10.2857	−0.446780
$531$	13.0989	0.568446
$532$	−60.0410	−2.60311
$533$	−53.2873	−2.30813
$534$	25.6858	1.11153
$535$	−27.1619	−1.17431
$536$	−22.0256	−0.951362
$537$	25.1099	1.08357
$538$	32.3335	1.39400
$539$	−3.45938	−0.149006
$540$	11.1376	0.479287
$541$	−22.2616	−0.957102	−0.478551	−	0.878060i	$-0.658838\pi$
$541$	−22.2616	−0.957102	−0.478551	+	0.878060i	$0.658838\pi$
$542$	−43.9767	−1.88896
$543$	2.09541	0.0899226
$544$	−6.66371	−0.285704
$545$	−2.84089	−0.121690
$546$	−38.0993	−1.63050
$547$	−5.97191	−0.255340	−0.127670	−	0.991817i	$-0.540750\pi$
$547$	−5.97191	−0.255340	−0.127670	+	0.991817i	$0.540750\pi$
$548$	−60.1474	−2.56937
$549$	14.3608	0.612903
$550$	22.4305	0.956441
$551$	−5.49162	−0.233951
$552$	−4.28018	−0.182177
$553$	−15.9532	−0.678401
$554$	−58.6237	−2.49068
$555$	11.9804	0.508538
$556$	80.0108	3.39321
$557$	15.4242	0.653546	0.326773	−	0.945103i	$-0.394039\pi$
$557$	15.4242	0.653546	0.326773	+	0.945103i	$0.394039\pi$
$558$	−13.4650	−0.570017
$559$	14.9841	0.633760
$560$	23.2620	0.983000
$561$	8.45898	0.357138
$562$	17.8881	0.754564
$563$	−25.8939	−1.09130	−0.545649	−	0.838014i	$-0.683717\pi$
$563$	−25.8939	−1.09130	−0.545649	+	0.838014i	$0.683717\pi$
$564$	38.0553	1.60242
$565$	−14.1271	−0.594330
$566$	66.6491	2.80147
$567$	2.89217	0.121460
$568$	14.7211	0.617682
$569$	17.1818	0.720300	0.360150	−	0.932894i	$-0.382725\pi$
$569$	17.1818	0.720300	0.360150	+	0.932894i	$0.382725\pi$
$570$	38.8995	1.62932
$571$	7.63458	0.319497	0.159749	−	0.987158i	$-0.448932\pi$
$571$	7.63458	0.319497	0.159749	+	0.987158i	$0.448932\pi$
$572$	−52.5068	−2.19542
$573$	13.3115	0.556094
$574$	67.6245	2.82259
$575$	3.68037	0.153482
$576$	−10.2610	−0.427544
$577$	15.4653	0.643829	0.321915	−	0.946769i	$-0.395674\pi$
$577$	15.4653	0.643829	0.321915	+	0.946769i	$0.395674\pi$
$578$	14.1008	0.586518
$579$	−11.8471	−0.492348
$580$	11.1376	0.462465
$581$	0.429992	0.0178391
$582$	−17.2290	−0.714165
$583$	−3.68097	−0.152450
$584$	−29.5334	−1.22210
$585$	16.1431	0.667436
$586$	23.8335	0.984553
$587$	−8.74351	−0.360883	−0.180442	−	0.983586i	$-0.557753\pi$
$587$	−8.74351	−0.360883	−0.180442	+	0.983586i	$0.557753\pi$
$588$	5.15879	0.212745
$589$	−30.7561	−1.26728
$590$	−92.7855	−3.81992
$591$	−8.41802	−0.346271
$592$	11.1008	0.456240
$593$	−5.30487	−0.217845	−0.108922	−	0.994050i	$-0.534740\pi$
$593$	−5.30487	−0.217845	−0.108922	+	0.994050i	$0.534740\pi$
$594$	6.09464	0.250066
$595$	−28.4340	−1.16568
$596$	−75.1223	−3.07713
$597$	−10.0318	−0.410574
$598$	−13.1732	−0.538694
$599$	23.0248	0.940766	0.470383	−	0.882462i	$-0.344116\pi$
$599$	23.0248	0.940766	0.470383	+	0.882462i	$0.344116\pi$
$600$	−15.7527	−0.643099
$601$	16.1564	0.659035	0.329517	−	0.944150i	$-0.393114\pi$
$601$	16.1564	0.659035	0.329517	+	0.944150i	$0.393114\pi$
$602$	−19.0156	−0.775019
$603$	5.14596	0.209560
$604$	−33.4837	−1.36243
$605$	−13.4759	−0.547871
$606$	16.5361	0.671735
$607$	−18.0036	−0.730744	−0.365372	−	0.930862i	$-0.619058\pi$
$607$	−18.0036	−0.730744	−0.365372	+	0.930862i	$0.619058\pi$
$608$	−10.9666	−0.444754
$609$	2.89217	0.117197
$610$	−101.724	−4.11866
$611$	55.1582	2.23146
$612$	−12.6144	−0.509909
$613$	−12.9637	−0.523598	−0.261799	−	0.965122i	$-0.584316\pi$
$613$	−12.9637	−0.523598	−0.261799	+	0.965122i	$0.584316\pi$
$614$	−27.6049	−1.11404
$615$	−28.6533	−1.15541
$616$	31.3805	1.26436
$617$	−28.0759	−1.13029	−0.565147	−	0.824990i	$-0.691181\pi$
$617$	−28.0759	−1.13029	−0.565147	+	0.824990i	$0.691181\pi$
$618$	6.54637	0.263333
$619$	10.8016	0.434155	0.217077	−	0.976154i	$-0.430348\pi$
$619$	10.8016	0.434155	0.217077	+	0.976154i	$0.430348\pi$
$620$	62.3769	2.50511
$621$	1.00000	0.0401286
$622$	23.8702	0.957109
$623$	−30.8989	−1.23794
$624$	14.9580	0.598798
$625$	−29.8567	−1.19427
$626$	10.1607	0.406104
$627$	13.9211	0.555955
$628$	−27.7899	−1.10894
$629$	−13.5689	−0.541028
$630$	−20.4865	−0.816201
$631$	5.84331	0.232618	0.116309	−	0.993213i	$-0.462894\pi$
$631$	5.84331	0.232618	0.116309	+	0.993213i	$0.462894\pi$
$632$	23.6095	0.939136
$633$	−26.3386	−1.04687
$634$	−0.574387	−0.0228118
$635$	−11.0328	−0.437822
$636$	5.48924	0.217663
$637$	7.47726	0.296260
$638$	6.09464	0.241289
$639$	−3.43935	−0.136059
$640$	60.9163	2.40793
$641$	7.15996	0.282802	0.141401	−	0.989952i	$-0.454839\pi$
$641$	7.15996	0.282802	0.141401	+	0.989952i	$0.454839\pi$
$642$	22.1649	0.874779
$643$	26.2405	1.03483	0.517413	−	0.855736i	$-0.326895\pi$
$643$	26.2405	1.03483	0.517413	+	0.855736i	$0.326895\pi$
$644$	10.9332	0.430829
$645$	8.05714	0.317250
$646$	−44.0574	−1.73342
$647$	6.56156	0.257961	0.128981	−	0.991647i	$-0.458829\pi$
$647$	6.56156	0.257961	0.128981	+	0.991647i	$0.458829\pi$
$648$	−4.28018	−0.168141
$649$	−33.2055	−1.30343
$650$	−48.4824	−1.90164
$651$	16.1978	0.634840
$652$	57.9280	2.26864
$653$	32.9805	1.29063	0.645313	−	0.763919i	$-0.276727\pi$
$653$	32.9805	1.29063	0.645313	+	0.763919i	$0.276727\pi$
$654$	2.31825	0.0906507
$655$	48.9773	1.91370
$656$	−26.5497	−1.03659
$657$	6.90003	0.269196
$658$	−69.9987	−2.72883
$659$	−15.8366	−0.616906	−0.308453	−	0.951240i	$-0.599811\pi$
$659$	−15.8366	−0.616906	−0.308453	+	0.951240i	$0.599811\pi$
$660$	−28.2336	−1.09899
$661$	34.3249	1.33508	0.667541	−	0.744573i	$-0.267347\pi$
$661$	34.3249	1.33508	0.667541	+	0.744573i	$0.267347\pi$
$662$	−38.3192	−1.48932
$663$	−18.2836	−0.710078
$664$	−0.636354	−0.0246953
$665$	−46.7944	−1.81461
$666$	−9.77631	−0.378824
$667$	1.00000	0.0387202
$668$	53.6503	2.07579
$669$	−21.2327	−0.820904
$670$	−36.4510	−1.40823
$671$	−36.4042	−1.40537
$672$	5.77558	0.222798
$673$	−45.5926	−1.75746	−0.878732	−	0.477316i	$-0.841610\pi$
$673$	−45.5926	−1.75746	−0.878732	+	0.477316i	$0.841610\pi$
$674$	−24.9027	−0.959216
$675$	3.68037	0.141657
$676$	64.3472	2.47489
$677$	29.3381	1.12756	0.563778	−	0.825926i	$-0.309347\pi$
$677$	29.3381	1.12756	0.563778	+	0.825926i	$0.309347\pi$
$678$	11.5281	0.442733
$679$	20.7257	0.795380
$680$	42.0800	1.61369
$681$	23.8417	0.913614
$682$	34.1333	1.30703
$683$	−29.7307	−1.13761	−0.568806	−	0.822472i	$-0.692594\pi$
$683$	−29.7307	−1.13761	−0.568806	+	0.822472i	$0.692594\pi$
$684$	−20.7598	−0.793772
$685$	−46.8772	−1.79109
$686$	39.1849	1.49609
$687$	16.4089	0.626038
$688$	7.46563	0.284624
$689$	7.95623	0.303108
$690$	−7.08343	−0.269661
$691$	30.2644	1.15131	0.575656	−	0.817692i	$-0.304747\pi$
$691$	30.2644	1.15131	0.575656	+	0.817692i	$0.304747\pi$
$692$	−27.2183	−1.03468
$693$	−7.33158	−0.278504
$694$	51.7022	1.96259
$695$	62.3583	2.36538
$696$	−4.28018	−0.162240
$697$	32.4526	1.22923
$698$	40.6413	1.53829
$699$	−13.3058	−0.503270
$700$	40.2383	1.52086
$701$	−37.9983	−1.43517	−0.717587	−	0.696468i	$-0.754754\pi$
$701$	−37.9983	−1.43517	−0.717587	+	0.696468i	$0.754754\pi$
$702$	−13.1732	−0.497192
$703$	−22.3306	−0.842215
$704$	26.0115	0.980345
$705$	29.6593	1.11703
$706$	52.4346	1.97340
$707$	−19.8923	−0.748125
$708$	49.5177	1.86099
$709$	10.9125	0.409829	0.204914	−	0.978780i	$-0.434308\pi$
$709$	10.9125	0.409829	0.204914	+	0.978780i	$0.434308\pi$
$710$	24.3624	0.914305
$711$	−5.51601	−0.206866
$712$	45.7279	1.71373
$713$	5.60055	0.209742
$714$	23.2029	0.868348
$715$	−40.9224	−1.53041
$716$	94.9222	3.54741
$717$	14.4324	0.538988
$718$	14.3110	0.534083
$719$	5.25817	0.196097	0.0980483	−	0.995182i	$-0.468740\pi$
$719$	5.25817	0.196097	0.0980483	+	0.995182i	$0.468740\pi$
$720$	8.04310	0.299748
$721$	−7.87499	−0.293280
$722$	−26.8260	−0.998359
$723$	−5.94893	−0.221243
$724$	7.92123	0.294390
$725$	3.68037	0.136685
$726$	10.9967	0.408125
$727$	−38.0970	−1.41294	−0.706470	−	0.707743i	$-0.749714\pi$
$727$	−38.0970	−1.41294	−0.706470	+	0.707743i	$0.749714\pi$
$728$	−67.8273	−2.51385
$729$	1.00000	0.0370370
$730$	−48.8759	−1.80898
$731$	−9.12550	−0.337519
$732$	54.2877	2.00653
$733$	34.9903	1.29240	0.646199	−	0.763169i	$-0.276358\pi$
$733$	34.9903	1.29240	0.646199	+	0.763169i	$0.276358\pi$
$734$	−18.6805	−0.689511
$735$	4.02062	0.148303
$736$	1.99697	0.0736093
$737$	−13.0449	−0.480514
$738$	23.3819	0.860700
$739$	−0.714040	−0.0262664	−0.0131332	−	0.999914i	$-0.504181\pi$
$739$	−0.714040	−0.0262664	−0.0131332	+	0.999914i	$0.504181\pi$
$740$	45.2891	1.66486
$741$	−30.0898	−1.10537
$742$	−10.0969	−0.370668
$743$	2.80223	0.102804	0.0514020	−	0.998678i	$-0.483631\pi$
$743$	2.80223	0.102804	0.0514020	+	0.998678i	$0.483631\pi$
$744$	−23.9714	−0.878833
$745$	−58.5483	−2.14504
$746$	74.1712	2.71560
$747$	0.148675	0.00543972
$748$	31.9773	1.16921
$749$	−26.6634	−0.974260
$750$	9.34751	0.341323
$751$	35.2668	1.28690	0.643452	−	0.765486i	$-0.277502\pi$
$751$	35.2668	1.28690	0.643452	+	0.765486i	$0.277502\pi$
$752$	27.4818	1.00216
$753$	−15.4453	−0.562860
$754$	−13.1732	−0.479741
$755$	−26.0963	−0.949741
$756$	10.9332	0.397637
$757$	−25.8154	−0.938275	−0.469138	−	0.883125i	$-0.655435\pi$
$757$	−25.8154	−0.938275	−0.469138	+	0.883125i	$0.655435\pi$
$758$	84.1704	3.05721
$759$	−2.53497	−0.0920137
$760$	69.2519	2.51203
$761$	19.3370	0.700967	0.350483	−	0.936569i	$-0.386017\pi$
$761$	19.3370	0.700967	0.350483	+	0.936569i	$0.386017\pi$
$762$	9.00305	0.326146
$763$	−2.78875	−0.100960
$764$	50.3210	1.82055
$765$	−9.83136	−0.355454
$766$	16.1074	0.581986
$767$	71.7720	2.59154
$768$	−29.1873	−1.05321
$769$	9.14798	0.329884	0.164942	−	0.986303i	$-0.447256\pi$
$769$	9.14798	0.329884	0.164942	+	0.986303i	$0.447256\pi$
$770$	51.9327	1.87153
$771$	23.3758	0.841857
$772$	−44.7853	−1.61186
$773$	23.4795	0.844497	0.422249	−	0.906480i	$-0.361241\pi$
$773$	23.4795	0.844497	0.422249	+	0.906480i	$0.361241\pi$
$774$	−6.57486	−0.236328
$775$	20.6121	0.740408
$776$	−30.6724	−1.10108
$777$	11.7605	0.421904
$778$	−70.8739	−2.54095
$779$	53.4080	1.91354
$780$	61.0255	2.18506
$781$	8.71867	0.311979
$782$	8.02267	0.286890
$783$	1.00000	0.0357371
$784$	3.72545	0.133052
$785$	−21.6587	−0.773033
$786$	−39.9669	−1.42557
$787$	25.5258	0.909895	0.454947	−	0.890518i	$-0.349658\pi$
$787$	25.5258	0.909895	0.454947	+	0.890518i	$0.349658\pi$
$788$	−31.8225	−1.13363
$789$	3.88612	0.138350
$790$	39.0722	1.39013
$791$	−13.8678	−0.493081
$792$	10.8502	0.385543
$793$	78.6858	2.79421
$794$	−1.98717	−0.0705220
$795$	4.27817	0.151731
$796$	−37.9229	−1.34414
$797$	13.3605	0.473252	0.236626	−	0.971601i	$-0.423958\pi$
$797$	13.3605	0.473252	0.236626	+	0.971601i	$0.423958\pi$
$798$	38.1855	1.35175
$799$	−33.5920	−1.18840
$800$	7.34958	0.259847
$801$	−10.6836	−0.377488
$802$	−88.3421	−3.11947
$803$	−17.4914	−0.617258
$804$	19.4531	0.686060
$805$	8.52105	0.300328
$806$	−73.7774	−2.59870
$807$	−13.4486	−0.473414
$808$	29.4389	1.03566
$809$	−24.0390	−0.845168	−0.422584	−	0.906324i	$-0.638877\pi$
$809$	−24.0390	−0.845168	−0.422584	+	0.906324i	$0.638877\pi$
$810$	−7.08343	−0.248886
$811$	34.1766	1.20010	0.600052	−	0.799961i	$-0.295146\pi$
$811$	34.1766	1.20010	0.600052	+	0.799961i	$0.295146\pi$
$812$	10.9332	0.383681
$813$	18.2914	0.641509
$814$	24.7827	0.868633
$815$	45.1476	1.58145
$816$	−9.10958	−0.318899
$817$	−15.0180	−0.525414
$818$	69.6372	2.43481
$819$	15.8468	0.553733
$820$	−108.317	−3.78261
$821$	−38.4884	−1.34326	−0.671628	−	0.740889i	$-0.734405\pi$
$821$	−38.4884	−1.34326	−0.671628	+	0.740889i	$0.734405\pi$
$822$	38.2532	1.33423
$823$	36.4264	1.26974	0.634872	−	0.772618i	$-0.281053\pi$
$823$	36.4264	1.26974	0.634872	+	0.772618i	$0.281053\pi$
$824$	11.6544	0.405999
$825$	−9.32964	−0.324816
$826$	−91.0825	−3.16917
$827$	31.0706	1.08043	0.540216	−	0.841527i	$-0.318343\pi$
$827$	31.0706	1.08043	0.540216	+	0.841527i	$0.318343\pi$
$828$	3.78028	0.131374
$829$	−4.24754	−0.147523	−0.0737617	−	0.997276i	$-0.523500\pi$
$829$	−4.24754	−0.147523	−0.0737617	+	0.997276i	$0.523500\pi$
$830$	−1.05313	−0.0365545
$831$	24.3837	0.845860
$832$	−56.2225	−1.94916
$833$	−4.55374	−0.157778
$834$	−50.8861	−1.76204
$835$	41.8136	1.44702
$836$	52.6257	1.82010
$837$	5.60055	0.193583
$838$	38.4758	1.32912
$839$	−41.2662	−1.42467	−0.712334	−	0.701840i	$-0.752362\pi$
$839$	−41.2662	−1.42467	−0.712334	+	0.701840i	$0.752362\pi$
$840$	−36.4717	−1.25839
$841$	1.00000	0.0344828
$842$	32.1356	1.10747
$843$	−7.44029	−0.256257
$844$	−99.5674	−3.42725
$845$	50.1505	1.72523
$846$	−24.2028	−0.832110
$847$	−13.2285	−0.454537
$848$	3.96408	0.136127
$849$	−27.7217	−0.951407
$850$	29.5264	1.01275
$851$	4.06631	0.139391
$852$	−13.0017	−0.445431
$853$	−39.2466	−1.34378	−0.671888	−	0.740652i	$-0.734517\pi$
$853$	−39.2466	−1.34378	−0.671888	+	0.740652i	$0.734517\pi$
$854$	−99.8565	−3.41702
$855$	−16.1797	−0.553333
$856$	39.4597	1.34871
$857$	30.7802	1.05143	0.525716	−	0.850660i	$-0.323797\pi$
$857$	30.7802	1.05143	0.525716	+	0.850660i	$0.323797\pi$
$858$	33.3938	1.14005
$859$	30.1159	1.02754	0.513770	−	0.857928i	$-0.328248\pi$
$859$	30.1159	1.02754	0.513770	+	0.857928i	$0.328248\pi$
$860$	30.4582	1.03862
$861$	−28.1274	−0.958580
$862$	−52.1022	−1.77461
$863$	45.6275	1.55318	0.776589	−	0.630007i	$-0.216948\pi$
$863$	45.6275	1.55318	0.776589	+	0.630007i	$0.216948\pi$
$864$	1.99697	0.0679383
$865$	−21.2132	−0.721270
$866$	23.7126	0.805786
$867$	−5.86503	−0.199187
$868$	61.2320	2.07835
$869$	13.9829	0.474339
$870$	−7.08343	−0.240151
$871$	28.1958	0.955378
$872$	4.12713	0.139762
$873$	7.16615	0.242537
$874$	13.2031	0.446600
$875$	−11.2446	−0.380138
$876$	26.0840	0.881298
$877$	−23.7833	−0.803107	−0.401553	−	0.915836i	$-0.631530\pi$
$877$	−23.7833	−0.803107	−0.401553	+	0.915836i	$0.631530\pi$
$878$	4.26720	0.144011
$879$	−9.91319	−0.334364
$880$	−20.3890	−0.687314
$881$	−0.298307	−0.0100502	−0.00502511	−	0.999987i	$-0.501600\pi$
$881$	−0.298307	−0.0100502	−0.00502511	+	0.999987i	$0.501600\pi$
$882$	−3.28094	−0.110475
$883$	−43.1568	−1.45234	−0.726171	−	0.687514i	$-0.758702\pi$
$883$	−43.1568	−1.45234	−0.726171	+	0.687514i	$0.758702\pi$
$884$	−69.1173	−2.32467
$885$	38.5927	1.29728
$886$	−29.0636	−0.976410
$887$	38.7604	1.30145	0.650724	−	0.759314i	$-0.274466\pi$
$887$	38.7604	1.30145	0.650724	+	0.759314i	$0.274466\pi$
$888$	−17.4045	−0.584058
$889$	−10.8303	−0.363236
$890$	75.6768	2.53669
$891$	−2.53497	−0.0849248
$892$	−80.2655	−2.68749
$893$	−55.2830	−1.84997
$894$	47.7771	1.59790
$895$	73.9798	2.47287
$896$	59.7982	1.99772
$897$	5.47922	0.182946
$898$	−87.4663	−2.91879
$899$	5.60055	0.186789
$900$	13.9128	0.463761
$901$	−4.84544	−0.161425
$902$	−59.2725	−1.97356
$903$	7.90927	0.263204
$904$	20.5232	0.682591
$905$	6.17359	0.205217
$906$	21.2953	0.707489
$907$	−32.4189	−1.07645	−0.538226	−	0.842800i	$-0.680905\pi$
$907$	−32.4189	−1.07645	−0.538226	+	0.842800i	$0.680905\pi$
$908$	90.1281	2.99101
$909$	−6.87796	−0.228128
$910$	−112.250	−3.72105
$911$	27.6195	0.915075	0.457538	−	0.889190i	$-0.348732\pi$
$911$	27.6195	0.915075	0.457538	+	0.889190i	$0.348732\pi$
$912$	−14.9918	−0.496429
$913$	−0.376886	−0.0124731
$914$	71.1009	2.35181
$915$	42.3104	1.39874
$916$	62.0301	2.04953
$917$	48.0784	1.58769
$918$	8.02267	0.264787
$919$	21.4245	0.706729	0.353364	−	0.935486i	$-0.385038\pi$
$919$	21.4245	0.706729	0.353364	+	0.935486i	$0.385038\pi$
$920$	−12.6105	−0.415755
$921$	11.4819	0.378340
$922$	21.4510	0.706451
$923$	−18.8450	−0.620289
$924$	−27.7154	−0.911770
$925$	14.9655	0.492063
$926$	5.16599	0.169765
$927$	−2.72286	−0.0894306
$928$	1.99697	0.0655537
$929$	−52.6913	−1.72874	−0.864372	−	0.502852i	$-0.832284\pi$
$929$	−52.6913	−1.72874	−0.864372	+	0.502852i	$0.832284\pi$
$930$	−39.6711	−1.30087
$931$	−7.49419	−0.245612
$932$	−50.2995	−1.64761
$933$	−9.92846	−0.325043
$934$	11.6493	0.381175
$935$	24.9222	0.815044
$936$	−23.4520	−0.766554
$937$	33.9135	1.10791	0.553953	−	0.832548i	$-0.313119\pi$
$937$	33.9135	1.10791	0.553953	+	0.832548i	$0.313119\pi$
$938$	−35.7820	−1.16832
$939$	−4.22620	−0.137917
$940$	112.120	3.65696
$941$	26.7835	0.873118	0.436559	−	0.899676i	$-0.356197\pi$
$941$	26.7835	0.873118	0.436559	+	0.899676i	$0.356197\pi$
$942$	17.6741	0.575854
$943$	−9.72536	−0.316701
$944$	35.7594	1.16387
$945$	8.52105	0.277190
$946$	16.6671	0.541894
$947$	28.9246	0.939924	0.469962	−	0.882687i	$-0.344268\pi$
$947$	28.9246	0.939924	0.469962	+	0.882687i	$0.344268\pi$
$948$	−20.8520	−0.677243
$949$	37.8068	1.22726
$950$	48.5921	1.57654
$951$	0.238908	0.00774711
$952$	41.3077	1.33879
$953$	−38.7068	−1.25384	−0.626918	−	0.779085i	$-0.715684\pi$
$953$	−38.7068	−1.25384	−0.626918	+	0.779085i	$0.715684\pi$
$954$	−3.49111	−0.113029
$955$	39.2188	1.26909
$956$	54.5585	1.76455
$957$	−2.53497	−0.0819441
$958$	89.9914	2.90749
$959$	−46.0169	−1.48596
$960$	−30.2316	−0.975720
$961$	0.366147	0.0118112
$962$	−53.5665	−1.72705
$963$	−9.21917	−0.297083
$964$	−22.4886	−0.724309
$965$	−34.9044	−1.12361
$966$	−6.95342	−0.223723
$967$	−55.2190	−1.77572	−0.887861	−	0.460112i	$-0.847809\pi$
$967$	−55.2190	−1.77572	−0.887861	+	0.460112i	$0.847809\pi$
$968$	19.5772	0.629233
$969$	18.3250	0.588685
$970$	−50.7609	−1.62983
$971$	28.4582	0.913266	0.456633	−	0.889655i	$-0.349055\pi$
$971$	28.4582	0.913266	0.456633	+	0.889655i	$0.349055\pi$
$972$	3.78028	0.121252
$973$	61.2138	1.96242
$974$	94.6142	3.03163
$975$	20.1655	0.645814
$976$	39.2041	1.25489
$977$	22.1394	0.708301	0.354151	−	0.935188i	$-0.384770\pi$
$977$	22.1394	0.708301	0.354151	+	0.935188i	$0.384770\pi$
$978$	−36.8417	−1.17807
$979$	27.0827	0.865568
$980$	15.1991	0.485517
$981$	−0.964241	−0.0307858
$982$	16.2186	0.517556
$983$	−20.5852	−0.656567	−0.328283	−	0.944579i	$-0.606470\pi$
$983$	−20.5852	−0.656567	−0.328283	+	0.944579i	$0.606470\pi$
$984$	41.6263	1.32700
$985$	−24.8016	−0.790243
$986$	8.02267	0.255494
$987$	29.1149	0.926738
$988$	−113.748	−3.61880
$989$	2.73471	0.0869589
$990$	17.9563	0.570689
$991$	1.48952	0.0473161	0.0236580	−	0.999720i	$-0.492469\pi$
$991$	1.48952	0.0473161	0.0236580	+	0.999720i	$0.492469\pi$
$992$	11.1841	0.355096
$993$	15.9383	0.505787
$994$	23.9153	0.758546
$995$	−29.5561	−0.936992
$996$	0.562031	0.0178086
$997$	−21.2966	−0.674471	−0.337235	−	0.941420i	$-0.609492\pi$
$997$	−21.2966	−0.674471	−0.337235	+	0.941420i	$0.609492\pi$
$998$	98.9660	3.13271
$999$	4.06631	0.128652

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.o.1.3	✓	20
3.2	odd	2		6003.2.a.s.1.18		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.o.1.3	✓	20	1.1	even	1	trivial
6003.2.a.s.1.18		20	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)

\(f(q)\)	\(=\)	\(q-2.40422 q^{2} +1.00000 q^{3} +3.78028 q^{4} +2.94625 q^{5} -2.40422 q^{6} +2.89217 q^{7} -4.28018 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.40422 q^{2} +1.00000 q^{3} +3.78028 q^{4} +2.94625 q^{5} -2.40422 q^{6} +2.89217 q^{7} -4.28018 q^{8} +1.00000 q^{9} -7.08343 q^{10} -2.53497 q^{11} +3.78028 q^{12} +5.47922 q^{13} -6.95342 q^{14} +2.94625 q^{15} +2.72995 q^{16} -3.33691 q^{17} -2.40422 q^{18} -5.49162 q^{19} +11.1376 q^{20} +2.89217 q^{21} +6.09464 q^{22} +1.00000 q^{23} -4.28018 q^{24} +3.68037 q^{25} -13.1732 q^{26} +1.00000 q^{27} +10.9332 q^{28} +1.00000 q^{29} -7.08343 q^{30} +5.60055 q^{31} +1.99697 q^{32} -2.53497 q^{33} +8.02267 q^{34} +8.52105 q^{35} +3.78028 q^{36} +4.06631 q^{37} +13.2031 q^{38} +5.47922 q^{39} -12.6105 q^{40} -9.72536 q^{41} -6.95342 q^{42} +2.73471 q^{43} -9.58291 q^{44} +2.94625 q^{45} -2.40422 q^{46} +10.0668 q^{47} +2.72995 q^{48} +1.36466 q^{49} -8.84842 q^{50} -3.33691 q^{51} +20.7130 q^{52} +1.45207 q^{53} -2.40422 q^{54} -7.46866 q^{55} -12.3790 q^{56} -5.49162 q^{57} -2.40422 q^{58} +13.0989 q^{59} +11.1376 q^{60} +14.3608 q^{61} -13.4650 q^{62} +2.89217 q^{63} -10.2610 q^{64} +16.1431 q^{65} +6.09464 q^{66} +5.14596 q^{67} -12.6144 q^{68} +1.00000 q^{69} -20.4865 q^{70} -3.43935 q^{71} -4.28018 q^{72} +6.90003 q^{73} -9.77631 q^{74} +3.68037 q^{75} -20.7598 q^{76} -7.33158 q^{77} -13.1732 q^{78} -5.51601 q^{79} +8.04310 q^{80} +1.00000 q^{81} +23.3819 q^{82} +0.148675 q^{83} +10.9332 q^{84} -9.83136 q^{85} -6.57486 q^{86} +1.00000 q^{87} +10.8502 q^{88} -10.6836 q^{89} -7.08343 q^{90} +15.8468 q^{91} +3.78028 q^{92} +5.60055 q^{93} -24.2028 q^{94} -16.1797 q^{95} +1.99697 q^{96} +7.16615 q^{97} -3.28094 q^{98} -2.53497 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + 20 * q^3 + 30 * q^4 - q^5 + 2 * q^6 + 9 * q^7 + 6 * q^8 + 20 * q^9	\( 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9} + 7 q^{10} + 30 q^{12} + 21 q^{13} - q^{14} - q^{15} + 58 q^{16} - 4 q^{17} + 2 q^{18} + 7 q^{19} - 20 q^{20} + 9 q^{21} + 7 q^{22} + 20 q^{23} + 6 q^{24} + 47 q^{25} + 8 q^{26} + 20 q^{27} + 11 q^{28} + 20 q^{29} + 7 q^{30} + 28 q^{31} + 14 q^{32} + 16 q^{34} + 9 q^{35} + 30 q^{36} + 14 q^{37} - 20 q^{38} + 21 q^{39} + 34 q^{40} + 7 q^{41} - q^{42} + 3 q^{43} - q^{44} - q^{45} + 2 q^{46} + 3 q^{47} + 58 q^{48} + 35 q^{49} - 24 q^{50} - 4 q^{51} + 73 q^{52} - 19 q^{53} + 2 q^{54} + 29 q^{55} - 30 q^{56} + 7 q^{57} + 2 q^{58} + 20 q^{59} - 20 q^{60} + 15 q^{61} + 12 q^{62} + 9 q^{63} + 82 q^{64} - 28 q^{65} + 7 q^{66} + 20 q^{67} - 23 q^{68} + 20 q^{69} - 24 q^{70} + 63 q^{71} + 6 q^{72} + 19 q^{73} + 16 q^{74} + 47 q^{75} - 44 q^{76} - 7 q^{77} + 8 q^{78} + 32 q^{79} - 56 q^{80} + 20 q^{81} - 20 q^{82} - 21 q^{83} + 11 q^{84} + 4 q^{85} - 6 q^{86} + 20 q^{87} + 55 q^{88} - 13 q^{89} + 7 q^{90} + 70 q^{91} + 30 q^{92} + 28 q^{93} - 12 q^{94} + 9 q^{95} + 14 q^{96} - 9 q^{97} + 31 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 + 20 * q^3 + 30 * q^4 - q^5 + 2 * q^6 + 9 * q^7 + 6 * q^8 + 20 * q^9 + 7 * q^10 + 30 * q^12 + 21 * q^13 - q^14 - q^15 + 58 * q^16 - 4 * q^17 + 2 * q^18 + 7 * q^19 - 20 * q^20 + 9 * q^21 + 7 * q^22 + 20 * q^23 + 6 * q^24 + 47 * q^25 + 8 * q^26 + 20 * q^27 + 11 * q^28 + 20 * q^29 + 7 * q^30 + 28 * q^31 + 14 * q^32 + 16 * q^34 + 9 * q^35 + 30 * q^36 + 14 * q^37 - 20 * q^38 + 21 * q^39 + 34 * q^40 + 7 * q^41 - q^42 + 3 * q^43 - q^44 - q^45 + 2 * q^46 + 3 * q^47 + 58 * q^48 + 35 * q^49 - 24 * q^50 - 4 * q^51 + 73 * q^52 - 19 * q^53 + 2 * q^54 + 29 * q^55 - 30 * q^56 + 7 * q^57 + 2 * q^58 + 20 * q^59 - 20 * q^60 + 15 * q^61 + 12 * q^62 + 9 * q^63 + 82 * q^64 - 28 * q^65 + 7 * q^66 + 20 * q^67 - 23 * q^68 + 20 * q^69 - 24 * q^70 + 63 * q^71 + 6 * q^72 + 19 * q^73 + 16 * q^74 + 47 * q^75 - 44 * q^76 - 7 * q^77 + 8 * q^78 + 32 * q^79 - 56 * q^80 + 20 * q^81 - 20 * q^82 - 21 * q^83 + 11 * q^84 + 4 * q^85 - 6 * q^86 + 20 * q^87 + 55 * q^88 - 13 * q^89 + 7 * q^90 + 70 * q^91 + 30 * q^92 + 28 * q^93 - 12 * q^94 + 9 * q^95 + 14 * q^96 - 9 * q^97 + 31 * q^98

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