LMFDB - Embedded newform 2001.2.a.l.1.2

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:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 18 x^{9} + 30 x^{8} + 124 x^{7} - 152 x^{6} - 408 x^{5} + 285 x^{4} + 634 x^{3} + \cdots - 108 $ x^11 - 2x^10 - 18x^9 + 30x^8 + 124x^7 - 152x^6 - 408x^5 + 285x^4 + 634x^3 - 93x^2 - 369x - 108
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.96728$ 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)

$f(q)$	$=$	$q-1.96728 q^{2} -1.00000 q^{3} +1.87020 q^{4} -3.90206 q^{5} +1.96728 q^{6} -0.839519 q^{7} +0.255353 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.96728 q^{2} -1.00000 q^{3} +1.87020 q^{4} -3.90206 q^{5} +1.96728 q^{6} -0.839519 q^{7} +0.255353 q^{8} +1.00000 q^{9} +7.67646 q^{10} +4.08430 q^{11} -1.87020 q^{12} -6.57808 q^{13} +1.65157 q^{14} +3.90206 q^{15} -4.24275 q^{16} +0.379112 q^{17} -1.96728 q^{18} -6.25665 q^{19} -7.29764 q^{20} +0.839519 q^{21} -8.03497 q^{22} +1.00000 q^{23} -0.255353 q^{24} +10.2261 q^{25} +12.9409 q^{26} -1.00000 q^{27} -1.57007 q^{28} -1.00000 q^{29} -7.67646 q^{30} +3.23356 q^{31} +7.83599 q^{32} -4.08430 q^{33} -0.745820 q^{34} +3.27585 q^{35} +1.87020 q^{36} -7.47652 q^{37} +12.3086 q^{38} +6.57808 q^{39} -0.996402 q^{40} -9.84358 q^{41} -1.65157 q^{42} -6.99632 q^{43} +7.63846 q^{44} -3.90206 q^{45} -1.96728 q^{46} -9.65140 q^{47} +4.24275 q^{48} -6.29521 q^{49} -20.1176 q^{50} -0.379112 q^{51} -12.3023 q^{52} +10.9060 q^{53} +1.96728 q^{54} -15.9372 q^{55} -0.214373 q^{56} +6.25665 q^{57} +1.96728 q^{58} -11.3965 q^{59} +7.29764 q^{60} +2.37385 q^{61} -6.36133 q^{62} -0.839519 q^{63} -6.93009 q^{64} +25.6681 q^{65} +8.03497 q^{66} -11.1611 q^{67} +0.709015 q^{68} -1.00000 q^{69} -6.44453 q^{70} +4.24762 q^{71} +0.255353 q^{72} -8.99243 q^{73} +14.7084 q^{74} -10.2261 q^{75} -11.7012 q^{76} -3.42884 q^{77} -12.9409 q^{78} +1.79119 q^{79} +16.5555 q^{80} +1.00000 q^{81} +19.3651 q^{82} -6.12986 q^{83} +1.57007 q^{84} -1.47932 q^{85} +13.7637 q^{86} +1.00000 q^{87} +1.04294 q^{88} +4.65351 q^{89} +7.67646 q^{90} +5.52242 q^{91} +1.87020 q^{92} -3.23356 q^{93} +18.9870 q^{94} +24.4138 q^{95} -7.83599 q^{96} -2.57912 q^{97} +12.3845 q^{98} +4.08430 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9} + 14 q^{10} + 11 q^{11} - 18 q^{12} - 5 q^{13} + 17 q^{14} - 2 q^{15} + 20 q^{16} + 15 q^{17} + 2 q^{18} - 6 q^{19} + 21 q^{20} - 3 q^{21} - 10 q^{22} + 11 q^{23} - 18 q^{24} + 3 q^{25} - 5 q^{26} - 11 q^{27} + 7 q^{28} - 11 q^{29} - 14 q^{30} + 35 q^{31} + 28 q^{32} - 11 q^{33} + 28 q^{34} + 15 q^{35} + 18 q^{36} - 28 q^{37} - 2 q^{38} + 5 q^{39} - q^{40} + 10 q^{41} - 17 q^{42} - 6 q^{43} + 18 q^{44} + 2 q^{45} + 2 q^{46} + 15 q^{47} - 20 q^{48} + 22 q^{49} + 15 q^{50} - 15 q^{51} - 36 q^{52} - 7 q^{53} - 2 q^{54} - 12 q^{55} + 56 q^{56} + 6 q^{57} - 2 q^{58} - 20 q^{59} - 21 q^{60} - 20 q^{61} - 11 q^{62} + 3 q^{63} + 36 q^{64} + 11 q^{65} + 10 q^{66} - 39 q^{67} + 35 q^{68} - 11 q^{69} + 38 q^{70} + 49 q^{71} + 18 q^{72} - 3 q^{73} + 37 q^{74} - 3 q^{75} - 18 q^{76} + 25 q^{77} + 5 q^{78} + 41 q^{79} + 51 q^{80} + 11 q^{81} - 19 q^{82} + 13 q^{83} - 7 q^{84} + 62 q^{86} + 11 q^{87} - 40 q^{88} + 34 q^{89} + 14 q^{90} + 2 q^{91} + 18 q^{92} - 35 q^{93} - 14 q^{94} + 25 q^{95} - 28 q^{96} - 11 q^{97} + 53 q^{98} + 11 q^{99}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9 + 14 * q^10 + 11 * q^11 - 18 * q^12 - 5 * q^13 + 17 * q^14 - 2 * q^15 + 20 * q^16 + 15 * q^17 + 2 * q^18 - 6 * q^19 + 21 * q^20 - 3 * q^21 - 10 * q^22 + 11 * q^23 - 18 * q^24 + 3 * q^25 - 5 * q^26 - 11 * q^27 + 7 * q^28 - 11 * q^29 - 14 * q^30 + 35 * q^31 + 28 * q^32 - 11 * q^33 + 28 * q^34 + 15 * q^35 + 18 * q^36 - 28 * q^37 - 2 * q^38 + 5 * q^39 - q^40 + 10 * q^41 - 17 * q^42 - 6 * q^43 + 18 * q^44 + 2 * q^45 + 2 * q^46 + 15 * q^47 - 20 * q^48 + 22 * q^49 + 15 * q^50 - 15 * q^51 - 36 * q^52 - 7 * q^53 - 2 * q^54 - 12 * q^55 + 56 * q^56 + 6 * q^57 - 2 * q^58 - 20 * q^59 - 21 * q^60 - 20 * q^61 - 11 * q^62 + 3 * q^63 + 36 * q^64 + 11 * q^65 + 10 * q^66 - 39 * q^67 + 35 * q^68 - 11 * q^69 + 38 * q^70 + 49 * q^71 + 18 * q^72 - 3 * q^73 + 37 * q^74 - 3 * q^75 - 18 * q^76 + 25 * q^77 + 5 * q^78 + 41 * q^79 + 51 * q^80 + 11 * q^81 - 19 * q^82 + 13 * q^83 - 7 * q^84 + 62 * q^86 + 11 * q^87 - 40 * q^88 + 34 * q^89 + 14 * q^90 + 2 * q^91 + 18 * q^92 - 35 * q^93 - 14 * q^94 + 25 * q^95 - 28 * q^96 - 11 * q^97 + 53 * q^98 + 11 * 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 $

$2$	−1.96728	−1.39108	−0.695539	−	0.718488i	$-0.744835\pi$
$2$	−1.96728	−1.39108	−0.695539	+	0.718488i	$0.744835\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.87020	0.935100
$5$	−3.90206	−1.74505	−0.872527	−	0.488565i	$-0.837520\pi$
$5$	−3.90206	−1.74505	−0.872527	+	0.488565i	$0.837520\pi$
$6$	1.96728	0.803140
$7$	−0.839519	−0.317308	−0.158654	−	0.987334i	$-0.550715\pi$
$7$	−0.839519	−0.317308	−0.158654	+	0.987334i	$0.550715\pi$
$8$	0.255353	0.0902808
$9$	1.00000	0.333333
$10$	7.67646	2.42751
$11$	4.08430	1.23146	0.615731	−	0.787956i	$-0.288861\pi$
$11$	4.08430	1.23146	0.615731	+	0.787956i	$0.288861\pi$
$12$	−1.87020	−0.539880
$13$	−6.57808	−1.82443	−0.912215	−	0.409712i	$-0.865629\pi$
$13$	−6.57808	−1.82443	−0.912215	+	0.409712i	$0.865629\pi$
$14$	1.65157	0.441401
$15$	3.90206	1.00751
$16$	−4.24275	−1.06069
$17$	0.379112	0.0919481	0.0459741	−	0.998943i	$-0.485361\pi$
$17$	0.379112	0.0919481	0.0459741	+	0.998943i	$0.485361\pi$
$18$	−1.96728	−0.463693
$19$	−6.25665	−1.43537	−0.717687	−	0.696366i	$-0.754799\pi$
$19$	−6.25665	−1.43537	−0.717687	+	0.696366i	$0.754799\pi$
$20$	−7.29764	−1.63180
$21$	0.839519	0.183198
$22$	−8.03497	−1.71306
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−0.255353	−0.0521236
$25$	10.2261	2.04522
$26$	12.9409	2.53793
$27$	−1.00000	−0.192450
$28$	−1.57007	−0.296715
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−7.67646	−1.40152
$31$	3.23356	0.580765	0.290383	−	0.956911i	$-0.406217\pi$
$31$	3.23356	0.580765	0.290383	+	0.956911i	$0.406217\pi$
$32$	7.83599	1.38522
$33$	−4.08430	−0.710985
$34$	−0.745820	−0.127907
$35$	3.27585	0.553720
$36$	1.87020	0.311700
$37$	−7.47652	−1.22913	−0.614566	−	0.788865i	$-0.710669\pi$
$37$	−7.47652	−1.22913	−0.614566	+	0.788865i	$0.710669\pi$
$38$	12.3086	1.99672
$39$	6.57808	1.05334
$40$	−0.996402	−0.157545
$41$	−9.84358	−1.53731	−0.768655	−	0.639664i	$-0.779073\pi$
$41$	−9.84358	−1.53731	−0.768655	+	0.639664i	$0.779073\pi$
$42$	−1.65157	−0.254843
$43$	−6.99632	−1.06693	−0.533465	−	0.845822i	$-0.679110\pi$
$43$	−6.99632	−1.06693	−0.533465	+	0.845822i	$0.679110\pi$
$44$	7.63846	1.15154
$45$	−3.90206	−0.581685
$46$	−1.96728	−0.290060
$47$	−9.65140	−1.40780	−0.703900	−	0.710299i	$-0.748560\pi$
$47$	−9.65140	−1.40780	−0.703900	+	0.710299i	$0.748560\pi$
$48$	4.24275	0.612388
$49$	−6.29521	−0.899316
$50$	−20.1176	−2.84506
$51$	−0.379112	−0.0530863
$52$	−12.3023	−1.70602
$53$	10.9060	1.49805	0.749027	−	0.662540i	$-0.230521\pi$
$53$	10.9060	1.49805	0.749027	+	0.662540i	$0.230521\pi$
$54$	1.96728	0.267713
$55$	−15.9372	−2.14897
$56$	−0.214373	−0.0286468
$57$	6.25665	0.828713
$58$	1.96728	0.258317
$59$	−11.3965	−1.48370	−0.741850	−	0.670566i	$-0.766051\pi$
$59$	−11.3965	−1.48370	−0.741850	+	0.670566i	$0.766051\pi$
$60$	7.29764	0.942121
$61$	2.37385	0.303940	0.151970	−	0.988385i	$-0.451438\pi$
$61$	2.37385	0.303940	0.151970	+	0.988385i	$0.451438\pi$
$62$	−6.36133	−0.807890
$63$	−0.839519	−0.105769
$64$	−6.93009	−0.866262
$65$	25.6681	3.18373
$66$	8.03497	0.989036
$67$	−11.1611	−1.36355	−0.681774	−	0.731563i	$-0.738791\pi$
$67$	−11.1611	−1.36355	−0.681774	+	0.731563i	$0.738791\pi$
$68$	0.709015	0.0859807
$69$	−1.00000	−0.120386
$70$	−6.44453	−0.770268
$71$	4.24762	0.504100	0.252050	−	0.967714i	$-0.418895\pi$
$71$	4.24762	0.504100	0.252050	+	0.967714i	$0.418895\pi$
$72$	0.255353	0.0300936
$73$	−8.99243	−1.05248	−0.526242	−	0.850335i	$-0.676400\pi$
$73$	−8.99243	−1.05248	−0.526242	+	0.850335i	$0.676400\pi$
$74$	14.7084	1.70982
$75$	−10.2261	−1.18081
$76$	−11.7012	−1.34222
$77$	−3.42884	−0.390753
$78$	−12.9409	−1.46527
$79$	1.79119	0.201524	0.100762	−	0.994911i	$-0.467872\pi$
$79$	1.79119	0.201524	0.100762	+	0.994911i	$0.467872\pi$
$80$	16.5555	1.85096
$81$	1.00000	0.111111
$82$	19.3651	2.13852
$83$	−6.12986	−0.672839	−0.336420	−	0.941712i	$-0.609216\pi$
$83$	−6.12986	−0.672839	−0.336420	+	0.941712i	$0.609216\pi$
$84$	1.57007	0.171308
$85$	−1.47932	−0.160455
$86$	13.7637	1.48418
$87$	1.00000	0.107211
$88$	1.04294	0.111177
$89$	4.65351	0.493271	0.246636	−	0.969108i	$-0.420675\pi$
$89$	4.65351	0.493271	0.246636	+	0.969108i	$0.420675\pi$
$90$	7.67646	0.809170
$91$	5.52242	0.578907
$92$	1.87020	0.194982
$93$	−3.23356	−0.335305
$94$	18.9870	1.95836
$95$	24.4138	2.50480
$96$	−7.83599	−0.799757
$97$	−2.57912	−0.261870	−0.130935	−	0.991391i	$-0.541798\pi$
$97$	−2.57912	−0.261870	−0.130935	+	0.991391i	$0.541798\pi$
$98$	12.3845	1.25102
$99$	4.08430	0.410487
$100$	19.1248	1.91248
$101$	17.5570	1.74699	0.873495	−	0.486834i	$-0.161848\pi$
$101$	17.5570	1.74699	0.873495	+	0.486834i	$0.161848\pi$
$102$	0.745820	0.0738472
$103$	10.5650	1.04100	0.520500	−	0.853862i	$-0.325746\pi$
$103$	10.5650	1.04100	0.520500	+	0.853862i	$0.325746\pi$
$104$	−1.67973	−0.164711
$105$	−3.27585	−0.319691
$106$	−21.4552	−2.08391
$107$	−10.3172	−0.997405	−0.498703	−	0.866773i	$-0.666190\pi$
$107$	−10.3172	−0.997405	−0.498703	+	0.866773i	$0.666190\pi$
$108$	−1.87020	−0.179960
$109$	5.06258	0.484907	0.242454	−	0.970163i	$-0.422048\pi$
$109$	5.06258	0.484907	0.242454	+	0.970163i	$0.422048\pi$
$110$	31.3529	2.98939
$111$	7.47652	0.709640
$112$	3.56187	0.336565
$113$	3.10215	0.291826	0.145913	−	0.989297i	$-0.453388\pi$
$113$	3.10215	0.291826	0.145913	+	0.989297i	$0.453388\pi$
$114$	−12.3086	−1.15281
$115$	−3.90206	−0.363869
$116$	−1.87020	−0.173644
$117$	−6.57808	−0.608143
$118$	22.4202	2.06394
$119$	−0.318271	−0.0291759
$120$	0.996402	0.0909586
$121$	5.68150	0.516500
$122$	−4.67003	−0.422805
$123$	9.84358	0.887566
$124$	6.04741	0.543074
$125$	−20.3925	−1.82396
$126$	1.65157	0.147134
$127$	−10.0701	−0.893578	−0.446789	−	0.894639i	$-0.647433\pi$
$127$	−10.0701	−0.893578	−0.446789	+	0.894639i	$0.647433\pi$
$128$	−2.03852	−0.180181
$129$	6.99632	0.615992
$130$	−50.4963	−4.42882
$131$	−16.4759	−1.43950	−0.719752	−	0.694231i	$-0.755744\pi$
$131$	−16.4759	−1.43950	−0.719752	+	0.694231i	$0.755744\pi$
$132$	−7.63846	−0.664842
$133$	5.25257	0.455456
$134$	21.9571	1.89680
$135$	3.90206	0.335836
$136$	0.0968072	0.00830115
$137$	19.6782	1.68122	0.840610	−	0.541640i	$-0.182196\pi$
$137$	19.6782	1.68122	0.840610	+	0.541640i	$0.182196\pi$
$138$	1.96728	0.167466
$139$	19.0807	1.61840	0.809202	−	0.587530i	$-0.199900\pi$
$139$	19.0807	1.61840	0.809202	+	0.587530i	$0.199900\pi$
$140$	6.12650	0.517784
$141$	9.65140	0.812794
$142$	−8.35628	−0.701243
$143$	−26.8668	−2.24672
$144$	−4.24275	−0.353563
$145$	3.90206	0.324049
$146$	17.6907	1.46409
$147$	6.29521	0.519220
$148$	−13.9826	−1.14936
$149$	0.870886	0.0713457	0.0356729	−	0.999364i	$-0.488643\pi$
$149$	0.870886	0.0713457	0.0356729	+	0.999364i	$0.488643\pi$
$150$	20.1176	1.64259
$151$	11.5494	0.939873	0.469937	−	0.882700i	$-0.344277\pi$
$151$	11.5494	0.939873	0.469937	+	0.882700i	$0.344277\pi$
$152$	−1.59765	−0.129587
$153$	0.379112	0.0306494
$154$	6.74551	0.543568
$155$	−12.6176	−1.01347
$156$	12.3023	0.984974
$157$	−6.51319	−0.519810	−0.259905	−	0.965634i	$-0.583691\pi$
$157$	−6.51319	−0.519810	−0.259905	+	0.965634i	$0.583691\pi$
$158$	−3.52377	−0.280336
$159$	−10.9060	−0.864901
$160$	−30.5765	−2.41728
$161$	−0.839519	−0.0661633
$162$	−1.96728	−0.154564
$163$	1.58258	0.123957	0.0619786	−	0.998077i	$-0.480259\pi$
$163$	1.58258	0.123957	0.0619786	+	0.998077i	$0.480259\pi$
$164$	−18.4095	−1.43754
$165$	15.9372	1.24071
$166$	12.0592	0.935972
$167$	6.04190	0.467536	0.233768	−	0.972292i	$-0.424894\pi$
$167$	6.04190	0.467536	0.233768	+	0.972292i	$0.424894\pi$
$168$	0.214373	0.0165393
$169$	30.2711	2.32854
$170$	2.91024	0.223205
$171$	−6.25665	−0.478458
$172$	−13.0845	−0.997686
$173$	−2.34652	−0.178403	−0.0892013	−	0.996014i	$-0.528431\pi$
$173$	−2.34652	−0.178403	−0.0892013	+	0.996014i	$0.528431\pi$
$174$	−1.96728	−0.149139
$175$	−8.58499	−0.648964
$176$	−17.3287	−1.30620
$177$	11.3965	0.856614
$178$	−9.15477	−0.686179
$179$	8.16175	0.610038	0.305019	−	0.952346i	$-0.401337\pi$
$179$	8.16175	0.610038	0.305019	+	0.952346i	$0.401337\pi$
$180$	−7.29764	−0.543934
$181$	−3.58883	−0.266756	−0.133378	−	0.991065i	$-0.542582\pi$
$181$	−3.58883	−0.266756	−0.133378	+	0.991065i	$0.542582\pi$
$182$	−10.8642	−0.805305
$183$	−2.37385	−0.175480
$184$	0.255353	0.0188248
$185$	29.1738	2.14490
$186$	6.36133	0.466436
$187$	1.54841	0.113231
$188$	−18.0500	−1.31643
$189$	0.839519	0.0610660
$190$	−48.0289	−3.48438
$191$	25.9036	1.87432	0.937159	−	0.348902i	$-0.113445\pi$
$191$	25.9036	1.87432	0.937159	+	0.348902i	$0.113445\pi$
$192$	6.93009	0.500136
$193$	−12.9762	−0.934050	−0.467025	−	0.884244i	$-0.654674\pi$
$193$	−12.9762	−0.934050	−0.467025	+	0.884244i	$0.654674\pi$
$194$	5.07386	0.364282
$195$	−25.6681	−1.83813
$196$	−11.7733	−0.840950
$197$	−10.6793	−0.760867	−0.380433	−	0.924808i	$-0.624225\pi$
$197$	−10.6793	−0.760867	−0.380433	+	0.924808i	$0.624225\pi$
$198$	−8.03497	−0.571020
$199$	3.77912	0.267895	0.133947	−	0.990988i	$-0.457235\pi$
$199$	3.77912	0.267895	0.133947	+	0.990988i	$0.457235\pi$
$200$	2.61126	0.184644
$201$	11.1611	0.787245
$202$	−34.5396	−2.43020
$203$	0.839519	0.0589226
$204$	−0.709015	−0.0496410
$205$	38.4103	2.68269
$206$	−20.7843	−1.44811
$207$	1.00000	0.0695048
$208$	27.9091	1.93515
$209$	−25.5540	−1.76761
$210$	6.44453	0.444715
$211$	19.8083	1.36366	0.681829	−	0.731512i	$-0.261185\pi$
$211$	19.8083	1.36366	0.681829	+	0.731512i	$0.261185\pi$
$212$	20.3964	1.40083
$213$	−4.24762	−0.291042
$214$	20.2969	1.38747
$215$	27.3001	1.86185
$216$	−0.255353	−0.0173745
$217$	−2.71464	−0.184282
$218$	−9.95953	−0.674544
$219$	8.99243	0.607652
$220$	−29.8057	−2.00950
$221$	−2.49383	−0.167753
$222$	−14.7084	−0.987165
$223$	21.9181	1.46775	0.733874	−	0.679286i	$-0.237710\pi$
$223$	21.9181	1.46775	0.733874	+	0.679286i	$0.237710\pi$
$224$	−6.57845	−0.439541
$225$	10.2261	0.681739
$226$	−6.10281	−0.405953
$227$	−12.5521	−0.833113	−0.416556	−	0.909110i	$-0.636763\pi$
$227$	−12.5521	−0.833113	−0.416556	+	0.909110i	$0.636763\pi$
$228$	11.7012	0.774930
$229$	4.66018	0.307953	0.153977	−	0.988074i	$-0.450792\pi$
$229$	4.66018	0.307953	0.153977	+	0.988074i	$0.450792\pi$
$230$	7.67646	0.506171
$231$	3.42884	0.225601
$232$	−0.255353	−0.0167647
$233$	13.1954	0.864459	0.432229	−	0.901764i	$-0.357727\pi$
$233$	13.1954	0.864459	0.432229	+	0.901764i	$0.357727\pi$
$234$	12.9409	0.845975
$235$	37.6603	2.45669
$236$	−21.3138	−1.38741
$237$	−1.79119	−0.116350
$238$	0.626130	0.0405860
$239$	−4.52134	−0.292461	−0.146231	−	0.989251i	$-0.546714\pi$
$239$	−4.52134	−0.292461	−0.146231	+	0.989251i	$0.546714\pi$
$240$	−16.5555	−1.06865
$241$	0.464697	0.0299338	0.0149669	−	0.999888i	$-0.495236\pi$
$241$	0.464697	0.0299338	0.0149669	+	0.999888i	$0.495236\pi$
$242$	−11.1771	−0.718492
$243$	−1.00000	−0.0641500
$244$	4.43958	0.284215
$245$	24.5643	1.56936
$246$	−19.3651	−1.23467
$247$	41.1567	2.61874
$248$	0.825699	0.0524319
$249$	6.12986	0.388464
$250$	40.1178	2.53727
$251$	−8.29616	−0.523649	−0.261825	−	0.965115i	$-0.584324\pi$
$251$	−8.29616	−0.523649	−0.261825	+	0.965115i	$0.584324\pi$
$252$	−1.57007	−0.0989050
$253$	4.08430	0.256778
$254$	19.8108	1.24304
$255$	1.47932	0.0926384
$256$	17.8705	1.11691
$257$	−9.38027	−0.585125	−0.292563	−	0.956246i	$-0.594508\pi$
$257$	−9.38027	−0.585125	−0.292563	+	0.956246i	$0.594508\pi$
$258$	−13.7637	−0.856893
$259$	6.27668	0.390014
$260$	48.0044	2.97711
$261$	−1.00000	−0.0618984
$262$	32.4127	2.00246
$263$	−19.7330	−1.21679	−0.608394	−	0.793635i	$-0.708186\pi$
$263$	−19.7330	−1.21679	−0.608394	+	0.793635i	$0.708186\pi$
$264$	−1.04294	−0.0641883
$265$	−42.5559	−2.61419
$266$	−10.3333	−0.633575
$267$	−4.65351	−0.284790
$268$	−20.8735	−1.27505
$269$	23.5286	1.43457	0.717283	−	0.696782i	$-0.245385\pi$
$269$	23.5286	1.43457	0.717283	+	0.696782i	$0.245385\pi$
$270$	−7.67646	−0.467174
$271$	−9.85432	−0.598607	−0.299304	−	0.954158i	$-0.596754\pi$
$271$	−9.85432	−0.598607	−0.299304	+	0.954158i	$0.596754\pi$
$272$	−1.60848	−0.0975282
$273$	−5.52242	−0.334232
$274$	−38.7126	−2.33871
$275$	41.7664	2.51861
$276$	−1.87020	−0.112573
$277$	−27.2188	−1.63542	−0.817709	−	0.575632i	$-0.804756\pi$
$277$	−27.2188	−1.63542	−0.817709	+	0.575632i	$0.804756\pi$
$278$	−37.5371	−2.25133
$279$	3.23356	0.193588
$280$	0.836498	0.0499903
$281$	−19.1639	−1.14322	−0.571611	−	0.820525i	$-0.693681\pi$
$281$	−19.1639	−1.14322	−0.571611	+	0.820525i	$0.693681\pi$
$282$	−18.9870	−1.13066
$283$	−18.5391	−1.10203	−0.551017	−	0.834494i	$-0.685760\pi$
$283$	−18.5391	−1.10203	−0.551017	+	0.834494i	$0.685760\pi$
$284$	7.94391	0.471384
$285$	−24.4138	−1.44615
$286$	52.8546	3.12536
$287$	8.26387	0.487801
$288$	7.83599	0.461740
$289$	−16.8563	−0.991546
$290$	−7.67646	−0.450777
$291$	2.57912	0.151191
$292$	−16.8177	−0.984179
$293$	13.4465	0.785550	0.392775	−	0.919635i	$-0.371515\pi$
$293$	13.4465	0.785550	0.392775	+	0.919635i	$0.371515\pi$
$294$	−12.3845	−0.722276
$295$	44.4699	2.58914
$296$	−1.90915	−0.110967
$297$	−4.08430	−0.236995
$298$	−1.71328	−0.0992476
$299$	−6.57808	−0.380420
$300$	−19.1248	−1.10417
$301$	5.87354	0.338545
$302$	−22.7208	−1.30744
$303$	−17.5570	−1.00862
$304$	26.5454	1.52248
$305$	−9.26291	−0.530393
$306$	−0.745820	−0.0426357
$307$	20.2033	1.15306	0.576532	−	0.817074i	$-0.304406\pi$
$307$	20.2033	1.15306	0.576532	+	0.817074i	$0.304406\pi$
$308$	−6.41263	−0.365393
$309$	−10.5650	−0.601021
$310$	24.8223	1.40981
$311$	−7.95378	−0.451017	−0.225509	−	0.974241i	$-0.572404\pi$
$311$	−7.95378	−0.451017	−0.225509	+	0.974241i	$0.572404\pi$
$312$	1.67973	0.0950959
$313$	5.26012	0.297319	0.148660	−	0.988888i	$-0.452504\pi$
$313$	5.26012	0.297319	0.148660	+	0.988888i	$0.452504\pi$
$314$	12.8133	0.723096
$315$	3.27585	0.184573
$316$	3.34988	0.188446
$317$	32.0143	1.79810	0.899052	−	0.437841i	$-0.144257\pi$
$317$	32.0143	1.79810	0.899052	+	0.437841i	$0.144257\pi$
$318$	21.4552	1.20315
$319$	−4.08430	−0.228677
$320$	27.0417	1.51167
$321$	10.3172	0.575852
$322$	1.65157	0.0920384
$323$	−2.37197	−0.131980
$324$	1.87020	0.103900
$325$	−67.2680	−3.73135
$326$	−3.11338	−0.172434
$327$	−5.06258	−0.279961
$328$	−2.51358	−0.138789
$329$	8.10253	0.446707
$330$	−31.3529	−1.72592
$331$	−27.8202	−1.52914	−0.764569	−	0.644542i	$-0.777048\pi$
$331$	−27.8202	−1.52914	−0.764569	+	0.644542i	$0.777048\pi$
$332$	−11.4641	−0.629172
$333$	−7.47652	−0.409711
$334$	−11.8861	−0.650380
$335$	43.5514	2.37947
$336$	−3.56187	−0.194316
$337$	−20.1838	−1.09948	−0.549742	−	0.835334i	$-0.685274\pi$
$337$	−20.1838	−1.09948	−0.549742	+	0.835334i	$0.685274\pi$
$338$	−59.5518	−3.23919
$339$	−3.10215	−0.168486
$340$	−2.76662	−0.150041
$341$	13.2068	0.715190
$342$	12.3086	0.665572
$343$	11.1616	0.602668
$344$	−1.78653	−0.0963232
$345$	3.90206	0.210080
$346$	4.61627	0.248172
$347$	1.48365	0.0796466	0.0398233	−	0.999207i	$-0.487320\pi$
$347$	1.48365	0.0796466	0.0398233	+	0.999207i	$0.487320\pi$
$348$	1.87020	0.100253
$349$	12.5241	0.670398	0.335199	−	0.942147i	$-0.391197\pi$
$349$	12.5241	0.670398	0.335199	+	0.942147i	$0.391197\pi$
$350$	16.8891	0.902760
$351$	6.57808	0.351112
$352$	32.0045	1.70585
$353$	22.5177	1.19850	0.599248	−	0.800564i	$-0.295466\pi$
$353$	22.5177	1.19850	0.599248	+	0.800564i	$0.295466\pi$
$354$	−22.4202	−1.19162
$355$	−16.5745	−0.879683
$356$	8.70300	0.461258
$357$	0.318271	0.0168447
$358$	−16.0565	−0.848610
$359$	−31.5736	−1.66639	−0.833196	−	0.552978i	$-0.813492\pi$
$359$	−31.5736	−1.66639	−0.833196	+	0.552978i	$0.813492\pi$
$360$	−0.996402	−0.0525150
$361$	20.1456	1.06030
$362$	7.06024	0.371078
$363$	−5.68150	−0.298201
$364$	10.3280	0.541336
$365$	35.0890	1.83664
$366$	4.67003	0.244107
$367$	13.4332	0.701207	0.350604	−	0.936524i	$-0.385976\pi$
$367$	13.4332	0.701207	0.350604	+	0.936524i	$0.385976\pi$
$368$	−4.24275	−0.221169
$369$	−9.84358	−0.512436
$370$	−57.3932	−2.98373
$371$	−9.15578	−0.475345
$372$	−6.04741	−0.313544
$373$	6.88479	0.356481	0.178240	−	0.983987i	$-0.442960\pi$
$373$	6.88479	0.356481	0.178240	+	0.983987i	$0.442960\pi$
$374$	−3.04615	−0.157513
$375$	20.3925	1.05306
$376$	−2.46451	−0.127097
$377$	6.57808	0.338788
$378$	−1.65157	−0.0849476
$379$	3.53749	0.181708	0.0908542	−	0.995864i	$-0.471040\pi$
$379$	3.53749	0.181708	0.0908542	+	0.995864i	$0.471040\pi$
$380$	45.6587	2.34224
$381$	10.0701	0.515908
$382$	−50.9597	−2.60732
$383$	34.7172	1.77396	0.886982	−	0.461804i	$-0.152798\pi$
$383$	34.7172	1.77396	0.886982	+	0.461804i	$0.152798\pi$
$384$	2.03852	0.104028
$385$	13.3796	0.681886
$386$	25.5279	1.29934
$387$	−6.99632	−0.355643
$388$	−4.82348	−0.244875
$389$	−34.0537	−1.72659	−0.863294	−	0.504701i	$-0.831603\pi$
$389$	−34.0537	−1.72659	−0.863294	+	0.504701i	$0.831603\pi$
$390$	50.4963	2.55698
$391$	0.379112	0.0191725
$392$	−1.60750	−0.0811909
$393$	16.4759	0.831098
$394$	21.0092	1.05843
$395$	−6.98933	−0.351671
$396$	7.63846	0.383847
$397$	−18.1742	−0.912135	−0.456068	−	0.889945i	$-0.650743\pi$
$397$	−18.1742	−0.912135	−0.456068	+	0.889945i	$0.650743\pi$
$398$	−7.43460	−0.372663
$399$	−5.25257	−0.262957
$400$	−43.3867	−2.16934
$401$	8.34533	0.416746	0.208373	−	0.978049i	$-0.433183\pi$
$401$	8.34533	0.416746	0.208373	+	0.978049i	$0.433183\pi$
$402$	−21.9571	−1.09512
$403$	−21.2706	−1.05957
$404$	32.8352	1.63361
$405$	−3.90206	−0.193895
$406$	−1.65157	−0.0819660
$407$	−30.5363	−1.51363
$408$	−0.0968072	−0.00479267
$409$	24.6842	1.22056	0.610278	−	0.792188i	$-0.291058\pi$
$409$	24.6842	1.22056	0.610278	+	0.792188i	$0.291058\pi$
$410$	−75.5638	−3.73183
$411$	−19.6782	−0.970653
$412$	19.7586	0.973439
$413$	9.56758	0.470790
$414$	−1.96728	−0.0966867
$415$	23.9191	1.17414
$416$	−51.5457	−2.52724
$417$	−19.0807	−0.934386
$418$	50.2720	2.45888
$419$	−0.233296	−0.0113972	−0.00569862	−	0.999984i	$-0.501814\pi$
$419$	−0.233296	−0.0113972	−0.00569862	+	0.999984i	$0.501814\pi$
$420$	−6.12650	−0.298943
$421$	15.0075	0.731421	0.365710	−	0.930729i	$-0.380826\pi$
$421$	15.0075	0.731421	0.365710	+	0.930729i	$0.380826\pi$
$422$	−38.9685	−1.89696
$423$	−9.65140	−0.469267
$424$	2.78487	0.135245
$425$	3.87683	0.188054
$426$	8.35628	0.404863
$427$	−1.99289	−0.0964428
$428$	−19.2953	−0.932674
$429$	26.8668	1.29714
$430$	−53.7070	−2.58998
$431$	33.8478	1.63039	0.815195	−	0.579187i	$-0.196630\pi$
$431$	33.8478	1.63039	0.815195	+	0.579187i	$0.196630\pi$
$432$	4.24275	0.204129
$433$	−25.3136	−1.21649	−0.608247	−	0.793748i	$-0.708127\pi$
$433$	−25.3136	−1.21649	−0.608247	+	0.793748i	$0.708127\pi$
$434$	5.34046	0.256350
$435$	−3.90206	−0.187090
$436$	9.46804	0.453437
$437$	−6.25665	−0.299296
$438$	−17.6907	−0.845292
$439$	−1.60242	−0.0764793	−0.0382397	−	0.999269i	$-0.512175\pi$
$439$	−1.60242	−0.0764793	−0.0382397	+	0.999269i	$0.512175\pi$
$440$	−4.06960	−0.194011
$441$	−6.29521	−0.299772
$442$	4.90606	0.233357
$443$	12.6508	0.601055	0.300528	−	0.953773i	$-0.402837\pi$
$443$	12.6508	0.601055	0.300528	+	0.953773i	$0.402837\pi$
$444$	13.9826	0.663584
$445$	−18.1583	−0.860785
$446$	−43.1192	−2.04175
$447$	−0.870886	−0.0411915
$448$	5.81794	0.274872
$449$	−4.38659	−0.207016	−0.103508	−	0.994629i	$-0.533007\pi$
$449$	−4.38659	−0.207016	−0.103508	+	0.994629i	$0.533007\pi$
$450$	−20.1176	−0.948353
$451$	−40.2041	−1.89314
$452$	5.80165	0.272886
$453$	−11.5494	−0.542636
$454$	24.6935	1.15893
$455$	−21.5488	−1.01022
$456$	1.59765	0.0748169
$457$	−11.9937	−0.561040	−0.280520	−	0.959848i	$-0.590507\pi$
$457$	−11.9937	−0.561040	−0.280520	+	0.959848i	$0.590507\pi$
$458$	−9.16789	−0.428387
$459$	−0.379112	−0.0176954
$460$	−7.29764	−0.340254
$461$	6.56938	0.305967	0.152983	−	0.988229i	$-0.451112\pi$
$461$	6.56938	0.305967	0.152983	+	0.988229i	$0.451112\pi$
$462$	−6.74551	−0.313829
$463$	−25.2208	−1.17211	−0.586054	−	0.810272i	$-0.699319\pi$
$463$	−25.2208	−1.17211	−0.586054	+	0.810272i	$0.699319\pi$
$464$	4.24275	0.196965
$465$	12.6176	0.585125
$466$	−25.9591	−1.20253
$467$	18.1238	0.838671	0.419336	−	0.907831i	$-0.362263\pi$
$467$	18.1238	0.838671	0.419336	+	0.907831i	$0.362263\pi$
$468$	−12.3023	−0.568675
$469$	9.36997	0.432665
$470$	−74.0885	−3.41745
$471$	6.51319	0.300112
$472$	−2.91013	−0.133950
$473$	−28.5751	−1.31388
$474$	3.52377	0.161852
$475$	−63.9810	−2.93565
$476$	−0.595231	−0.0272824
$477$	10.9060	0.499351
$478$	8.89475	0.406837
$479$	−29.4997	−1.34787	−0.673937	−	0.738789i	$-0.735398\pi$
$479$	−29.4997	−1.34787	−0.673937	+	0.738789i	$0.735398\pi$
$480$	30.5765	1.39562
$481$	49.1811	2.24247
$482$	−0.914190	−0.0416402
$483$	0.839519	0.0381994
$484$	10.6255	0.482979
$485$	10.0639	0.456978
$486$	1.96728	0.0892377
$487$	−1.65098	−0.0748129	−0.0374064	−	0.999300i	$-0.511910\pi$
$487$	−1.65098	−0.0748129	−0.0374064	+	0.999300i	$0.511910\pi$
$488$	0.606169	0.0274400
$489$	−1.58258	−0.0715667
$490$	−48.3249	−2.18310
$491$	30.3853	1.37127	0.685636	−	0.727945i	$-0.259524\pi$
$491$	30.3853	1.37127	0.685636	+	0.727945i	$0.259524\pi$
$492$	18.4095	0.829963
$493$	−0.379112	−0.0170743
$494$	−80.9668	−3.64287
$495$	−15.9372	−0.716323
$496$	−13.7192	−0.616010
$497$	−3.56596	−0.159955
$498$	−12.0592	−0.540384
$499$	−29.1755	−1.30607	−0.653037	−	0.757326i	$-0.726505\pi$
$499$	−29.1755	−1.30607	−0.653037	+	0.757326i	$0.726505\pi$
$500$	−38.1381	−1.70559
$501$	−6.04190	−0.269932
$502$	16.3209	0.728437
$503$	33.6484	1.50031	0.750155	−	0.661262i	$-0.229979\pi$
$503$	33.6484	1.50031	0.750155	+	0.661262i	$0.229979\pi$
$504$	−0.214373	−0.00954895
$505$	−68.5086	−3.04859
$506$	−8.03497	−0.357198
$507$	−30.2711	−1.34439
$508$	−18.8331	−0.835585
$509$	−6.99105	−0.309873	−0.154937	−	0.987924i	$-0.549517\pi$
$509$	−6.99105	−0.309873	−0.154937	+	0.987924i	$0.549517\pi$
$510$	−2.91024	−0.128867
$511$	7.54931	0.333962
$512$	−31.0793	−1.37353
$513$	6.25665	0.276238
$514$	18.4536	0.813955
$515$	−41.2252	−1.81660
$516$	13.0845	0.576014
$517$	−39.4192	−1.73365
$518$	−12.3480	−0.542540
$519$	2.34652	0.103001
$520$	6.55441	0.287430
$521$	8.97472	0.393189	0.196595	−	0.980485i	$-0.437012\pi$
$521$	8.97472	0.393189	0.196595	+	0.980485i	$0.437012\pi$
$522$	1.96728	0.0861056
$523$	−29.4473	−1.28764	−0.643819	−	0.765177i	$-0.722651\pi$
$523$	−29.4473	−1.28764	−0.643819	+	0.765177i	$0.722651\pi$
$524$	−30.8132	−1.34608
$525$	8.58499	0.374680
$526$	38.8203	1.69265
$527$	1.22588	0.0534003
$528$	17.3287	0.754133
$529$	1.00000	0.0434783
$530$	83.7194	3.63654
$531$	−11.3965	−0.494566
$532$	9.82336	0.425897
$533$	64.7518	2.80471
$534$	9.15477	0.396166
$535$	40.2585	1.74053
$536$	−2.85002	−0.123102
$537$	−8.16175	−0.352205
$538$	−46.2875	−1.99560
$539$	−25.7115	−1.10747
$540$	7.29764	0.314040
$541$	−1.59606	−0.0686201	−0.0343101	−	0.999411i	$-0.510923\pi$
$541$	−1.59606	−0.0686201	−0.0343101	+	0.999411i	$0.510923\pi$
$542$	19.3862	0.832710
$543$	3.58883	0.154011
$544$	2.97071	0.127368
$545$	−19.7545	−0.846190
$546$	10.8642	0.464943
$547$	13.6372	0.583086	0.291543	−	0.956558i	$-0.405831\pi$
$547$	13.6372	0.583086	0.291543	+	0.956558i	$0.405831\pi$
$548$	36.8022	1.57211
$549$	2.37385	0.101313
$550$	−82.1663	−3.50358
$551$	6.25665	0.266542
$552$	−0.255353	−0.0108685
$553$	−1.50374	−0.0639454
$554$	53.5470	2.27499
$555$	−29.1738	−1.23836
$556$	35.6847	1.51337
$557$	−1.68424	−0.0713636	−0.0356818	−	0.999363i	$-0.511360\pi$
$557$	−1.68424	−0.0713636	−0.0356818	+	0.999363i	$0.511360\pi$
$558$	−6.36133	−0.269297
$559$	46.0224	1.94654
$560$	−13.8986	−0.587324
$561$	−1.54841	−0.0653737
$562$	37.7008	1.59031
$563$	0.563021	0.0237285	0.0118643	−	0.999930i	$-0.496223\pi$
$563$	0.563021	0.0237285	0.0118643	+	0.999930i	$0.496223\pi$
$564$	18.0500	0.760044
$565$	−12.1048	−0.509252
$566$	36.4716	1.53302
$567$	−0.839519	−0.0352565
$568$	1.08464	0.0455106
$569$	−30.3716	−1.27324	−0.636622	−	0.771176i	$-0.719669\pi$
$569$	−30.3716	−1.27324	−0.636622	+	0.771176i	$0.719669\pi$
$570$	48.0289	2.01171
$571$	9.24952	0.387080	0.193540	−	0.981092i	$-0.438003\pi$
$571$	9.24952	0.387080	0.193540	+	0.981092i	$0.438003\pi$
$572$	−50.2464	−2.10091
$573$	−25.9036	−1.08214
$574$	−16.2574	−0.678569
$575$	10.2261	0.426457
$576$	−6.93009	−0.288754
$577$	35.0432	1.45887	0.729433	−	0.684052i	$-0.239784\pi$
$577$	35.0432	1.45887	0.729433	+	0.684052i	$0.239784\pi$
$578$	33.1611	1.37932
$579$	12.9762	0.539274
$580$	7.29764	0.303018
$581$	5.14613	0.213497
$582$	−5.07386	−0.210318
$583$	44.5433	1.84480
$584$	−2.29624	−0.0950192
$585$	25.6681	1.06124
$586$	−26.4530	−1.09276
$587$	−5.85702	−0.241745	−0.120873	−	0.992668i	$-0.538569\pi$
$587$	−5.85702	−0.241745	−0.120873	+	0.992668i	$0.538569\pi$
$588$	11.7733	0.485523
$589$	−20.2313	−0.833615
$590$	−87.4848	−3.60169
$591$	10.6793	0.439287
$592$	31.7210	1.30373
$593$	−13.3743	−0.549217	−0.274608	−	0.961556i	$-0.588548\pi$
$593$	−13.3743	−0.549217	−0.274608	+	0.961556i	$0.588548\pi$
$594$	8.03497	0.329679
$595$	1.24191	0.0509135
$596$	1.62873	0.0667154
$597$	−3.77912	−0.154669
$598$	12.9409	0.529194
$599$	17.1311	0.699958	0.349979	−	0.936758i	$-0.386189\pi$
$599$	17.1311	0.699958	0.349979	+	0.936758i	$0.386189\pi$
$600$	−2.61126	−0.106604
$601$	39.8948	1.62734	0.813671	−	0.581325i	$-0.197466\pi$
$601$	39.8948	1.62734	0.813671	+	0.581325i	$0.197466\pi$
$602$	−11.5549	−0.470943
$603$	−11.1611	−0.454516
$604$	21.5996	0.878876
$605$	−22.1696	−0.901320
$606$	34.5396	1.40308
$607$	29.2826	1.18854	0.594272	−	0.804264i	$-0.297440\pi$
$607$	29.2826	1.18854	0.594272	+	0.804264i	$0.297440\pi$
$608$	−49.0270	−1.98831
$609$	−0.839519	−0.0340190
$610$	18.2228	0.737818
$611$	63.4876	2.56843
$612$	0.709015	0.0286602
$613$	23.7708	0.960093	0.480046	−	0.877243i	$-0.340620\pi$
$613$	23.7708	0.960093	0.480046	+	0.877243i	$0.340620\pi$
$614$	−39.7456	−1.60400
$615$	−38.4103	−1.54885
$616$	−0.875565	−0.0352775
$617$	−12.5181	−0.503958	−0.251979	−	0.967733i	$-0.581081\pi$
$617$	−12.5181	−0.503958	−0.251979	+	0.967733i	$0.581081\pi$
$618$	20.7843	0.836068
$619$	−27.2765	−1.09633	−0.548167	−	0.836369i	$-0.684674\pi$
$619$	−27.2765	−1.09633	−0.548167	+	0.836369i	$0.684674\pi$
$620$	−23.5974	−0.947693
$621$	−1.00000	−0.0401286
$622$	15.6473	0.627401
$623$	−3.90671	−0.156519
$624$	−27.9091	−1.11726
$625$	28.4424	1.13769
$626$	−10.3481	−0.413595
$627$	25.5540	1.02053
$628$	−12.1810	−0.486074
$629$	−2.83444	−0.113016
$630$	−6.44453	−0.256756
$631$	−17.2183	−0.685448	−0.342724	−	0.939436i	$-0.611350\pi$
$631$	−17.2183	−0.685448	−0.342724	+	0.939436i	$0.611350\pi$
$632$	0.457385	0.0181938
$633$	−19.8083	−0.787308
$634$	−62.9813	−2.50131
$635$	39.2942	1.55934
$636$	−20.3964	−0.808769
$637$	41.4104	1.64074
$638$	8.03497	0.318107
$639$	4.24762	0.168033
$640$	7.95443	0.314426
$641$	31.7850	1.25543	0.627715	−	0.778443i	$-0.283990\pi$
$641$	31.7850	1.25543	0.627715	+	0.778443i	$0.283990\pi$
$642$	−20.2969	−0.801056
$643$	27.2635	1.07517	0.537584	−	0.843210i	$-0.319337\pi$
$643$	27.2635	1.07517	0.537584	+	0.843210i	$0.319337\pi$
$644$	−1.57007	−0.0618693
$645$	−27.3001	−1.07494
$646$	4.66633	0.183594
$647$	−6.76480	−0.265952	−0.132976	−	0.991119i	$-0.542453\pi$
$647$	−6.76480	−0.265952	−0.132976	+	0.991119i	$0.542453\pi$
$648$	0.255353	0.0100312
$649$	−46.5468	−1.82712
$650$	132.335	5.19061
$651$	2.71464	0.106395
$652$	2.95974	0.115912
$653$	−9.63997	−0.377241	−0.188621	−	0.982050i	$-0.560402\pi$
$653$	−9.63997	−0.377241	−0.188621	+	0.982050i	$0.560402\pi$
$654$	9.95953	0.389448
$655$	64.2899	2.51201
$656$	41.7639	1.63061
$657$	−8.99243	−0.350828
$658$	−15.9400	−0.621404
$659$	37.9893	1.47985	0.739927	−	0.672687i	$-0.234860\pi$
$659$	37.9893	1.47985	0.739927	+	0.672687i	$0.234860\pi$
$660$	29.8057	1.16019
$661$	−11.8372	−0.460414	−0.230207	−	0.973142i	$-0.573940\pi$
$661$	−11.8372	−0.460414	−0.230207	+	0.973142i	$0.573940\pi$
$662$	54.7302	2.12715
$663$	2.49383	0.0968522
$664$	−1.56528	−0.0607445
$665$	−20.4959	−0.794795
$666$	14.7084	0.569940
$667$	−1.00000	−0.0387202
$668$	11.2996	0.437193
$669$	−21.9181	−0.847405
$670$	−85.6779	−3.31003
$671$	9.69551	0.374291
$672$	6.57845	0.253769
$673$	−11.9904	−0.462196	−0.231098	−	0.972931i	$-0.574232\pi$
$673$	−11.9904	−0.462196	−0.231098	+	0.972931i	$0.574232\pi$
$674$	39.7073	1.52947
$675$	−10.2261	−0.393602
$676$	56.6130	2.17742
$677$	−36.3152	−1.39571	−0.697853	−	0.716241i	$-0.745861\pi$
$677$	−36.3152	−1.39571	−0.697853	+	0.716241i	$0.745861\pi$
$678$	6.10281	0.234377
$679$	2.16522	0.0830936
$680$	−0.377748	−0.0144860
$681$	12.5521	0.480998
$682$	−25.9816	−0.994886
$683$	−46.4937	−1.77903	−0.889516	−	0.456904i	$-0.848958\pi$
$683$	−46.4937	−1.77903	−0.889516	+	0.456904i	$0.848958\pi$
$684$	−11.7012	−0.447406
$685$	−76.7855	−2.93382
$686$	−21.9580	−0.838359
$687$	−4.66018	−0.177797
$688$	29.6837	1.13168
$689$	−71.7404	−2.73309
$690$	−7.67646	−0.292238
$691$	19.1780	0.729564	0.364782	−	0.931093i	$-0.381143\pi$
$691$	19.1780	0.729564	0.364782	+	0.931093i	$0.381143\pi$
$692$	−4.38846	−0.166824
$693$	−3.42884	−0.130251
$694$	−2.91876	−0.110795
$695$	−74.4541	−2.82420
$696$	0.255353	0.00967912
$697$	−3.73182	−0.141353
$698$	−24.6384	−0.932576
$699$	−13.1954	−0.499095
$700$	−16.0556	−0.606846
$701$	16.6639	0.629387	0.314694	−	0.949193i	$-0.398098\pi$
$701$	16.6639	0.629387	0.314694	+	0.949193i	$0.398098\pi$
$702$	−12.9409	−0.488424
$703$	46.7779	1.76426
$704$	−28.3046	−1.06677
$705$	−37.6603	−1.41837
$706$	−44.2987	−1.66720
$707$	−14.7394	−0.554334
$708$	21.3138	0.801020
$709$	−34.2240	−1.28531	−0.642655	−	0.766155i	$-0.722167\pi$
$709$	−34.2240	−1.28531	−0.642655	+	0.766155i	$0.722167\pi$
$710$	32.6067	1.22371
$711$	1.79119	0.0671748
$712$	1.18829	0.0445329
$713$	3.23356	0.121098
$714$	−0.626130	−0.0234323
$715$	104.836	3.92064
$716$	15.2641	0.570446
$717$	4.52134	0.168853
$718$	62.1142	2.31808
$719$	−19.1950	−0.715851	−0.357926	−	0.933750i	$-0.616516\pi$
$719$	−19.1950	−0.715851	−0.357926	+	0.933750i	$0.616516\pi$
$720$	16.5555	0.616986
$721$	−8.86951	−0.330318
$722$	−39.6321	−1.47495
$723$	−0.464697	−0.0172823
$724$	−6.71183	−0.249443
$725$	−10.2261	−0.379787
$726$	11.1771	0.414821
$727$	−1.78597	−0.0662380	−0.0331190	−	0.999451i	$-0.510544\pi$
$727$	−1.78597	−0.0662380	−0.0331190	+	0.999451i	$0.510544\pi$
$728$	1.41016	0.0522641
$729$	1.00000	0.0370370
$730$	−69.0300	−2.55492
$731$	−2.65239	−0.0981021
$732$	−4.43958	−0.164091
$733$	−12.2076	−0.450898	−0.225449	−	0.974255i	$-0.572385\pi$
$733$	−12.2076	−0.450898	−0.225449	+	0.974255i	$0.572385\pi$
$734$	−26.4269	−0.975435
$735$	−24.5643	−0.906068
$736$	7.83599	0.288838
$737$	−45.5854	−1.67916
$738$	19.3651	0.712839
$739$	13.4944	0.496399	0.248200	−	0.968709i	$-0.420161\pi$
$739$	13.4944	0.496399	0.248200	+	0.968709i	$0.420161\pi$
$740$	54.5609	2.00570
$741$	−41.1567	−1.51193
$742$	18.0120	0.661242
$743$	29.3204	1.07566	0.537830	−	0.843053i	$-0.319244\pi$
$743$	29.3204	1.07566	0.537830	+	0.843053i	$0.319244\pi$
$744$	−0.825699	−0.0302716
$745$	−3.39825	−0.124502
$746$	−13.5443	−0.495893
$747$	−6.12986	−0.224280
$748$	2.89583	0.105882
$749$	8.66151	0.316485
$750$	−40.1178	−1.46490
$751$	−20.9802	−0.765577	−0.382789	−	0.923836i	$-0.625036\pi$
$751$	−20.9802	−0.765577	−0.382789	+	0.923836i	$0.625036\pi$
$752$	40.9485	1.49324
$753$	8.29616	0.302329
$754$	−12.9409	−0.471281
$755$	−45.0663	−1.64013
$756$	1.57007	0.0571028
$757$	−47.6763	−1.73283	−0.866413	−	0.499328i	$-0.833580\pi$
$757$	−47.6763	−1.73283	−0.866413	+	0.499328i	$0.833580\pi$
$758$	−6.95923	−0.252771
$759$	−4.08430	−0.148251
$760$	6.23413	0.226136
$761$	35.1401	1.27383	0.636913	−	0.770935i	$-0.280211\pi$
$761$	35.1401	1.27383	0.636913	+	0.770935i	$0.280211\pi$
$762$	−19.8108	−0.717668
$763$	−4.25013	−0.153865
$764$	48.4449	1.75268
$765$	−1.47932	−0.0534848
$766$	−68.2985	−2.46772
$767$	74.9671	2.70691
$768$	−17.8705	−0.644847
$769$	7.10129	0.256079	0.128040	−	0.991769i	$-0.459132\pi$
$769$	7.10129	0.256079	0.128040	+	0.991769i	$0.459132\pi$
$770$	−26.3214	−0.948557
$771$	9.38027	0.337822
$772$	−24.2682	−0.873430
$773$	−20.1935	−0.726311	−0.363155	−	0.931729i	$-0.618301\pi$
$773$	−20.1935	−0.726311	−0.363155	+	0.931729i	$0.618301\pi$
$774$	13.7637	0.494728
$775$	33.0667	1.18779
$776$	−0.658586	−0.0236419
$777$	−6.27668	−0.225174
$778$	66.9932	2.40182
$779$	61.5878	2.20661
$780$	−48.0044	−1.71883
$781$	17.3486	0.620780
$782$	−0.745820	−0.0266705
$783$	1.00000	0.0357371
$784$	26.7090	0.953893
$785$	25.4149	0.907096
$786$	−32.4127	−1.15612
$787$	19.3983	0.691476	0.345738	−	0.938331i	$-0.387629\pi$
$787$	19.3983	0.691476	0.345738	+	0.938331i	$0.387629\pi$
$788$	−19.9724	−0.711487
$789$	19.7330	0.702513
$790$	13.7500	0.489202
$791$	−2.60431	−0.0925988
$792$	1.04294	0.0370591
$793$	−15.6154	−0.554518
$794$	35.7537	1.26885
$795$	42.5559	1.50930
$796$	7.06772	0.250509
$797$	−15.2083	−0.538704	−0.269352	−	0.963042i	$-0.586810\pi$
$797$	−15.2083	−0.538704	−0.269352	+	0.963042i	$0.586810\pi$
$798$	10.3333	0.365794
$799$	−3.65896	−0.129445
$800$	80.1314	2.83307
$801$	4.65351	0.164424
$802$	−16.4176	−0.579727
$803$	−36.7278	−1.29610
$804$	20.8735	0.736153
$805$	3.27585	0.115459
$806$	41.8453	1.47394
$807$	−23.5286	−0.828247
$808$	4.48323	0.157720
$809$	−25.7908	−0.906755	−0.453377	−	0.891319i	$-0.649781\pi$
$809$	−25.7908	−0.906755	−0.453377	+	0.891319i	$0.649781\pi$
$810$	7.67646	0.269723
$811$	−28.2524	−0.992076	−0.496038	−	0.868301i	$-0.665212\pi$
$811$	−28.2524	−0.992076	−0.496038	+	0.868301i	$0.665212\pi$
$812$	1.57007	0.0550986
$813$	9.85432	0.345606
$814$	60.0736	2.10558
$815$	−6.17532	−0.216312
$816$	1.60848	0.0563080
$817$	43.7735	1.53144
$818$	−48.5608	−1.69789
$819$	5.52242	0.192969
$820$	71.8349	2.50858
$821$	48.0439	1.67674	0.838372	−	0.545099i	$-0.183508\pi$
$821$	48.0439	1.67674	0.838372	+	0.545099i	$0.183508\pi$
$822$	38.7126	1.35026
$823$	−11.9942	−0.418092	−0.209046	−	0.977906i	$-0.567036\pi$
$823$	−11.9942	−0.418092	−0.209046	+	0.977906i	$0.567036\pi$
$824$	2.69780	0.0939823
$825$	−41.7664	−1.45412
$826$	−18.8221	−0.654906
$827$	14.4329	0.501880	0.250940	−	0.968003i	$-0.419260\pi$
$827$	14.4329	0.501880	0.250940	+	0.968003i	$0.419260\pi$
$828$	1.87020	0.0649940
$829$	11.6772	0.405568	0.202784	−	0.979224i	$-0.435001\pi$
$829$	11.6772	0.405568	0.202784	+	0.979224i	$0.435001\pi$
$830$	−47.0556	−1.63332
$831$	27.2188	0.944209
$832$	45.5867	1.58043
$833$	−2.38659	−0.0826904
$834$	37.5371	1.29980
$835$	−23.5759	−0.815877
$836$	−47.7911	−1.65289
$837$	−3.23356	−0.111768
$838$	0.458958	0.0158545
$839$	38.6936	1.33585	0.667925	−	0.744228i	$-0.267183\pi$
$839$	38.6936	1.33585	0.667925	+	0.744228i	$0.267183\pi$
$840$	−0.836498	−0.0288619
$841$	1.00000	0.0344828
$842$	−29.5240	−1.01746
$843$	19.1639	0.660039
$844$	37.0454	1.27516
$845$	−118.120	−4.06344
$846$	18.9870	0.652787
$847$	−4.76972	−0.163890
$848$	−46.2714	−1.58897
$849$	18.5391	0.636259
$850$	−7.62682	−0.261598
$851$	−7.47652	−0.256292
$852$	−7.94391	−0.272154
$853$	−4.48283	−0.153489	−0.0767446	−	0.997051i	$-0.524453\pi$
$853$	−4.48283	−0.153489	−0.0767446	+	0.997051i	$0.524453\pi$
$854$	3.92058	0.134159
$855$	24.4138	0.834935
$856$	−2.63453	−0.0900465
$857$	4.53684	0.154976	0.0774878	−	0.996993i	$-0.475310\pi$
$857$	4.53684	0.154976	0.0774878	+	0.996993i	$0.475310\pi$
$858$	−52.8546	−1.80443
$859$	36.2457	1.23669	0.618343	−	0.785908i	$-0.287804\pi$
$859$	36.2457	1.23669	0.618343	+	0.785908i	$0.287804\pi$
$860$	51.0566	1.74102
$861$	−8.26387	−0.281632
$862$	−66.5881	−2.26800
$863$	39.8579	1.35678	0.678390	−	0.734702i	$-0.262678\pi$
$863$	39.8579	1.35678	0.678390	+	0.734702i	$0.262678\pi$
$864$	−7.83599	−0.266586
$865$	9.15626	0.311322
$866$	49.7990	1.69224
$867$	16.8563	0.572469
$868$	−5.07691	−0.172322
$869$	7.31575	0.248170
$870$	7.67646	0.260256
$871$	73.4187	2.48770
$872$	1.29274	0.0437778
$873$	−2.57912	−0.0872901
$874$	12.3086	0.416344
$875$	17.1199	0.578758
$876$	16.8177	0.568216
$877$	−49.1279	−1.65893	−0.829466	−	0.558557i	$-0.811355\pi$
$877$	−49.1279	−1.65893	−0.829466	+	0.558557i	$0.811355\pi$
$878$	3.15241	0.106389
$879$	−13.4465	−0.453538
$880$	67.6175	2.27939
$881$	−34.2531	−1.15402	−0.577008	−	0.816738i	$-0.695780\pi$
$881$	−34.2531	−1.15402	−0.577008	+	0.816738i	$0.695780\pi$
$882$	12.3845	0.417006
$883$	−6.47062	−0.217754	−0.108877	−	0.994055i	$-0.534725\pi$
$883$	−6.47062	−0.217754	−0.108877	+	0.994055i	$0.534725\pi$
$884$	−4.66395	−0.156866
$885$	−44.4699	−1.49484
$886$	−24.8876	−0.836115
$887$	5.70034	0.191399	0.0956993	−	0.995410i	$-0.469491\pi$
$887$	5.70034	0.191399	0.0956993	+	0.995410i	$0.469491\pi$
$888$	1.90915	0.0640668
$889$	8.45405	0.283540
$890$	35.7225	1.19742
$891$	4.08430	0.136829
$892$	40.9913	1.37249
$893$	60.3854	2.02072
$894$	1.71328	0.0573006
$895$	−31.8476	−1.06455
$896$	1.71137	0.0571730
$897$	6.57808	0.219636
$898$	8.62967	0.287976
$899$	−3.23356	−0.107845
$900$	19.1248	0.637494
$901$	4.13459	0.137743
$902$	79.0929	2.63350
$903$	−5.87354	−0.195459
$904$	0.792143	0.0263463
$905$	14.0038	0.465503
$906$	22.7208	0.754850
$907$	−10.6632	−0.354066	−0.177033	−	0.984205i	$-0.556650\pi$
$907$	−10.6632	−0.354066	−0.177033	+	0.984205i	$0.556650\pi$
$908$	−23.4750	−0.779044
$909$	17.5570	0.582330
$910$	42.3926	1.40530
$911$	3.27255	0.108424	0.0542122	−	0.998529i	$-0.482735\pi$
$911$	3.27255	0.108424	0.0542122	+	0.998529i	$0.482735\pi$
$912$	−26.5454	−0.879006
$913$	−25.0362	−0.828576
$914$	23.5949	0.780451
$915$	9.26291	0.306222
$916$	8.71546	0.287967
$917$	13.8318	0.456766
$918$	0.745820	0.0246157
$919$	43.3072	1.42857	0.714286	−	0.699854i	$-0.246752\pi$
$919$	43.3072	1.42857	0.714286	+	0.699854i	$0.246752\pi$
$920$	−0.996402	−0.0328504
$921$	−20.2033	−0.665722
$922$	−12.9238	−0.425624
$923$	−27.9412	−0.919696
$924$	6.41263	0.210960
$925$	−76.4555	−2.51384
$926$	49.6164	1.63050
$927$	10.5650	0.347000
$928$	−7.83599	−0.257229
$929$	6.72374	0.220599	0.110299	−	0.993898i	$-0.464819\pi$
$929$	6.72374	0.220599	0.110299	+	0.993898i	$0.464819\pi$
$930$	−24.8223	−0.813956
$931$	39.3869	1.29085
$932$	24.6780	0.808355
$933$	7.95378	0.260395
$934$	−35.6547	−1.16666
$935$	−6.04197	−0.197594
$936$	−1.67973	−0.0549037
$937$	−34.4674	−1.12600	−0.563000	−	0.826457i	$-0.690353\pi$
$937$	−34.4674	−1.12600	−0.563000	+	0.826457i	$0.690353\pi$
$938$	−18.4334	−0.601871
$939$	−5.26012	−0.171657
$940$	70.4324	2.29725
$941$	−20.1814	−0.657895	−0.328947	−	0.944348i	$-0.606694\pi$
$941$	−20.1814	−0.657895	−0.328947	+	0.944348i	$0.606694\pi$
$942$	−12.8133	−0.417480
$943$	−9.84358	−0.320551
$944$	48.3526	1.57374
$945$	−3.27585	−0.106564
$946$	56.2153	1.82772
$947$	54.5419	1.77237	0.886186	−	0.463329i	$-0.153345\pi$
$947$	54.5419	1.77237	0.886186	+	0.463329i	$0.153345\pi$
$948$	−3.34988	−0.108799
$949$	59.1529	1.92018
$950$	125.869	4.08372
$951$	−32.0143	−1.03814
$952$	−0.0812714	−0.00263402
$953$	−40.3802	−1.30804	−0.654021	−	0.756476i	$-0.726919\pi$
$953$	−40.3802	−1.30804	−0.654021	+	0.756476i	$0.726919\pi$
$954$	−21.4552	−0.694637
$955$	−101.077	−3.27079
$956$	−8.45581	−0.273481
$957$	4.08430	0.132027
$958$	58.0342	1.87500
$959$	−16.5202	−0.533465
$960$	−27.0417	−0.872766
$961$	−20.5441	−0.662712
$962$	−96.7531	−3.11945
$963$	−10.3172	−0.332468
$964$	0.869076	0.0279911
$965$	50.6341	1.62997
$966$	−1.65157	−0.0531384
$967$	31.3292	1.00748	0.503740	−	0.863855i	$-0.331957\pi$
$967$	31.3292	1.00748	0.503740	+	0.863855i	$0.331957\pi$
$968$	1.45079	0.0466300
$969$	2.37197	0.0761986
$970$	−19.7985	−0.635692
$971$	13.1463	0.421886	0.210943	−	0.977498i	$-0.432346\pi$
$971$	13.1463	0.421886	0.210943	+	0.977498i	$0.432346\pi$
$972$	−1.87020	−0.0599867
$973$	−16.0186	−0.513533
$974$	3.24794	0.104071
$975$	67.2680	2.15430
$976$	−10.0717	−0.322386
$977$	−57.3837	−1.83587	−0.917934	−	0.396732i	$-0.870144\pi$
$977$	−57.3837	−1.83587	−0.917934	+	0.396732i	$0.870144\pi$
$978$	3.11338	0.0995550
$979$	19.0063	0.607445
$980$	45.9401	1.46750
$981$	5.06258	0.161636
$982$	−59.7765	−1.90755
$983$	50.1387	1.59918	0.799588	−	0.600549i	$-0.205051\pi$
$983$	50.1387	1.59918	0.799588	+	0.600549i	$0.205051\pi$
$984$	2.51358	0.0801301
$985$	41.6712	1.32775
$986$	0.745820	0.0237517
$987$	−8.10253	−0.257906
$988$	76.9713	2.44878
$989$	−6.99632	−0.222470
$990$	31.3529	0.996462
$991$	−3.14635	−0.0999472	−0.0499736	−	0.998751i	$-0.515914\pi$
$991$	−3.14635	−0.0999472	−0.0499736	+	0.998751i	$0.515914\pi$
$992$	25.3382	0.804487
$993$	27.8202	0.882848
$994$	7.01525	0.222510
$995$	−14.7464	−0.467491
$996$	11.4641	0.363253
$997$	24.3387	0.770813	0.385406	−	0.922747i	$-0.374061\pi$
$997$	24.3387	0.770813	0.385406	+	0.922747i	$0.374061\pi$
$998$	57.3964	1.81685
$999$	7.47652	0.236547

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.l.1.2	✓	11
3.2	odd	2		6003.2.a.m.1.10		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.l.1.2	✓	11	1.1	even	1	trivial
6003.2.a.m.1.10		11	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)

\(f(q)\)	\(=\)	\(q-1.96728 q^{2} -1.00000 q^{3} +1.87020 q^{4} -3.90206 q^{5} +1.96728 q^{6} -0.839519 q^{7} +0.255353 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.96728 q^{2} -1.00000 q^{3} +1.87020 q^{4} -3.90206 q^{5} +1.96728 q^{6} -0.839519 q^{7} +0.255353 q^{8} +1.00000 q^{9} +7.67646 q^{10} +4.08430 q^{11} -1.87020 q^{12} -6.57808 q^{13} +1.65157 q^{14} +3.90206 q^{15} -4.24275 q^{16} +0.379112 q^{17} -1.96728 q^{18} -6.25665 q^{19} -7.29764 q^{20} +0.839519 q^{21} -8.03497 q^{22} +1.00000 q^{23} -0.255353 q^{24} +10.2261 q^{25} +12.9409 q^{26} -1.00000 q^{27} -1.57007 q^{28} -1.00000 q^{29} -7.67646 q^{30} +3.23356 q^{31} +7.83599 q^{32} -4.08430 q^{33} -0.745820 q^{34} +3.27585 q^{35} +1.87020 q^{36} -7.47652 q^{37} +12.3086 q^{38} +6.57808 q^{39} -0.996402 q^{40} -9.84358 q^{41} -1.65157 q^{42} -6.99632 q^{43} +7.63846 q^{44} -3.90206 q^{45} -1.96728 q^{46} -9.65140 q^{47} +4.24275 q^{48} -6.29521 q^{49} -20.1176 q^{50} -0.379112 q^{51} -12.3023 q^{52} +10.9060 q^{53} +1.96728 q^{54} -15.9372 q^{55} -0.214373 q^{56} +6.25665 q^{57} +1.96728 q^{58} -11.3965 q^{59} +7.29764 q^{60} +2.37385 q^{61} -6.36133 q^{62} -0.839519 q^{63} -6.93009 q^{64} +25.6681 q^{65} +8.03497 q^{66} -11.1611 q^{67} +0.709015 q^{68} -1.00000 q^{69} -6.44453 q^{70} +4.24762 q^{71} +0.255353 q^{72} -8.99243 q^{73} +14.7084 q^{74} -10.2261 q^{75} -11.7012 q^{76} -3.42884 q^{77} -12.9409 q^{78} +1.79119 q^{79} +16.5555 q^{80} +1.00000 q^{81} +19.3651 q^{82} -6.12986 q^{83} +1.57007 q^{84} -1.47932 q^{85} +13.7637 q^{86} +1.00000 q^{87} +1.04294 q^{88} +4.65351 q^{89} +7.67646 q^{90} +5.52242 q^{91} +1.87020 q^{92} -3.23356 q^{93} +18.9870 q^{94} +24.4138 q^{95} -7.83599 q^{96} -2.57912 q^{97} +12.3845 q^{98} +4.08430 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9} + 14 q^{10} + 11 q^{11} - 18 q^{12} - 5 q^{13} + 17 q^{14} - 2 q^{15} + 20 q^{16} + 15 q^{17} + 2 q^{18} - 6 q^{19} + 21 q^{20} - 3 q^{21} - 10 q^{22} + 11 q^{23} - 18 q^{24} + 3 q^{25} - 5 q^{26} - 11 q^{27} + 7 q^{28} - 11 q^{29} - 14 q^{30} + 35 q^{31} + 28 q^{32} - 11 q^{33} + 28 q^{34} + 15 q^{35} + 18 q^{36} - 28 q^{37} - 2 q^{38} + 5 q^{39} - q^{40} + 10 q^{41} - 17 q^{42} - 6 q^{43} + 18 q^{44} + 2 q^{45} + 2 q^{46} + 15 q^{47} - 20 q^{48} + 22 q^{49} + 15 q^{50} - 15 q^{51} - 36 q^{52} - 7 q^{53} - 2 q^{54} - 12 q^{55} + 56 q^{56} + 6 q^{57} - 2 q^{58} - 20 q^{59} - 21 q^{60} - 20 q^{61} - 11 q^{62} + 3 q^{63} + 36 q^{64} + 11 q^{65} + 10 q^{66} - 39 q^{67} + 35 q^{68} - 11 q^{69} + 38 q^{70} + 49 q^{71} + 18 q^{72} - 3 q^{73} + 37 q^{74} - 3 q^{75} - 18 q^{76} + 25 q^{77} + 5 q^{78} + 41 q^{79} + 51 q^{80} + 11 q^{81} - 19 q^{82} + 13 q^{83} - 7 q^{84} + 62 q^{86} + 11 q^{87} - 40 q^{88} + 34 q^{89} + 14 q^{90} + 2 q^{91} + 18 q^{92} - 35 q^{93} - 14 q^{94} + 25 q^{95} - 28 q^{96} - 11 q^{97} + 53 q^{98} + 11 q^{99}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9 + 14 * q^10 + 11 * q^11 - 18 * q^12 - 5 * q^13 + 17 * q^14 - 2 * q^15 + 20 * q^16 + 15 * q^17 + 2 * q^18 - 6 * q^19 + 21 * q^20 - 3 * q^21 - 10 * q^22 + 11 * q^23 - 18 * q^24 + 3 * q^25 - 5 * q^26 - 11 * q^27 + 7 * q^28 - 11 * q^29 - 14 * q^30 + 35 * q^31 + 28 * q^32 - 11 * q^33 + 28 * q^34 + 15 * q^35 + 18 * q^36 - 28 * q^37 - 2 * q^38 + 5 * q^39 - q^40 + 10 * q^41 - 17 * q^42 - 6 * q^43 + 18 * q^44 + 2 * q^45 + 2 * q^46 + 15 * q^47 - 20 * q^48 + 22 * q^49 + 15 * q^50 - 15 * q^51 - 36 * q^52 - 7 * q^53 - 2 * q^54 - 12 * q^55 + 56 * q^56 + 6 * q^57 - 2 * q^58 - 20 * q^59 - 21 * q^60 - 20 * q^61 - 11 * q^62 + 3 * q^63 + 36 * q^64 + 11 * q^65 + 10 * q^66 - 39 * q^67 + 35 * q^68 - 11 * q^69 + 38 * q^70 + 49 * q^71 + 18 * q^72 - 3 * q^73 + 37 * q^74 - 3 * q^75 - 18 * q^76 + 25 * q^77 + 5 * q^78 + 41 * q^79 + 51 * q^80 + 11 * q^81 - 19 * q^82 + 13 * q^83 - 7 * q^84 + 62 * q^86 + 11 * q^87 - 40 * q^88 + 34 * q^89 + 14 * q^90 + 2 * q^91 + 18 * q^92 - 35 * q^93 - 14 * q^94 + 25 * q^95 - 28 * q^96 - 11 * q^97 + 53 * q^98 + 11 * q^99

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