LMFDB - Embedded newform 2001.2.a.o.1.1

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			1.1
Root			$-2.80084$ 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)

$f(q)$	$=$	$q-2.80084 q^{2} +1.00000 q^{3} +5.84471 q^{4} -3.48103 q^{5} -2.80084 q^{6} -1.41384 q^{7} -10.7684 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.80084 q^{2} +1.00000 q^{3} +5.84471 q^{4} -3.48103 q^{5} -2.80084 q^{6} -1.41384 q^{7} -10.7684 q^{8} +1.00000 q^{9} +9.74980 q^{10} -4.43439 q^{11} +5.84471 q^{12} -2.37735 q^{13} +3.95993 q^{14} -3.48103 q^{15} +18.4712 q^{16} -3.28679 q^{17} -2.80084 q^{18} -3.46248 q^{19} -20.3456 q^{20} -1.41384 q^{21} +12.4200 q^{22} +1.00000 q^{23} -10.7684 q^{24} +7.11755 q^{25} +6.65859 q^{26} +1.00000 q^{27} -8.26345 q^{28} +1.00000 q^{29} +9.74980 q^{30} -4.18385 q^{31} -30.1980 q^{32} -4.43439 q^{33} +9.20579 q^{34} +4.92160 q^{35} +5.84471 q^{36} -10.7653 q^{37} +9.69784 q^{38} -2.37735 q^{39} +37.4851 q^{40} +3.71341 q^{41} +3.95993 q^{42} -7.08099 q^{43} -25.9177 q^{44} -3.48103 q^{45} -2.80084 q^{46} +1.63781 q^{47} +18.4712 q^{48} -5.00107 q^{49} -19.9351 q^{50} -3.28679 q^{51} -13.8949 q^{52} +6.97182 q^{53} -2.80084 q^{54} +15.4362 q^{55} +15.2248 q^{56} -3.46248 q^{57} -2.80084 q^{58} +12.2928 q^{59} -20.3456 q^{60} +5.25185 q^{61} +11.7183 q^{62} -1.41384 q^{63} +47.6374 q^{64} +8.27563 q^{65} +12.4200 q^{66} -11.9828 q^{67} -19.2103 q^{68} +1.00000 q^{69} -13.7846 q^{70} +12.3124 q^{71} -10.7684 q^{72} +8.68606 q^{73} +30.1520 q^{74} +7.11755 q^{75} -20.2372 q^{76} +6.26950 q^{77} +6.65859 q^{78} +9.51988 q^{79} -64.2986 q^{80} +1.00000 q^{81} -10.4007 q^{82} +2.12581 q^{83} -8.26345 q^{84} +11.4414 q^{85} +19.8327 q^{86} +1.00000 q^{87} +47.7513 q^{88} -11.0119 q^{89} +9.74980 q^{90} +3.36119 q^{91} +5.84471 q^{92} -4.18385 q^{93} -4.58725 q^{94} +12.0530 q^{95} -30.1980 q^{96} +12.3407 q^{97} +14.0072 q^{98} -4.43439 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.80084	−1.98049	−0.990247	−	0.139326i	$-0.955506\pi$
$2$	−2.80084	−1.98049	−0.990247	+	0.139326i	$0.955506\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.84471	2.92235
$5$	−3.48103	−1.55676	−0.778381	−	0.627792i	$-0.783959\pi$
$5$	−3.48103	−1.55676	−0.778381	+	0.627792i	$0.783959\pi$
$6$	−2.80084	−1.14344
$7$	−1.41384	−0.534380	−0.267190	−	0.963644i	$-0.586095\pi$
$7$	−1.41384	−0.534380	−0.267190	+	0.963644i	$0.586095\pi$
$8$	−10.7684	−3.80721
$9$	1.00000	0.333333
$10$	9.74980	3.08316
$11$	−4.43439	−1.33702	−0.668509	−	0.743704i	$-0.733067\pi$
$11$	−4.43439	−1.33702	−0.668509	+	0.743704i	$0.733067\pi$
$12$	5.84471	1.68722
$13$	−2.37735	−0.659359	−0.329680	−	0.944093i	$-0.606941\pi$
$13$	−2.37735	−0.659359	−0.329680	+	0.944093i	$0.606941\pi$
$14$	3.95993	1.05834
$15$	−3.48103	−0.898797
$16$	18.4712	4.61779
$17$	−3.28679	−0.797165	−0.398582	−	0.917133i	$-0.630498\pi$
$17$	−3.28679	−0.797165	−0.398582	+	0.917133i	$0.630498\pi$
$18$	−2.80084	−0.660164
$19$	−3.46248	−0.794347	−0.397173	−	0.917744i	$-0.630009\pi$
$19$	−3.46248	−0.794347	−0.397173	+	0.917744i	$0.630009\pi$
$20$	−20.3456	−4.54941
$21$	−1.41384	−0.308524
$22$	12.4200	2.64796
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−10.7684	−2.19809
$25$	7.11755	1.42351
$26$	6.65859	1.30586
$27$	1.00000	0.192450
$28$	−8.26345	−1.56165
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	9.74980	1.78006
$31$	−4.18385	−0.751443	−0.375721	−	0.926733i	$-0.622605\pi$
$31$	−4.18385	−0.751443	−0.375721	+	0.926733i	$0.622605\pi$
$32$	−30.1980	−5.33830
$33$	−4.43439	−0.771928
$34$	9.20579	1.57878
$35$	4.92160	0.831902
$36$	5.84471	0.974118
$37$	−10.7653	−1.76981	−0.884905	−	0.465771i	$-0.845777\pi$
$37$	−10.7653	−1.76981	−0.884905	+	0.465771i	$0.845777\pi$
$38$	9.69784	1.57320
$39$	−2.37735	−0.380681
$40$	37.4851	5.92691
$41$	3.71341	0.579937	0.289968	−	0.957036i	$-0.406355\pi$
$41$	3.71341	0.579937	0.289968	+	0.957036i	$0.406355\pi$
$42$	3.95993	0.611030
$43$	−7.08099	−1.07984	−0.539920	−	0.841716i	$-0.681546\pi$
$43$	−7.08099	−1.07984	−0.539920	+	0.841716i	$0.681546\pi$
$44$	−25.9177	−3.90724
$45$	−3.48103	−0.518921
$46$	−2.80084	−0.412961
$47$	1.63781	0.238899	0.119450	−	0.992840i	$-0.461887\pi$
$47$	1.63781	0.238899	0.119450	+	0.992840i	$0.461887\pi$
$48$	18.4712	2.66608
$49$	−5.00107	−0.714438
$50$	−19.9351	−2.81925
$51$	−3.28679	−0.460243
$52$	−13.8949	−1.92688
$53$	6.97182	0.957653	0.478827	−	0.877910i	$-0.341062\pi$
$53$	6.97182	0.957653	0.478827	+	0.877910i	$0.341062\pi$
$54$	−2.80084	−0.381146
$55$	15.4362	2.08142
$56$	15.2248	2.03449
$57$	−3.46248	−0.458616
$58$	−2.80084	−0.367768
$59$	12.2928	1.60039	0.800195	−	0.599740i	$-0.204729\pi$
$59$	12.2928	1.60039	0.800195	+	0.599740i	$0.204729\pi$
$60$	−20.3456	−2.62660
$61$	5.25185	0.672431	0.336215	−	0.941785i	$-0.390853\pi$
$61$	5.25185	0.672431	0.336215	+	0.941785i	$0.390853\pi$
$62$	11.7183	1.48823
$63$	−1.41384	−0.178127
$64$	47.6374	5.95467
$65$	8.27563	1.02647
$66$	12.4200	1.52880
$67$	−11.9828	−1.46393	−0.731965	−	0.681342i	$-0.761397\pi$
$67$	−11.9828	−1.46393	−0.731965	+	0.681342i	$0.761397\pi$
$68$	−19.2103	−2.32960
$69$	1.00000	0.120386
$70$	−13.7846	−1.64758
$71$	12.3124	1.46121	0.730604	−	0.682802i	$-0.239239\pi$
$71$	12.3124	1.46121	0.730604	+	0.682802i	$0.239239\pi$
$72$	−10.7684	−1.26907
$73$	8.68606	1.01663	0.508313	−	0.861172i	$-0.330269\pi$
$73$	8.68606	1.01663	0.508313	+	0.861172i	$0.330269\pi$
$74$	30.1520	3.50510
$75$	7.11755	0.821863
$76$	−20.2372	−2.32136
$77$	6.26950	0.714476
$78$	6.65859	0.753936
$79$	9.51988	1.07107	0.535535	−	0.844513i	$-0.320110\pi$
$79$	9.51988	1.07107	0.535535	+	0.844513i	$0.320110\pi$
$80$	−64.2986	−7.18881
$81$	1.00000	0.111111
$82$	−10.4007	−1.14856
$83$	2.12581	0.233338	0.116669	−	0.993171i	$-0.462778\pi$
$83$	2.12581	0.233338	0.116669	+	0.993171i	$0.462778\pi$
$84$	−8.26345	−0.901617
$85$	11.4414	1.24100
$86$	19.8327	2.13862
$87$	1.00000	0.107211
$88$	47.7513	5.09031
$89$	−11.0119	−1.16726	−0.583632	−	0.812018i	$-0.698369\pi$
$89$	−11.0119	−1.16726	−0.583632	+	0.812018i	$0.698369\pi$
$90$	9.74980	1.02772
$91$	3.36119	0.352348
$92$	5.84471	0.609353
$93$	−4.18385	−0.433846
$94$	−4.58725	−0.473139
$95$	12.0530	1.23661
$96$	−30.1980	−3.08207
$97$	12.3407	1.25301	0.626505	−	0.779417i	$-0.284485\pi$
$97$	12.3407	1.25301	0.626505	+	0.779417i	$0.284485\pi$
$98$	14.0072	1.41494
$99$	−4.43439	−0.445673
$100$	41.6000	4.16000
$101$	−17.4826	−1.73959	−0.869794	−	0.493416i	$-0.835748\pi$
$101$	−17.4826	−1.73959	−0.869794	+	0.493416i	$0.835748\pi$
$102$	9.20579	0.911509
$103$	−10.0681	−0.992040	−0.496020	−	0.868311i	$-0.665206\pi$
$103$	−10.0681	−0.992040	−0.496020	+	0.868311i	$0.665206\pi$
$104$	25.6003	2.51032
$105$	4.92160	0.480299
$106$	−19.5270	−1.89663
$107$	−8.64089	−0.835346	−0.417673	−	0.908597i	$-0.637154\pi$
$107$	−8.64089	−0.835346	−0.417673	+	0.908597i	$0.637154\pi$
$108$	5.84471	0.562407
$109$	−7.68708	−0.736289	−0.368144	−	0.929769i	$-0.620007\pi$
$109$	−7.68708	−0.736289	−0.368144	+	0.929769i	$0.620007\pi$
$110$	−43.2344	−4.12224
$111$	−10.7653	−1.02180
$112$	−26.1152	−2.46765
$113$	−5.51803	−0.519092	−0.259546	−	0.965731i	$-0.583573\pi$
$113$	−5.51803	−0.519092	−0.259546	+	0.965731i	$0.583573\pi$
$114$	9.69784	0.908286
$115$	−3.48103	−0.324607
$116$	5.84471	0.542667
$117$	−2.37735	−0.219786
$118$	−34.4302	−3.16956
$119$	4.64699	0.425989
$120$	37.4851	3.42191
$121$	8.66381	0.787619
$122$	−14.7096	−1.33174
$123$	3.71341	0.334827
$124$	−24.4534	−2.19598
$125$	−7.37123	−0.659303
$126$	3.95993	0.352778
$127$	12.7499	1.13137	0.565684	−	0.824622i	$-0.308612\pi$
$127$	12.7499	1.13137	0.565684	+	0.824622i	$0.308612\pi$
$128$	−73.0287	−6.45489
$129$	−7.08099	−0.623446
$130$	−23.1787	−2.03291
$131$	−14.4611	−1.26347	−0.631735	−	0.775185i	$-0.717657\pi$
$131$	−14.4611	−1.26347	−0.631735	+	0.775185i	$0.717657\pi$
$132$	−25.9177	−2.25585
$133$	4.89537	0.424483
$134$	33.5619	2.89930
$135$	−3.48103	−0.299599
$136$	35.3935	3.03497
$137$	9.36729	0.800302	0.400151	−	0.916449i	$-0.368958\pi$
$137$	9.36729	0.800302	0.400151	+	0.916449i	$0.368958\pi$
$138$	−2.80084	−0.238423
$139$	−7.17859	−0.608880	−0.304440	−	0.952532i	$-0.598469\pi$
$139$	−7.17859	−0.608880	−0.304440	+	0.952532i	$0.598469\pi$
$140$	28.7653	2.43111
$141$	1.63781	0.137929
$142$	−34.4849	−2.89391
$143$	10.5421	0.881575
$144$	18.4712	1.53926
$145$	−3.48103	−0.289084
$146$	−24.3283	−2.01342
$147$	−5.00107	−0.412481
$148$	−62.9202	−5.17201
$149$	12.0231	0.984974	0.492487	−	0.870320i	$-0.336088\pi$
$149$	12.0231	0.984974	0.492487	+	0.870320i	$0.336088\pi$
$150$	−19.9351	−1.62769
$151$	14.1232	1.14933	0.574665	−	0.818389i	$-0.305132\pi$
$151$	14.1232	1.14933	0.574665	+	0.818389i	$0.305132\pi$
$152$	37.2853	3.02424
$153$	−3.28679	−0.265722
$154$	−17.5599	−1.41501
$155$	14.5641	1.16982
$156$	−13.8949	−1.11248
$157$	12.7785	1.01983	0.509917	−	0.860224i	$-0.329676\pi$
$157$	12.7785	1.01983	0.509917	+	0.860224i	$0.329676\pi$
$158$	−26.6637	−2.12125
$159$	6.97182	0.552901
$160$	105.120	8.31046
$161$	−1.41384	−0.111426
$162$	−2.80084	−0.220055
$163$	18.0242	1.41177	0.705883	−	0.708328i	$-0.250550\pi$
$163$	18.0242	1.41177	0.705883	+	0.708328i	$0.250550\pi$
$164$	21.7038	1.69478
$165$	15.4362	1.20171
$166$	−5.95405	−0.462124
$167$	6.24398	0.483174	0.241587	−	0.970379i	$-0.422332\pi$
$167$	6.24398	0.483174	0.241587	+	0.970379i	$0.422332\pi$
$168$	15.2248	1.17462
$169$	−7.34819	−0.565246
$170$	−32.0456	−2.45778
$171$	−3.46248	−0.264782
$172$	−41.3863	−3.15567
$173$	−21.4424	−1.63024	−0.815119	−	0.579293i	$-0.803329\pi$
$173$	−21.4424	−1.63024	−0.815119	+	0.579293i	$0.803329\pi$
$174$	−2.80084	−0.212331
$175$	−10.0630	−0.760694
$176$	−81.9084	−6.17407
$177$	12.2928	0.923985
$178$	30.8427	2.31176
$179$	19.8711	1.48524	0.742618	−	0.669715i	$-0.233584\pi$
$179$	19.8711	1.48524	0.742618	+	0.669715i	$0.233584\pi$
$180$	−20.3456	−1.51647
$181$	−0.142040	−0.0105578	−0.00527889	−	0.999986i	$-0.501680\pi$
$181$	−0.142040	−0.0105578	−0.00527889	+	0.999986i	$0.501680\pi$
$182$	−9.41415	−0.697823
$183$	5.25185	0.388228
$184$	−10.7684	−0.793857
$185$	37.4744	2.75517
$186$	11.7183	0.859228
$187$	14.5749	1.06582
$188$	9.57253	0.698148
$189$	−1.41384	−0.102841
$190$	−33.7584	−2.44910
$191$	−14.5967	−1.05618	−0.528091	−	0.849188i	$-0.677092\pi$
$191$	−14.5967	−1.05618	−0.528091	+	0.849188i	$0.677092\pi$
$192$	47.6374	3.43793
$193$	−17.3067	−1.24576	−0.622881	−	0.782317i	$-0.714038\pi$
$193$	−17.3067	−1.24576	−0.622881	+	0.782317i	$0.714038\pi$
$194$	−34.5644	−2.48158
$195$	8.27563	0.592630
$196$	−29.2298	−2.08784
$197$	2.11009	0.150338	0.0751689	−	0.997171i	$-0.476050\pi$
$197$	2.11009	0.150338	0.0751689	+	0.997171i	$0.476050\pi$
$198$	12.4200	0.882652
$199$	16.4313	1.16478	0.582391	−	0.812909i	$-0.302117\pi$
$199$	16.4313	1.16478	0.582391	+	0.812909i	$0.302117\pi$
$200$	−76.6446	−5.41959
$201$	−11.9828	−0.845201
$202$	48.9661	3.44524
$203$	−1.41384	−0.0992318
$204$	−19.2103	−1.34499
$205$	−12.9265	−0.902824
$206$	28.1992	1.96473
$207$	1.00000	0.0695048
$208$	−43.9125	−3.04478
$209$	15.3540	1.06206
$210$	−13.7846	−0.951229
$211$	5.03335	0.346510	0.173255	−	0.984877i	$-0.444572\pi$
$211$	5.03335	0.346510	0.173255	+	0.984877i	$0.444572\pi$
$212$	40.7482	2.79860
$213$	12.3124	0.843629
$214$	24.2018	1.65440
$215$	24.6491	1.68105
$216$	−10.7684	−0.732697
$217$	5.91528	0.401556
$218$	21.5303	1.45821
$219$	8.68606	0.586949
$220$	90.2202	6.08264
$221$	7.81387	0.525618
$222$	30.1520	2.02367
$223$	−4.74485	−0.317739	−0.158869	−	0.987300i	$-0.550785\pi$
$223$	−4.74485	−0.317739	−0.158869	+	0.987300i	$0.550785\pi$
$224$	42.6950	2.85268
$225$	7.11755	0.474503
$226$	15.4551	1.02806
$227$	−15.9414	−1.05806	−0.529032	−	0.848602i	$-0.677445\pi$
$227$	−15.9414	−1.05806	−0.529032	+	0.848602i	$0.677445\pi$
$228$	−20.2372	−1.34024
$229$	24.6062	1.62602	0.813012	−	0.582247i	$-0.197826\pi$
$229$	24.6062	1.62602	0.813012	+	0.582247i	$0.197826\pi$
$230$	9.74980	0.642883
$231$	6.26950	0.412503
$232$	−10.7684	−0.706980
$233$	−3.43090	−0.224765	−0.112383	−	0.993665i	$-0.535848\pi$
$233$	−3.43090	−0.224765	−0.112383	+	0.993665i	$0.535848\pi$
$234$	6.65859	0.435285
$235$	−5.70127	−0.371910
$236$	71.8479	4.67690
$237$	9.51988	0.618382
$238$	−13.0155	−0.843668
$239$	5.76650	0.373004	0.186502	−	0.982455i	$-0.440285\pi$
$239$	5.76650	0.373004	0.186502	+	0.982455i	$0.440285\pi$
$240$	−64.2986	−4.15046
$241$	19.8383	1.27790	0.638948	−	0.769250i	$-0.279370\pi$
$241$	19.8383	1.27790	0.638948	+	0.769250i	$0.279370\pi$
$242$	−24.2659	−1.55987
$243$	1.00000	0.0641500
$244$	30.6955	1.96508
$245$	17.4089	1.11221
$246$	−10.4007	−0.663122
$247$	8.23153	0.523760
$248$	45.0534	2.86090
$249$	2.12581	0.134718
$250$	20.6456	1.30574
$251$	−1.97792	−0.124845	−0.0624226	−	0.998050i	$-0.519883\pi$
$251$	−1.97792	−0.124845	−0.0624226	+	0.998050i	$0.519883\pi$
$252$	−8.26345	−0.520549
$253$	−4.43439	−0.278788
$254$	−35.7103	−2.24067
$255$	11.4414	0.716489
$256$	109.267	6.82919
$257$	−0.846927	−0.0528298	−0.0264149	−	0.999651i	$-0.508409\pi$
$257$	−0.846927	−0.0528298	−0.0264149	+	0.999651i	$0.508409\pi$
$258$	19.8327	1.23473
$259$	15.2204	0.945751
$260$	48.3686	2.99969
$261$	1.00000	0.0618984
$262$	40.5031	2.50229
$263$	0.347153	0.0214064	0.0107032	−	0.999943i	$-0.496593\pi$
$263$	0.347153	0.0214064	0.0107032	+	0.999943i	$0.496593\pi$
$264$	47.7513	2.93889
$265$	−24.2691	−1.49084
$266$	−13.7112	−0.840685
$267$	−11.0119	−0.673920
$268$	−70.0359	−4.27812
$269$	22.3131	1.36045	0.680227	−	0.733002i	$-0.261881\pi$
$269$	22.3131	1.36045	0.680227	+	0.733002i	$0.261881\pi$
$270$	9.74980	0.593354
$271$	−21.0578	−1.27917	−0.639584	−	0.768721i	$-0.720893\pi$
$271$	−21.0578	−1.27917	−0.639584	+	0.768721i	$0.720893\pi$
$272$	−60.7109	−3.68114
$273$	3.36119	0.203428
$274$	−26.2363	−1.58499
$275$	−31.5620	−1.90326
$276$	5.84471	0.351810
$277$	2.42766	0.145864	0.0729320	−	0.997337i	$-0.476764\pi$
$277$	2.42766	0.145864	0.0729320	+	0.997337i	$0.476764\pi$
$278$	20.1061	1.20588
$279$	−4.18385	−0.250481
$280$	−52.9978	−3.16722
$281$	11.6621	0.695703	0.347852	−	0.937550i	$-0.386911\pi$
$281$	11.6621	0.695703	0.347852	+	0.937550i	$0.386911\pi$
$282$	−4.58725	−0.273167
$283$	−7.95812	−0.473061	−0.236530	−	0.971624i	$-0.576010\pi$
$283$	−7.95812	−0.473061	−0.236530	+	0.971624i	$0.576010\pi$
$284$	71.9621	4.27016
$285$	12.0530	0.713956
$286$	−29.5268	−1.74595
$287$	−5.25015	−0.309906
$288$	−30.1980	−1.77943
$289$	−6.19698	−0.364528
$290$	9.74980	0.572528
$291$	12.3407	0.723426
$292$	50.7675	2.97094
$293$	−25.6929	−1.50099	−0.750497	−	0.660874i	$-0.770186\pi$
$293$	−25.6929	−1.50099	−0.750497	+	0.660874i	$0.770186\pi$
$294$	14.0072	0.816916
$295$	−42.7917	−2.49143
$296$	115.926	6.73803
$297$	−4.43439	−0.257309
$298$	−33.6749	−1.95073
$299$	−2.37735	−0.137486
$300$	41.6000	2.40177
$301$	10.0114	0.577045
$302$	−39.5568	−2.27624
$303$	−17.4826	−1.00435
$304$	−63.9560	−3.66813
$305$	−18.2818	−1.04681
$306$	9.20579	0.526260
$307$	18.5614	1.05936	0.529679	−	0.848198i	$-0.322312\pi$
$307$	18.5614	1.05936	0.529679	+	0.848198i	$0.322312\pi$
$308$	36.6434	2.08795
$309$	−10.0681	−0.572755
$310$	−40.7917	−2.31682
$311$	9.91454	0.562202	0.281101	−	0.959678i	$-0.409300\pi$
$311$	9.91454	0.562202	0.281101	+	0.959678i	$0.409300\pi$
$312$	25.6003	1.44933
$313$	15.3040	0.865032	0.432516	−	0.901626i	$-0.357626\pi$
$313$	15.3040	0.865032	0.432516	+	0.901626i	$0.357626\pi$
$314$	−35.7905	−2.01977
$315$	4.92160	0.277301
$316$	55.6409	3.13004
$317$	17.3563	0.974829	0.487414	−	0.873171i	$-0.337940\pi$
$317$	17.3563	0.974829	0.487414	+	0.873171i	$0.337940\pi$
$318$	−19.5270	−1.09502
$319$	−4.43439	−0.248278
$320$	−165.827	−9.27001
$321$	−8.64089	−0.482288
$322$	3.95993	0.220678
$323$	11.3804	0.633225
$324$	5.84471	0.324706
$325$	−16.9209	−0.938604
$326$	−50.4830	−2.79599
$327$	−7.68708	−0.425096
$328$	−39.9875	−2.20794
$329$	−2.31560	−0.127663
$330$	−43.2344	−2.37998
$331$	−25.6184	−1.40811	−0.704057	−	0.710144i	$-0.748630\pi$
$331$	−25.6184	−1.40811	−0.704057	+	0.710144i	$0.748630\pi$
$332$	12.4247	0.681895
$333$	−10.7653	−0.589937
$334$	−17.4884	−0.956922
$335$	41.7124	2.27899
$336$	−26.1152	−1.42470
$337$	−16.3884	−0.892734	−0.446367	−	0.894850i	$-0.647282\pi$
$337$	−16.3884	−0.892734	−0.446367	+	0.894850i	$0.647282\pi$
$338$	20.5811	1.11947
$339$	−5.51803	−0.299698
$340$	66.8717	3.62663
$341$	18.5528	1.00469
$342$	9.69784	0.524399
$343$	16.9675	0.916161
$344$	76.2509	4.11117
$345$	−3.48103	−0.187412
$346$	60.0568	3.22868
$347$	−25.0667	−1.34565	−0.672826	−	0.739800i	$-0.734920\pi$
$347$	−25.0667	−1.34565	−0.672826	+	0.739800i	$0.734920\pi$
$348$	5.84471	0.313309
$349$	22.4766	1.20315	0.601573	−	0.798818i	$-0.294541\pi$
$349$	22.4766	1.20315	0.601573	+	0.798818i	$0.294541\pi$
$350$	28.1850	1.50655
$351$	−2.37735	−0.126894
$352$	133.910	7.13741
$353$	−2.42803	−0.129231	−0.0646156	−	0.997910i	$-0.520582\pi$
$353$	−2.42803	−0.129231	−0.0646156	+	0.997910i	$0.520582\pi$
$354$	−34.4302	−1.82995
$355$	−42.8596	−2.27475
$356$	−64.3616	−3.41116
$357$	4.64699	0.245945
$358$	−55.6558	−2.94150
$359$	36.3433	1.91812	0.959062	−	0.283195i	$-0.0913943\pi$
$359$	36.3433	1.91812	0.959062	+	0.283195i	$0.0913943\pi$
$360$	37.4851	1.97564
$361$	−7.01126	−0.369014
$362$	0.397832	0.0209096
$363$	8.66381	0.454732
$364$	19.6451	1.02969
$365$	−30.2364	−1.58265
$366$	−14.7096	−0.768883
$367$	12.2035	0.637016	0.318508	−	0.947920i	$-0.396818\pi$
$367$	12.2035	0.637016	0.318508	+	0.947920i	$0.396818\pi$
$368$	18.4712	0.962876
$369$	3.71341	0.193312
$370$	−104.960	−5.45660
$371$	−9.85701	−0.511750
$372$	−24.4534	−1.26785
$373$	4.00742	0.207497	0.103748	−	0.994604i	$-0.466916\pi$
$373$	4.00742	0.207497	0.103748	+	0.994604i	$0.466916\pi$
$374$	−40.8220	−2.11086
$375$	−7.37123	−0.380649
$376$	−17.6366	−0.909539
$377$	−2.37735	−0.122440
$378$	3.95993	0.203677
$379$	3.66384	0.188199	0.0940993	−	0.995563i	$-0.470003\pi$
$379$	3.66384	0.188199	0.0940993	+	0.995563i	$0.470003\pi$
$380$	70.4461	3.61381
$381$	12.7499	0.653196
$382$	40.8831	2.09176
$383$	−12.5542	−0.641488	−0.320744	−	0.947166i	$-0.603933\pi$
$383$	−12.5542	−0.641488	−0.320744	+	0.947166i	$0.603933\pi$
$384$	−73.0287	−3.72673
$385$	−21.8243	−1.11227
$386$	48.4732	2.46722
$387$	−7.08099	−0.359947
$388$	72.1279	3.66174
$389$	18.2759	0.926623	0.463312	−	0.886195i	$-0.346661\pi$
$389$	18.2759	0.926623	0.463312	+	0.886195i	$0.346661\pi$
$390$	−23.1787	−1.17370
$391$	−3.28679	−0.166220
$392$	53.8535	2.72001
$393$	−14.4611	−0.729464
$394$	−5.91003	−0.297743
$395$	−33.1389	−1.66740
$396$	−25.9177	−1.30241
$397$	9.01959	0.452680	0.226340	−	0.974048i	$-0.427324\pi$
$397$	9.01959	0.452680	0.226340	+	0.974048i	$0.427324\pi$
$398$	−46.0213	−2.30684
$399$	4.89537	0.245075
$400$	131.469	6.57347
$401$	6.66076	0.332622	0.166311	−	0.986073i	$-0.446814\pi$
$401$	6.66076	0.332622	0.166311	+	0.986073i	$0.446814\pi$
$402$	33.5619	1.67391
$403$	9.94650	0.495470
$404$	−102.181	−5.08369
$405$	−3.48103	−0.172974
$406$	3.95993	0.196528
$407$	47.7377	2.36627
$408$	35.3935	1.75224
$409$	3.95276	0.195451	0.0977257	−	0.995213i	$-0.468843\pi$
$409$	3.95276	0.195451	0.0977257	+	0.995213i	$0.468843\pi$
$410$	36.2050	1.78804
$411$	9.36729	0.462054
$412$	−58.8451	−2.89909
$413$	−17.3800	−0.855216
$414$	−2.80084	−0.137654
$415$	−7.39999	−0.363251
$416$	71.7913	3.51986
$417$	−7.17859	−0.351537
$418$	−43.0040	−2.10339
$419$	4.41044	0.215464	0.107732	−	0.994180i	$-0.465641\pi$
$419$	4.41044	0.215464	0.107732	+	0.994180i	$0.465641\pi$
$420$	28.7653	1.40360
$421$	14.8860	0.725497	0.362748	−	0.931887i	$-0.381838\pi$
$421$	14.8860	0.725497	0.362748	+	0.931887i	$0.381838\pi$
$422$	−14.0976	−0.686260
$423$	1.63781	0.0796331
$424$	−75.0754	−3.64598
$425$	−23.3939	−1.13477
$426$	−34.4849	−1.67080
$427$	−7.42526	−0.359333
$428$	−50.5035	−2.44118
$429$	10.5421	0.508978
$430$	−69.0382	−3.32932
$431$	−2.60324	−0.125393	−0.0626967	−	0.998033i	$-0.519970\pi$
$431$	−2.60324	−0.125393	−0.0626967	+	0.998033i	$0.519970\pi$
$432$	18.4712	0.888695
$433$	5.93295	0.285119	0.142560	−	0.989786i	$-0.454467\pi$
$433$	5.93295	0.285119	0.142560	+	0.989786i	$0.454467\pi$
$434$	−16.5678	−0.795278
$435$	−3.48103	−0.166902
$436$	−44.9287	−2.15170
$437$	−3.46248	−0.165633
$438$	−24.3283	−1.16245
$439$	−8.48828	−0.405124	−0.202562	−	0.979269i	$-0.564927\pi$
$439$	−8.48828	−0.405124	−0.202562	+	0.979269i	$0.564927\pi$
$440$	−166.224	−7.92440
$441$	−5.00107	−0.238146
$442$	−21.8854	−1.04098
$443$	−21.2540	−1.00981	−0.504904	−	0.863176i	$-0.668472\pi$
$443$	−21.2540	−1.00981	−0.504904	+	0.863176i	$0.668472\pi$
$444$	−62.9202	−2.98606
$445$	38.3329	1.81715
$446$	13.2896	0.629279
$447$	12.0231	0.568675
$448$	−67.3514	−3.18206
$449$	−10.8308	−0.511139	−0.255570	−	0.966791i	$-0.582263\pi$
$449$	−10.8308	−0.511139	−0.255570	+	0.966791i	$0.582263\pi$
$450$	−19.9351	−0.939750
$451$	−16.4667	−0.775386
$452$	−32.2512	−1.51697
$453$	14.1232	0.663566
$454$	44.6492	2.09549
$455$	−11.7004	−0.548522
$456$	37.2853	1.74605
$457$	2.24941	0.105223	0.0526114	−	0.998615i	$-0.483246\pi$
$457$	2.24941	0.105223	0.0526114	+	0.998615i	$0.483246\pi$
$458$	−68.9180	−3.22033
$459$	−3.28679	−0.153414
$460$	−20.3456	−0.948617
$461$	2.51632	0.117197	0.0585984	−	0.998282i	$-0.481337\pi$
$461$	2.51632	0.117197	0.0585984	+	0.998282i	$0.481337\pi$
$462$	−17.5599	−0.816959
$463$	−15.2202	−0.707341	−0.353671	−	0.935370i	$-0.615067\pi$
$463$	−15.2202	−0.707341	−0.353671	+	0.935370i	$0.615067\pi$
$464$	18.4712	0.857502
$465$	14.5641	0.675394
$466$	9.60939	0.445146
$467$	−6.08666	−0.281657	−0.140829	−	0.990034i	$-0.544977\pi$
$467$	−6.08666	−0.281657	−0.140829	+	0.990034i	$0.544977\pi$
$468$	−13.8949	−0.642293
$469$	16.9417	0.782295
$470$	15.9683	0.736564
$471$	12.7785	0.588801
$472$	−132.374	−6.09301
$473$	31.3998	1.44377
$474$	−26.6637	−1.22470
$475$	−24.6443	−1.13076
$476$	27.1603	1.24489
$477$	6.97182	0.319218
$478$	−16.1510	−0.738732
$479$	−2.91970	−0.133405	−0.0667023	−	0.997773i	$-0.521248\pi$
$479$	−2.91970	−0.133405	−0.0667023	+	0.997773i	$0.521248\pi$
$480$	105.120	4.79805
$481$	25.5930	1.16694
$482$	−55.5639	−2.53087
$483$	−1.41384	−0.0643318
$484$	50.6374	2.30170
$485$	−42.9584	−1.95064
$486$	−2.80084	−0.127049
$487$	35.3220	1.60059	0.800297	−	0.599604i	$-0.204675\pi$
$487$	35.3220	1.60059	0.800297	+	0.599604i	$0.204675\pi$
$488$	−56.5541	−2.56008
$489$	18.0242	0.815084
$490$	−48.7594	−2.20273
$491$	−5.12284	−0.231190	−0.115595	−	0.993296i	$-0.536878\pi$
$491$	−5.12284	−0.231190	−0.115595	+	0.993296i	$0.536878\pi$
$492$	21.7038	0.978482
$493$	−3.28679	−0.148030
$494$	−23.0552	−1.03730
$495$	15.4362	0.693807
$496$	−77.2807	−3.47001
$497$	−17.4076	−0.780840
$498$	−5.95405	−0.266807
$499$	8.30239	0.371666	0.185833	−	0.982581i	$-0.440502\pi$
$499$	8.30239	0.371666	0.185833	+	0.982581i	$0.440502\pi$
$500$	−43.0827	−1.92672
$501$	6.24398	0.278961
$502$	5.53984	0.247255
$503$	−37.2320	−1.66009	−0.830045	−	0.557696i	$-0.811686\pi$
$503$	−37.2320	−1.66009	−0.830045	+	0.557696i	$0.811686\pi$
$504$	15.2248	0.678165
$505$	60.8575	2.70812
$506$	12.4200	0.552137
$507$	−7.34819	−0.326345
$508$	74.5192	3.30626
$509$	−41.3069	−1.83090	−0.915449	−	0.402434i	$-0.868164\pi$
$509$	−41.3069	−1.83090	−0.915449	+	0.402434i	$0.868164\pi$
$510$	−32.0456	−1.41900
$511$	−12.2807	−0.543264
$512$	−159.982	−7.07027
$513$	−3.46248	−0.152872
$514$	2.37211	0.104629
$515$	35.0474	1.54437
$516$	−41.3863	−1.82193
$517$	−7.26270	−0.319413
$518$	−42.6300	−1.87305
$519$	−21.4424	−0.941219
$520$	−89.1153	−3.90796
$521$	24.8969	1.09075	0.545377	−	0.838191i	$-0.316387\pi$
$521$	24.8969	1.09075	0.545377	+	0.838191i	$0.316387\pi$
$522$	−2.80084	−0.122589
$523$	10.7859	0.471634	0.235817	−	0.971797i	$-0.424223\pi$
$523$	10.7859	0.471634	0.235817	+	0.971797i	$0.424223\pi$
$524$	−84.5207	−3.69230
$525$	−10.0630	−0.439187
$526$	−0.972319	−0.0423951
$527$	13.7515	0.599024
$528$	−81.9084	−3.56460
$529$	1.00000	0.0434783
$530$	67.9738	2.95260
$531$	12.2928	0.533463
$532$	28.6120	1.24049
$533$	−8.82808	−0.382387
$534$	30.8427	1.33469
$535$	30.0792	1.30044
$536$	129.035	5.57348
$537$	19.8711	0.857501
$538$	−62.4954	−2.69437
$539$	22.1767	0.955217
$540$	−20.3456	−0.875534
$541$	−42.3958	−1.82274	−0.911368	−	0.411592i	$-0.864973\pi$
$541$	−42.3958	−1.82274	−0.911368	+	0.411592i	$0.864973\pi$
$542$	58.9794	2.53338
$543$	−0.142040	−0.00609554
$544$	99.2546	4.25550
$545$	26.7589	1.14623
$546$	−9.41415	−0.402888
$547$	−43.7711	−1.87151	−0.935757	−	0.352644i	$-0.885283\pi$
$547$	−43.7711	−1.87151	−0.935757	+	0.352644i	$0.885283\pi$
$548$	54.7491	2.33876
$549$	5.25185	0.224144
$550$	88.4000	3.76939
$551$	−3.46248	−0.147506
$552$	−10.7684	−0.458334
$553$	−13.4595	−0.572358
$554$	−6.79949	−0.288883
$555$	37.4744	1.59070
$556$	−41.9567	−1.77936
$557$	−10.4656	−0.443443	−0.221722	−	0.975110i	$-0.571168\pi$
$557$	−10.4656	−0.443443	−0.221722	+	0.975110i	$0.571168\pi$
$558$	11.7183	0.496076
$559$	16.8340	0.712002
$560$	90.9077	3.84155
$561$	14.5749	0.615354
$562$	−32.6637	−1.37784
$563$	30.1027	1.26868	0.634338	−	0.773055i	$-0.281273\pi$
$563$	30.1027	1.26868	0.634338	+	0.773055i	$0.281273\pi$
$564$	9.57253	0.403076
$565$	19.2084	0.808103
$566$	22.2894	0.936894
$567$	−1.41384	−0.0593755
$568$	−132.584	−5.56312
$569$	−7.93717	−0.332744	−0.166372	−	0.986063i	$-0.553205\pi$
$569$	−7.93717	−0.332744	−0.166372	+	0.986063i	$0.553205\pi$
$570$	−33.7584	−1.41399
$571$	42.1256	1.76290	0.881450	−	0.472277i	$-0.156568\pi$
$571$	42.1256	1.76290	0.881450	+	0.472277i	$0.156568\pi$
$572$	61.6155	2.57627
$573$	−14.5967	−0.609786
$574$	14.7048	0.613768
$575$	7.11755	0.296822
$576$	47.6374	1.98489
$577$	−24.2008	−1.00749	−0.503745	−	0.863852i	$-0.668045\pi$
$577$	−24.2008	−1.00749	−0.503745	+	0.863852i	$0.668045\pi$
$578$	17.3568	0.721946
$579$	−17.3067	−0.719241
$580$	−20.3456	−0.844804
$581$	−3.00554	−0.124691
$582$	−34.5644	−1.43274
$583$	−30.9158	−1.28040
$584$	−93.5350	−3.87051
$585$	8.27563	0.342155
$586$	71.9616	2.97271
$587$	1.25188	0.0516706	0.0258353	−	0.999666i	$-0.491775\pi$
$587$	1.25188	0.0516706	0.0258353	+	0.999666i	$0.491775\pi$
$588$	−29.2298	−1.20542
$589$	14.4865	0.596906
$590$	119.853	4.93425
$591$	2.11009	0.0867976
$592$	−198.848	−8.17262
$593$	16.3746	0.672426	0.336213	−	0.941786i	$-0.390854\pi$
$593$	16.3746	0.672426	0.336213	+	0.941786i	$0.390854\pi$
$594$	12.4200	0.509599
$595$	−16.1763	−0.663163
$596$	70.2717	2.87844
$597$	16.4313	0.672487
$598$	6.65859	0.272290
$599$	−13.9988	−0.571977	−0.285989	−	0.958233i	$-0.592322\pi$
$599$	−13.9988	−0.571977	−0.285989	+	0.958233i	$0.592322\pi$
$600$	−76.6446	−3.12900
$601$	−15.8577	−0.646850	−0.323425	−	0.946254i	$-0.604834\pi$
$601$	−15.8577	−0.646850	−0.323425	+	0.946254i	$0.604834\pi$
$602$	−28.0402	−1.14283
$603$	−11.9828	−0.487977
$604$	82.5460	3.35875
$605$	−30.1589	−1.22614
$606$	48.9661	1.98911
$607$	−44.6641	−1.81286	−0.906430	−	0.422356i	$-0.861203\pi$
$607$	−44.6641	−1.81286	−0.906430	+	0.422356i	$0.861203\pi$
$608$	104.560	4.24046
$609$	−1.41384	−0.0572915
$610$	51.2045	2.07321
$611$	−3.89366	−0.157521
$612$	−19.2103	−0.776532
$613$	41.5875	1.67971	0.839853	−	0.542814i	$-0.182641\pi$
$613$	41.5875	1.67971	0.839853	+	0.542814i	$0.182641\pi$
$614$	−51.9876	−2.09805
$615$	−12.9265	−0.521246
$616$	−67.5125	−2.72016
$617$	−38.3035	−1.54204	−0.771020	−	0.636811i	$-0.780253\pi$
$617$	−38.3035	−1.54204	−0.771020	+	0.636811i	$0.780253\pi$
$618$	28.1992	1.13434
$619$	−35.0276	−1.40788	−0.703939	−	0.710260i	$-0.748577\pi$
$619$	−35.0276	−1.40788	−0.703939	+	0.710260i	$0.748577\pi$
$620$	85.1229	3.41862
$621$	1.00000	0.0401286
$622$	−27.7690	−1.11344
$623$	15.5691	0.623762
$624$	−43.9125	−1.75791
$625$	−9.92828	−0.397131
$626$	−42.8640	−1.71319
$627$	15.3540	0.613178
$628$	74.6865	2.98031
$629$	35.3835	1.41083
$630$	−13.7846	−0.549192
$631$	0.0346178	0.00137811	0.000689056	−	1.00000i	$-0.499781\pi$
$631$	0.0346178	0.00137811	0.000689056		1.00000i	$0.499781\pi$
$632$	−102.514	−4.07778
$633$	5.03335	0.200058
$634$	−48.6123	−1.93064
$635$	−44.3826	−1.76127
$636$	40.7482	1.61577
$637$	11.8893	0.471071
$638$	12.4200	0.491713
$639$	12.3124	0.487069
$640$	254.215	10.0487
$641$	−1.97337	−0.0779435	−0.0389718	−	0.999240i	$-0.512408\pi$
$641$	−1.97337	−0.0779435	−0.0389718	+	0.999240i	$0.512408\pi$
$642$	24.2018	0.955167
$643$	−29.6819	−1.17054	−0.585270	−	0.810838i	$-0.699012\pi$
$643$	−29.6819	−1.17054	−0.585270	+	0.810838i	$0.699012\pi$
$644$	−8.26345	−0.325626
$645$	24.6491	0.970557
$646$	−31.8748	−1.25410
$647$	−8.97043	−0.352664	−0.176332	−	0.984331i	$-0.556423\pi$
$647$	−8.97043	−0.352664	−0.176332	+	0.984331i	$0.556423\pi$
$648$	−10.7684	−0.423023
$649$	−54.5112	−2.13975
$650$	47.3928	1.85890
$651$	5.91528	0.231838
$652$	105.346	4.12568
$653$	−24.5006	−0.958784	−0.479392	−	0.877601i	$-0.659143\pi$
$653$	−24.5006	−0.958784	−0.479392	+	0.877601i	$0.659143\pi$
$654$	21.5303	0.841901
$655$	50.3394	1.96692
$656$	68.5910	2.67803
$657$	8.68606	0.338875
$658$	6.48562	0.252836
$659$	−21.1494	−0.823863	−0.411931	−	0.911215i	$-0.635146\pi$
$659$	−21.1494	−0.823863	−0.411931	+	0.911215i	$0.635146\pi$
$660$	90.2202	3.51182
$661$	−29.9812	−1.16613	−0.583067	−	0.812424i	$-0.698147\pi$
$661$	−29.9812	−1.16613	−0.583067	+	0.812424i	$0.698147\pi$
$662$	71.7530	2.78876
$663$	7.81387	0.303466
$664$	−22.8915	−0.888364
$665$	−17.0409	−0.660819
$666$	30.1520	1.16837
$667$	1.00000	0.0387202
$668$	36.4942	1.41200
$669$	−4.74485	−0.183447
$670$	−116.830	−4.51353
$671$	−23.2888	−0.899052
$672$	42.6950	1.64699
$673$	−11.6843	−0.450398	−0.225199	−	0.974313i	$-0.572303\pi$
$673$	−11.6843	−0.450398	−0.225199	+	0.974313i	$0.572303\pi$
$674$	45.9013	1.76805
$675$	7.11755	0.273954
$676$	−42.9480	−1.65185
$677$	47.4614	1.82409	0.912046	−	0.410088i	$-0.134502\pi$
$677$	47.4614	1.82409	0.912046	+	0.410088i	$0.134502\pi$
$678$	15.4551	0.593550
$679$	−17.4478	−0.669583
$680$	−123.206	−4.72473
$681$	−15.9414	−0.610874
$682$	−51.9635	−1.98979
$683$	48.2425	1.84595	0.922975	−	0.384860i	$-0.125750\pi$
$683$	48.2425	1.84595	0.922975	+	0.384860i	$0.125750\pi$
$684$	−20.2372	−0.773787
$685$	−32.6078	−1.24588
$686$	−47.5234	−1.81445
$687$	24.6062	0.938785
$688$	−130.794	−4.98648
$689$	−16.5745	−0.631437
$690$	9.74980	0.371168
$691$	−17.1961	−0.654172	−0.327086	−	0.944995i	$-0.606067\pi$
$691$	−17.1961	−0.654172	−0.327086	+	0.944995i	$0.606067\pi$
$692$	−125.325	−4.76413
$693$	6.26950	0.238159
$694$	70.2079	2.66506
$695$	24.9889	0.947881
$696$	−10.7684	−0.408175
$697$	−12.2052	−0.462305
$698$	−62.9534	−2.38282
$699$	−3.43090	−0.129768
$700$	−58.8155	−2.22302
$701$	−27.6256	−1.04340	−0.521702	−	0.853128i	$-0.674703\pi$
$701$	−27.6256	−1.04340	−0.521702	+	0.853128i	$0.674703\pi$
$702$	6.65859	0.251312
$703$	37.2747	1.40584
$704$	−211.243	−7.96151
$705$	−5.70127	−0.214722
$706$	6.80053	0.255941
$707$	24.7176	0.929600
$708$	71.8479	2.70021
$709$	8.10255	0.304298	0.152149	−	0.988358i	$-0.451381\pi$
$709$	8.10255	0.304298	0.152149	+	0.988358i	$0.451381\pi$
$710$	120.043	4.50513
$711$	9.51988	0.357023
$712$	118.581	4.44402
$713$	−4.18385	−0.156687
$714$	−13.0155	−0.487092
$715$	−36.6974	−1.37240
$716$	116.141	4.34038
$717$	5.76650	0.215354
$718$	−101.792	−3.79883
$719$	21.9351	0.818041	0.409020	−	0.912525i	$-0.365870\pi$
$719$	21.9351	0.818041	0.409020	+	0.912525i	$0.365870\pi$
$720$	−64.2986	−2.39627
$721$	14.2347	0.530126
$722$	19.6374	0.730829
$723$	19.8383	0.737794
$724$	−0.830184	−0.0308536
$725$	7.11755	0.264339
$726$	−24.2659	−0.900594
$727$	49.7966	1.84685	0.923427	−	0.383773i	$-0.125376\pi$
$727$	49.7966	1.84685	0.923427	+	0.383773i	$0.125376\pi$
$728$	−36.1946	−1.34146
$729$	1.00000	0.0370370
$730$	84.6873	3.13442
$731$	23.2737	0.860811
$732$	30.6955	1.13454
$733$	−5.55178	−0.205060	−0.102530	−	0.994730i	$-0.532694\pi$
$733$	−5.55178	−0.205060	−0.102530	+	0.994730i	$0.532694\pi$
$734$	−34.1799	−1.26160
$735$	17.4089	0.642135
$736$	−30.1980	−1.11311
$737$	53.1363	1.95730
$738$	−10.4007	−0.382854
$739$	−35.1640	−1.29353	−0.646765	−	0.762689i	$-0.723879\pi$
$739$	−35.1640	−1.29353	−0.646765	+	0.762689i	$0.723879\pi$
$740$	219.027	8.05159
$741$	8.23153	0.302393
$742$	27.6079	1.01352
$743$	49.3711	1.81125	0.905625	−	0.424079i	$-0.139402\pi$
$743$	49.3711	1.81125	0.905625	+	0.424079i	$0.139402\pi$
$744$	45.0534	1.65174
$745$	−41.8529	−1.53337
$746$	−11.2242	−0.410946
$747$	2.12581	0.0777792
$748$	85.1862	3.11471
$749$	12.2168	0.446392
$750$	20.6456	0.753872
$751$	26.4065	0.963587	0.481793	−	0.876285i	$-0.339986\pi$
$751$	26.4065	0.963587	0.481793	+	0.876285i	$0.339986\pi$
$752$	30.2523	1.10319
$753$	−1.97792	−0.0720794
$754$	6.65859	0.242491
$755$	−49.1633	−1.78923
$756$	−8.26345	−0.300539
$757$	41.0628	1.49245	0.746227	−	0.665692i	$-0.231863\pi$
$757$	41.0628	1.49245	0.746227	+	0.665692i	$0.231863\pi$
$758$	−10.2618	−0.372726
$759$	−4.43439	−0.160958
$760$	−129.791	−4.70802
$761$	39.5526	1.43378	0.716890	−	0.697187i	$-0.245565\pi$
$761$	39.5526	1.43378	0.716890	+	0.697187i	$0.245565\pi$
$762$	−35.7103	−1.29365
$763$	10.8683	0.393458
$764$	−85.3135	−3.08653
$765$	11.4414	0.413665
$766$	35.1622	1.27046
$767$	−29.2244	−1.05523
$768$	109.267	3.94283
$769$	−9.25396	−0.333706	−0.166853	−	0.985982i	$-0.553361\pi$
$769$	−9.25396	−0.333706	−0.166853	+	0.985982i	$0.553361\pi$
$770$	61.1263	2.20284
$771$	−0.846927	−0.0305013
$772$	−101.152	−3.64055
$773$	−32.8456	−1.18137	−0.590687	−	0.806901i	$-0.701143\pi$
$773$	−32.8456	−1.18137	−0.590687	+	0.806901i	$0.701143\pi$
$774$	19.8327	0.712872
$775$	−29.7788	−1.06969
$776$	−132.890	−4.77047
$777$	15.2204	0.546030
$778$	−51.1878	−1.83517
$779$	−12.8576	−0.460671
$780$	48.3686	1.73187
$781$	−54.5978	−1.95366
$782$	9.20579	0.329198
$783$	1.00000	0.0357371
$784$	−92.3756	−3.29913
$785$	−44.4822	−1.58764
$786$	40.5031	1.44470
$787$	−25.5920	−0.912257	−0.456129	−	0.889914i	$-0.650764\pi$
$787$	−25.5920	−0.912257	−0.456129	+	0.889914i	$0.650764\pi$
$788$	12.3329	0.439340
$789$	0.347153	0.0123590
$790$	92.8169	3.30228
$791$	7.80158	0.277392
$792$	47.7513	1.69677
$793$	−12.4855	−0.443373
$794$	−25.2624	−0.896530
$795$	−24.2691	−0.860736
$796$	96.0359	3.40390
$797$	−11.2097	−0.397069	−0.198534	−	0.980094i	$-0.563618\pi$
$797$	−11.2097	−0.397069	−0.198534	+	0.980094i	$0.563618\pi$
$798$	−13.7112	−0.485370
$799$	−5.38315	−0.190442
$800$	−214.935	−7.59912
$801$	−11.0119	−0.389088
$802$	−18.6557	−0.658756
$803$	−38.5174	−1.35925
$804$	−70.0359	−2.46997
$805$	4.92160	0.173464
$806$	−27.8586	−0.981276
$807$	22.3131	0.785458
$808$	188.260	6.62297
$809$	8.56734	0.301212	0.150606	−	0.988594i	$-0.451878\pi$
$809$	8.56734	0.301212	0.150606	+	0.988594i	$0.451878\pi$
$810$	9.74980	0.342573
$811$	21.1612	0.743069	0.371535	−	0.928419i	$-0.378832\pi$
$811$	21.1612	0.743069	0.371535	+	0.928419i	$0.378832\pi$
$812$	−8.26345	−0.289990
$813$	−21.0578	−0.738528
$814$	−133.706	−4.68638
$815$	−62.7428	−2.19778
$816$	−60.7109	−2.12531
$817$	24.5177	0.857767
$818$	−11.0710	−0.387090
$819$	3.36119	0.117449
$820$	−75.5514	−2.63837
$821$	−11.7177	−0.408950	−0.204475	−	0.978872i	$-0.565549\pi$
$821$	−11.7177	−0.408950	−0.204475	+	0.978872i	$0.565549\pi$
$822$	−26.2363	−0.915096
$823$	−3.38360	−0.117945	−0.0589724	−	0.998260i	$-0.518782\pi$
$823$	−3.38360	−0.117945	−0.0589724	+	0.998260i	$0.518782\pi$
$824$	108.417	3.77690
$825$	−31.5620	−1.09885
$826$	48.6787	1.69375
$827$	10.4103	0.362003	0.181001	−	0.983483i	$-0.442066\pi$
$827$	10.4103	0.362003	0.181001	+	0.983483i	$0.442066\pi$
$828$	5.84471	0.203118
$829$	−14.8931	−0.517259	−0.258630	−	0.965977i	$-0.583271\pi$
$829$	−14.8931	−0.517259	−0.258630	+	0.965977i	$0.583271\pi$
$830$	20.7262	0.719417
$831$	2.42766	0.0842146
$832$	−113.251	−3.92627
$833$	16.4375	0.569525
$834$	20.1061	0.696217
$835$	−21.7355	−0.752187
$836$	89.7394	3.10370
$837$	−4.18385	−0.144615
$838$	−12.3529	−0.426725
$839$	−35.8545	−1.23784	−0.618918	−	0.785456i	$-0.712429\pi$
$839$	−35.8545	−1.23784	−0.618918	+	0.785456i	$0.712429\pi$
$840$	−52.9978	−1.82860
$841$	1.00000	0.0344828
$842$	−41.6932	−1.43684
$843$	11.6621	0.401664
$844$	29.4184	1.01262
$845$	25.5793	0.879953
$846$	−4.58725	−0.157713
$847$	−12.2492	−0.420888
$848$	128.778	4.42224
$849$	−7.95812	−0.273122
$850$	65.5226	2.24741
$851$	−10.7653	−0.369031
$852$	71.9621	2.46538
$853$	11.4424	0.391779	0.195890	−	0.980626i	$-0.437241\pi$
$853$	11.4424	0.391779	0.195890	+	0.980626i	$0.437241\pi$
$854$	20.7970	0.711657
$855$	12.0530	0.412203
$856$	93.0486	3.18034
$857$	−34.4455	−1.17664	−0.588319	−	0.808629i	$-0.700210\pi$
$857$	−34.4455	−1.17664	−0.588319	+	0.808629i	$0.700210\pi$
$858$	−29.5268	−1.00803
$859$	−2.68062	−0.0914617	−0.0457308	−	0.998954i	$-0.514562\pi$
$859$	−2.68062	−0.0914617	−0.0457308	+	0.998954i	$0.514562\pi$
$860$	144.067	4.91263
$861$	−5.25015	−0.178925
$862$	7.29125	0.248341
$863$	40.5322	1.37973	0.689866	−	0.723937i	$-0.257670\pi$
$863$	40.5322	1.37973	0.689866	+	0.723937i	$0.257670\pi$
$864$	−30.1980	−1.02736
$865$	74.6417	2.53789
$866$	−16.6172	−0.564677
$867$	−6.19698	−0.210460
$868$	34.5731	1.17349
$869$	−42.2148	−1.43204
$870$	9.74980	0.330549
$871$	28.4873	0.965256
$872$	82.7776	2.80320
$873$	12.3407	0.417670
$874$	9.69784	0.328034
$875$	10.4217	0.352318
$876$	50.7675	1.71527
$877$	26.5521	0.896600	0.448300	−	0.893883i	$-0.352030\pi$
$877$	26.5521	0.896600	0.448300	+	0.893883i	$0.352030\pi$
$878$	23.7743	0.802344
$879$	−25.6929	−0.866599
$880$	285.125	9.61157
$881$	2.87095	0.0967248	0.0483624	−	0.998830i	$-0.484600\pi$
$881$	2.87095	0.0967248	0.0483624	+	0.998830i	$0.484600\pi$
$882$	14.0072	0.471647
$883$	28.0387	0.943578	0.471789	−	0.881711i	$-0.343608\pi$
$883$	28.0387	0.943578	0.471789	+	0.881711i	$0.343608\pi$
$884$	45.6698	1.53604
$885$	−42.7917	−1.43843
$886$	59.5290	1.99992
$887$	17.7793	0.596972	0.298486	−	0.954414i	$-0.403518\pi$
$887$	17.7793	0.596972	0.298486	+	0.954414i	$0.403518\pi$
$888$	115.926	3.89021
$889$	−18.0262	−0.604580
$890$	−107.364	−3.59886
$891$	−4.43439	−0.148558
$892$	−27.7323	−0.928544
$893$	−5.67089	−0.189769
$894$	−33.6749	−1.12626
$895$	−69.1718	−2.31216
$896$	103.251	3.44936
$897$	−2.37735	−0.0793775
$898$	30.3355	1.01231
$899$	−4.18385	−0.139539
$900$	41.6000	1.38667
$901$	−22.9149	−0.763407
$902$	46.1206	1.53565
$903$	10.0114	0.333157
$904$	59.4203	1.97629
$905$	0.494446	0.0164360
$906$	−39.5568	−1.31419
$907$	48.0328	1.59490	0.797451	−	0.603383i	$-0.206181\pi$
$907$	48.0328	1.59490	0.797451	+	0.603383i	$0.206181\pi$
$908$	−93.1725	−3.09204
$909$	−17.4826	−0.579862
$910$	32.7709	1.08634
$911$	36.9017	1.22261	0.611304	−	0.791396i	$-0.290645\pi$
$911$	36.9017	1.22261	0.611304	+	0.791396i	$0.290645\pi$
$912$	−63.9560	−2.11779
$913$	−9.42666	−0.311977
$914$	−6.30023	−0.208393
$915$	−18.2818	−0.604379
$916$	143.816	4.75181
$917$	20.4456	0.675172
$918$	9.20579	0.303836
$919$	−9.31252	−0.307192	−0.153596	−	0.988134i	$-0.549085\pi$
$919$	−9.31252	−0.307192	−0.153596	+	0.988134i	$0.549085\pi$
$920$	37.4851	1.23585
$921$	18.5614	0.611620
$922$	−7.04781	−0.232107
$923$	−29.2708	−0.963460
$924$	36.6434	1.20548
$925$	−76.6228	−2.51934
$926$	42.6293	1.40088
$927$	−10.0681	−0.330680
$928$	−30.1980	−0.991297
$929$	−30.7813	−1.00990	−0.504951	−	0.863148i	$-0.668489\pi$
$929$	−30.7813	−1.00990	−0.504951	+	0.863148i	$0.668489\pi$
$930$	−40.7917	−1.33761
$931$	17.3161	0.567512
$932$	−20.0526	−0.656844
$933$	9.91454	0.324587
$934$	17.0478	0.557820
$935$	−50.7357	−1.65924
$936$	25.6003	0.836772
$937$	40.1120	1.31040	0.655202	−	0.755454i	$-0.272584\pi$
$937$	40.1120	1.31040	0.655202	+	0.755454i	$0.272584\pi$
$938$	−47.4510	−1.54933
$939$	15.3040	0.499426
$940$	−33.3222	−1.08685
$941$	−47.6356	−1.55287	−0.776437	−	0.630194i	$-0.782975\pi$
$941$	−47.6356	−1.55287	−0.776437	+	0.630194i	$0.782975\pi$
$942$	−35.7905	−1.16612
$943$	3.71341	0.120925
$944$	227.063	7.39027
$945$	4.92160	0.160100
$946$	−87.9460	−2.85937
$947$	36.9283	1.20001	0.600004	−	0.799997i	$-0.295166\pi$
$947$	36.9283	1.20001	0.600004	+	0.799997i	$0.295166\pi$
$948$	55.6409	1.80713
$949$	−20.6498	−0.670322
$950$	69.0248	2.23946
$951$	17.3563	0.562818
$952$	−50.0406	−1.62183
$953$	9.59892	0.310939	0.155470	−	0.987841i	$-0.450311\pi$
$953$	9.59892	0.310939	0.155470	+	0.987841i	$0.450311\pi$
$954$	−19.5270	−0.632208
$955$	50.8115	1.64422
$956$	33.7035	1.09005
$957$	−4.43439	−0.143343
$958$	8.17762	0.264207
$959$	−13.2438	−0.427665
$960$	−165.827	−5.35204
$961$	−13.4954	−0.435334
$962$	−71.6819	−2.31112
$963$	−8.64089	−0.278449
$964$	115.949	3.73446
$965$	60.2450	1.93935
$966$	3.95993	0.127409
$967$	−31.4665	−1.01190	−0.505948	−	0.862564i	$-0.668857\pi$
$967$	−31.4665	−1.01190	−0.505948	+	0.862564i	$0.668857\pi$
$968$	−93.2954	−2.99863
$969$	11.3804	0.365593
$970$	120.320	3.86323
$971$	31.9428	1.02509	0.512547	−	0.858659i	$-0.328702\pi$
$971$	31.9428	1.02509	0.512547	+	0.858659i	$0.328702\pi$
$972$	5.84471	0.187469
$973$	10.1493	0.325373
$974$	−98.9314	−3.16997
$975$	−16.9209	−0.541903
$976$	97.0078	3.10515
$977$	−18.8977	−0.604592	−0.302296	−	0.953214i	$-0.597753\pi$
$977$	−18.8977	−0.604592	−0.302296	+	0.953214i	$0.597753\pi$
$978$	−50.4830	−1.61427
$979$	48.8313	1.56065
$980$	101.750	3.25027
$981$	−7.68708	−0.245430
$982$	14.3482	0.457871
$983$	9.51432	0.303460	0.151730	−	0.988422i	$-0.451516\pi$
$983$	9.51432	0.303460	0.151730	+	0.988422i	$0.451516\pi$
$984$	−39.9875	−1.27475
$985$	−7.34528	−0.234040
$986$	9.20579	0.293172
$987$	−2.31560	−0.0737063
$988$	48.1109	1.53061
$989$	−7.08099	−0.225162
$990$	−43.2344	−1.37408
$991$	37.2984	1.18482	0.592412	−	0.805635i	$-0.298176\pi$
$991$	37.2984	1.18482	0.592412	+	0.805635i	$0.298176\pi$
$992$	126.344	4.01143
$993$	−25.6184	−0.812974
$994$	48.7560	1.54645
$995$	−57.1977	−1.81329
$996$	12.4247	0.393692
$997$	−5.35625	−0.169634	−0.0848171	−	0.996397i	$-0.527031\pi$
$997$	−5.35625	−0.169634	−0.0848171	+	0.996397i	$0.527031\pi$
$998$	−23.2537	−0.736082
$999$	−10.7653	−0.340600

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.o.1.1	✓	20
3.2	odd	2		6003.2.a.s.1.20		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.o.1.1	✓	20	1.1	even	1	trivial
6003.2.a.s.1.20		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)

\(f(q)\)	\(=\)	\(q-2.80084 q^{2} +1.00000 q^{3} +5.84471 q^{4} -3.48103 q^{5} -2.80084 q^{6} -1.41384 q^{7} -10.7684 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.80084 q^{2} +1.00000 q^{3} +5.84471 q^{4} -3.48103 q^{5} -2.80084 q^{6} -1.41384 q^{7} -10.7684 q^{8} +1.00000 q^{9} +9.74980 q^{10} -4.43439 q^{11} +5.84471 q^{12} -2.37735 q^{13} +3.95993 q^{14} -3.48103 q^{15} +18.4712 q^{16} -3.28679 q^{17} -2.80084 q^{18} -3.46248 q^{19} -20.3456 q^{20} -1.41384 q^{21} +12.4200 q^{22} +1.00000 q^{23} -10.7684 q^{24} +7.11755 q^{25} +6.65859 q^{26} +1.00000 q^{27} -8.26345 q^{28} +1.00000 q^{29} +9.74980 q^{30} -4.18385 q^{31} -30.1980 q^{32} -4.43439 q^{33} +9.20579 q^{34} +4.92160 q^{35} +5.84471 q^{36} -10.7653 q^{37} +9.69784 q^{38} -2.37735 q^{39} +37.4851 q^{40} +3.71341 q^{41} +3.95993 q^{42} -7.08099 q^{43} -25.9177 q^{44} -3.48103 q^{45} -2.80084 q^{46} +1.63781 q^{47} +18.4712 q^{48} -5.00107 q^{49} -19.9351 q^{50} -3.28679 q^{51} -13.8949 q^{52} +6.97182 q^{53} -2.80084 q^{54} +15.4362 q^{55} +15.2248 q^{56} -3.46248 q^{57} -2.80084 q^{58} +12.2928 q^{59} -20.3456 q^{60} +5.25185 q^{61} +11.7183 q^{62} -1.41384 q^{63} +47.6374 q^{64} +8.27563 q^{65} +12.4200 q^{66} -11.9828 q^{67} -19.2103 q^{68} +1.00000 q^{69} -13.7846 q^{70} +12.3124 q^{71} -10.7684 q^{72} +8.68606 q^{73} +30.1520 q^{74} +7.11755 q^{75} -20.2372 q^{76} +6.26950 q^{77} +6.65859 q^{78} +9.51988 q^{79} -64.2986 q^{80} +1.00000 q^{81} -10.4007 q^{82} +2.12581 q^{83} -8.26345 q^{84} +11.4414 q^{85} +19.8327 q^{86} +1.00000 q^{87} +47.7513 q^{88} -11.0119 q^{89} +9.74980 q^{90} +3.36119 q^{91} +5.84471 q^{92} -4.18385 q^{93} -4.58725 q^{94} +12.0530 q^{95} -30.1980 q^{96} +12.3407 q^{97} +14.0072 q^{98} -4.43439 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9}+O(q^{10}) \) 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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