LMFDB - Embedded newform 2001.2.a.o.1.18

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			1.18
Root			$2.45061$ 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)

$f(q)$	$=$	$q+2.45061 q^{2} +1.00000 q^{3} +4.00547 q^{4} +1.21123 q^{5} +2.45061 q^{6} +0.971463 q^{7} +4.91461 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.45061 q^{2} +1.00000 q^{3} +4.00547 q^{4} +1.21123 q^{5} +2.45061 q^{6} +0.971463 q^{7} +4.91461 q^{8} +1.00000 q^{9} +2.96824 q^{10} +3.60961 q^{11} +4.00547 q^{12} -6.61576 q^{13} +2.38067 q^{14} +1.21123 q^{15} +4.03285 q^{16} +4.82230 q^{17} +2.45061 q^{18} -2.80468 q^{19} +4.85154 q^{20} +0.971463 q^{21} +8.84573 q^{22} +1.00000 q^{23} +4.91461 q^{24} -3.53293 q^{25} -16.2126 q^{26} +1.00000 q^{27} +3.89117 q^{28} +1.00000 q^{29} +2.96824 q^{30} -0.879818 q^{31} +0.0536852 q^{32} +3.60961 q^{33} +11.8176 q^{34} +1.17666 q^{35} +4.00547 q^{36} -3.58964 q^{37} -6.87317 q^{38} -6.61576 q^{39} +5.95272 q^{40} +11.8028 q^{41} +2.38067 q^{42} -11.1806 q^{43} +14.4582 q^{44} +1.21123 q^{45} +2.45061 q^{46} +1.54804 q^{47} +4.03285 q^{48} -6.05626 q^{49} -8.65781 q^{50} +4.82230 q^{51} -26.4992 q^{52} +2.24340 q^{53} +2.45061 q^{54} +4.37206 q^{55} +4.77437 q^{56} -2.80468 q^{57} +2.45061 q^{58} +0.111475 q^{59} +4.85154 q^{60} -7.12252 q^{61} -2.15609 q^{62} +0.971463 q^{63} -7.93413 q^{64} -8.01320 q^{65} +8.84573 q^{66} +6.15784 q^{67} +19.3156 q^{68} +1.00000 q^{69} +2.88354 q^{70} +2.74676 q^{71} +4.91461 q^{72} +4.91369 q^{73} -8.79680 q^{74} -3.53293 q^{75} -11.2341 q^{76} +3.50660 q^{77} -16.2126 q^{78} +5.76461 q^{79} +4.88470 q^{80} +1.00000 q^{81} +28.9240 q^{82} -11.4558 q^{83} +3.89117 q^{84} +5.84090 q^{85} -27.3993 q^{86} +1.00000 q^{87} +17.7398 q^{88} +3.39528 q^{89} +2.96824 q^{90} -6.42697 q^{91} +4.00547 q^{92} -0.879818 q^{93} +3.79364 q^{94} -3.39711 q^{95} +0.0536852 q^{96} -7.46502 q^{97} -14.8415 q^{98} +3.60961 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.45061	1.73284	0.866420	−	0.499316i	$-0.166415\pi$
$2$	2.45061	1.73284	0.866420	+	0.499316i	$0.166415\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.00547	2.00273
$5$	1.21123	0.541678	0.270839	−	0.962625i	$-0.412699\pi$
$5$	1.21123	0.541678	0.270839	+	0.962625i	$0.412699\pi$
$6$	2.45061	1.00046
$7$	0.971463	0.367179	0.183589	−	0.983003i	$-0.441228\pi$
$7$	0.971463	0.367179	0.183589	+	0.983003i	$0.441228\pi$
$8$	4.91461	1.73758
$9$	1.00000	0.333333
$10$	2.96824	0.938641
$11$	3.60961	1.08834	0.544169	−	0.838975i	$-0.316845\pi$
$11$	3.60961	1.08834	0.544169	+	0.838975i	$0.316845\pi$
$12$	4.00547	1.15628
$13$	−6.61576	−1.83488	−0.917441	−	0.397872i	$-0.869749\pi$
$13$	−6.61576	−1.83488	−0.917441	+	0.397872i	$0.869749\pi$
$14$	2.38067	0.636262
$15$	1.21123	0.312738
$16$	4.03285	1.00821
$17$	4.82230	1.16958	0.584790	−	0.811185i	$-0.301177\pi$
$17$	4.82230	1.16958	0.584790	+	0.811185i	$0.301177\pi$
$18$	2.45061	0.577613
$19$	−2.80468	−0.643438	−0.321719	−	0.946835i	$-0.604261\pi$
$19$	−2.80468	−0.643438	−0.321719	+	0.946835i	$0.604261\pi$
$20$	4.85154	1.08484
$21$	0.971463	0.211991
$22$	8.84573	1.88592
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	4.91461	1.00319
$25$	−3.53293	−0.706585
$26$	−16.2126	−3.17956
$27$	1.00000	0.192450
$28$	3.89117	0.735361
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	2.96824	0.541925
$31$	−0.879818	−0.158020	−0.0790100	−	0.996874i	$-0.525176\pi$
$31$	−0.879818	−0.158020	−0.0790100	+	0.996874i	$0.525176\pi$
$32$	0.0536852	0.00949030
$33$	3.60961	0.628353
$34$	11.8176	2.02669
$35$	1.17666	0.198893
$36$	4.00547	0.667578
$37$	−3.58964	−0.590133	−0.295067	−	0.955477i	$-0.595342\pi$
$37$	−3.58964	−0.590133	−0.295067	+	0.955477i	$0.595342\pi$
$38$	−6.87317	−1.11498
$39$	−6.61576	−1.05937
$40$	5.95272	0.941208
$41$	11.8028	1.84329	0.921643	−	0.388038i	$-0.126847\pi$
$41$	11.8028	1.84329	0.921643	+	0.388038i	$0.126847\pi$
$42$	2.38067	0.367346
$43$	−11.1806	−1.70503	−0.852514	−	0.522704i	$-0.824923\pi$
$43$	−11.1806	−1.70503	−0.852514	+	0.522704i	$0.824923\pi$
$44$	14.4582	2.17965
$45$	1.21123	0.180559
$46$	2.45061	0.361322
$47$	1.54804	0.225805	0.112903	−	0.993606i	$-0.463985\pi$
$47$	1.54804	0.225805	0.112903	+	0.993606i	$0.463985\pi$
$48$	4.03285	0.582091
$49$	−6.05626	−0.865180
$50$	−8.65781	−1.22440
$51$	4.82230	0.675257
$52$	−26.4992	−3.67478
$53$	2.24340	0.308155	0.154078	−	0.988059i	$-0.450759\pi$
$53$	2.24340	0.308155	0.154078	+	0.988059i	$0.450759\pi$
$54$	2.45061	0.333485
$55$	4.37206	0.589529
$56$	4.77437	0.638002
$57$	−2.80468	−0.371489
$58$	2.45061	0.321780
$59$	0.111475	0.0145129	0.00725643	−	0.999974i	$-0.497690\pi$
$59$	0.111475	0.0145129	0.00725643	+	0.999974i	$0.497690\pi$
$60$	4.85154	0.626331
$61$	−7.12252	−0.911945	−0.455973	−	0.889994i	$-0.650709\pi$
$61$	−7.12252	−0.911945	−0.455973	+	0.889994i	$0.650709\pi$
$62$	−2.15609	−0.273823
$63$	0.971463	0.122393
$64$	−7.93413	−0.991766
$65$	−8.01320	−0.993915
$66$	8.84573	1.08883
$67$	6.15784	0.752300	0.376150	−	0.926559i	$-0.377248\pi$
$67$	6.15784	0.752300	0.376150	+	0.926559i	$0.377248\pi$
$68$	19.3156	2.34236
$69$	1.00000	0.120386
$70$	2.88354	0.344649
$71$	2.74676	0.325980	0.162990	−	0.986628i	$-0.447886\pi$
$71$	2.74676	0.325980	0.162990	+	0.986628i	$0.447886\pi$
$72$	4.91461	0.579193
$73$	4.91369	0.575104	0.287552	−	0.957765i	$-0.407159\pi$
$73$	4.91369	0.575104	0.287552	+	0.957765i	$0.407159\pi$
$74$	−8.79680	−1.02261
$75$	−3.53293	−0.407947
$76$	−11.2341	−1.28864
$77$	3.50660	0.399615
$78$	−16.2126	−1.83572
$79$	5.76461	0.648569	0.324285	−	0.945960i	$-0.394876\pi$
$79$	5.76461	0.648569	0.324285	+	0.945960i	$0.394876\pi$
$80$	4.88470	0.546126
$81$	1.00000	0.111111
$82$	28.9240	3.19412
$83$	−11.4558	−1.25743	−0.628717	−	0.777634i	$-0.716420\pi$
$83$	−11.4558	−1.25743	−0.628717	+	0.777634i	$0.716420\pi$
$84$	3.89117	0.424561
$85$	5.84090	0.633535
$86$	−27.3993	−2.95454
$87$	1.00000	0.107211
$88$	17.7398	1.89107
$89$	3.39528	0.359899	0.179949	−	0.983676i	$-0.442407\pi$
$89$	3.39528	0.359899	0.179949	+	0.983676i	$0.442407\pi$
$90$	2.96824	0.312880
$91$	−6.42697	−0.673729
$92$	4.00547	0.417599
$93$	−0.879818	−0.0912329
$94$	3.79364	0.391284
$95$	−3.39711	−0.348536
$96$	0.0536852	0.00547923
$97$	−7.46502	−0.757958	−0.378979	−	0.925405i	$-0.623725\pi$
$97$	−7.46502	−0.757958	−0.378979	+	0.925405i	$0.623725\pi$
$98$	−14.8415	−1.49922
$99$	3.60961	0.362780
$100$	−14.1510	−1.41510
$101$	0.796755	0.0792801	0.0396400	−	0.999214i	$-0.487379\pi$
$101$	0.796755	0.0792801	0.0396400	+	0.999214i	$0.487379\pi$
$102$	11.8176	1.17011
$103$	−0.447276	−0.0440714	−0.0220357	−	0.999757i	$-0.507015\pi$
$103$	−0.447276	−0.0440714	−0.0220357	+	0.999757i	$0.507015\pi$
$104$	−32.5139	−3.18825
$105$	1.17666	0.114831
$106$	5.49770	0.533984
$107$	−12.7827	−1.23575	−0.617874	−	0.786277i	$-0.712006\pi$
$107$	−12.7827	−1.23575	−0.617874	+	0.786277i	$0.712006\pi$
$108$	4.00547	0.385426
$109$	7.60998	0.728904	0.364452	−	0.931222i	$-0.381256\pi$
$109$	7.60998	0.728904	0.364452	+	0.931222i	$0.381256\pi$
$110$	10.7142	1.02156
$111$	−3.58964	−0.340714
$112$	3.91776	0.370194
$113$	−7.01294	−0.659722	−0.329861	−	0.944030i	$-0.607002\pi$
$113$	−7.01294	−0.659722	−0.329861	+	0.944030i	$0.607002\pi$
$114$	−6.87317	−0.643731
$115$	1.21123	0.112948
$116$	4.00547	0.371898
$117$	−6.61576	−0.611627
$118$	0.273182	0.0251485
$119$	4.68469	0.429444
$120$	5.95272	0.543407
$121$	2.02929	0.184481
$122$	−17.4545	−1.58026
$123$	11.8028	1.06422
$124$	−3.52408	−0.316472
$125$	−10.3353	−0.924419
$126$	2.38067	0.212087
$127$	16.0903	1.42778	0.713890	−	0.700258i	$-0.246932\pi$
$127$	16.0903	1.42778	0.713890	+	0.700258i	$0.246932\pi$
$128$	−19.5508	−1.72806
$129$	−11.1806	−0.984398
$130$	−19.6372	−1.72229
$131$	4.15912	0.363384	0.181692	−	0.983356i	$-0.441843\pi$
$131$	4.15912	0.363384	0.181692	+	0.983356i	$0.441843\pi$
$132$	14.4582	1.25842
$133$	−2.72465	−0.236257
$134$	15.0904	1.30362
$135$	1.21123	0.104246
$136$	23.6997	2.03224
$137$	9.02194	0.770797	0.385398	−	0.922750i	$-0.374064\pi$
$137$	9.02194	0.770797	0.385398	+	0.922750i	$0.374064\pi$
$138$	2.45061	0.208609
$139$	−2.93235	−0.248719	−0.124359	−	0.992237i	$-0.539688\pi$
$139$	−2.93235	−0.248719	−0.124359	+	0.992237i	$0.539688\pi$
$140$	4.71309	0.398329
$141$	1.54804	0.130369
$142$	6.73123	0.564872
$143$	−23.8803	−1.99697
$144$	4.03285	0.336070
$145$	1.21123	0.100587
$146$	12.0415	0.996562
$147$	−6.05626	−0.499512
$148$	−14.3782	−1.18188
$149$	18.6407	1.52711	0.763555	−	0.645743i	$-0.223452\pi$
$149$	18.6407	1.52711	0.763555	+	0.645743i	$0.223452\pi$
$150$	−8.65781	−0.706907
$151$	9.71968	0.790976	0.395488	−	0.918471i	$-0.370575\pi$
$151$	9.71968	0.790976	0.395488	+	0.918471i	$0.370575\pi$
$152$	−13.7839	−1.11802
$153$	4.82230	0.389860
$154$	8.59331	0.692468
$155$	−1.06566	−0.0855959
$156$	−26.4992	−2.12164
$157$	7.71197	0.615482	0.307741	−	0.951470i	$-0.400427\pi$
$157$	7.71197	0.615482	0.307741	+	0.951470i	$0.400427\pi$
$158$	14.1268	1.12387
$159$	2.24340	0.177914
$160$	0.0650251	0.00514068
$161$	0.971463	0.0765620
$162$	2.45061	0.192538
$163$	−11.9063	−0.932573	−0.466287	−	0.884634i	$-0.654408\pi$
$163$	−11.9063	−0.932573	−0.466287	+	0.884634i	$0.654408\pi$
$164$	47.2757	3.69161
$165$	4.37206	0.340365
$166$	−28.0736	−2.17893
$167$	5.87801	0.454854	0.227427	−	0.973795i	$-0.426969\pi$
$167$	5.87801	0.454854	0.227427	+	0.973795i	$0.426969\pi$
$168$	4.77437	0.368351
$169$	30.7683	2.36679
$170$	14.3138	1.09781
$171$	−2.80468	−0.214479
$172$	−44.7836	−3.41472
$173$	−8.58330	−0.652576	−0.326288	−	0.945270i	$-0.605798\pi$
$173$	−8.58330	−0.652576	−0.326288	+	0.945270i	$0.605798\pi$
$174$	2.45061	0.185780
$175$	−3.43211	−0.259443
$176$	14.5570	1.09728
$177$	0.111475	0.00837900
$178$	8.32049	0.623647
$179$	−18.7522	−1.40161	−0.700804	−	0.713354i	$-0.747175\pi$
$179$	−18.7522	−1.40161	−0.700804	+	0.713354i	$0.747175\pi$
$180$	4.85154	0.361612
$181$	−17.2713	−1.28377	−0.641883	−	0.766802i	$-0.721847\pi$
$181$	−17.2713	−1.28377	−0.641883	+	0.766802i	$0.721847\pi$
$182$	−15.7500	−1.16747
$183$	−7.12252	−0.526512
$184$	4.91461	0.362310
$185$	−4.34787	−0.319662
$186$	−2.15609	−0.158092
$187$	17.4066	1.27290
$188$	6.20064	0.452228
$189$	0.971463	0.0706636
$190$	−8.32498	−0.603957
$191$	10.8221	0.783063	0.391532	−	0.920165i	$-0.371945\pi$
$191$	10.8221	0.783063	0.391532	+	0.920165i	$0.371945\pi$
$192$	−7.93413	−0.572596
$193$	−10.0276	−0.721800	−0.360900	−	0.932605i	$-0.617530\pi$
$193$	−10.0276	−0.721800	−0.360900	+	0.932605i	$0.617530\pi$
$194$	−18.2938	−1.31342
$195$	−8.01320	−0.573837
$196$	−24.2582	−1.73273
$197$	19.2703	1.37295	0.686476	−	0.727152i	$-0.259157\pi$
$197$	19.2703	1.37295	0.686476	+	0.727152i	$0.259157\pi$
$198$	8.84573	0.628639
$199$	−26.3709	−1.86938	−0.934691	−	0.355461i	$-0.884324\pi$
$199$	−26.3709	−1.86938	−0.934691	+	0.355461i	$0.884324\pi$
$200$	−17.3630	−1.22775
$201$	6.15784	0.434341
$202$	1.95253	0.137380
$203$	0.971463	0.0681834
$204$	19.3156	1.35236
$205$	14.2959	0.998468
$206$	−1.09610	−0.0763687
$207$	1.00000	0.0695048
$208$	−26.6803	−1.84995
$209$	−10.1238	−0.700278
$210$	2.88354	0.198983
$211$	8.00666	0.551201	0.275600	−	0.961272i	$-0.411123\pi$
$211$	8.00666	0.551201	0.275600	+	0.961272i	$0.411123\pi$
$212$	8.98589	0.617153
$213$	2.74676	0.188205
$214$	−31.3253	−2.14135
$215$	−13.5423	−0.923576
$216$	4.91461	0.334397
$217$	−0.854711	−0.0580216
$218$	18.6491	1.26307
$219$	4.91369	0.332036
$220$	17.5122	1.18067
$221$	−31.9032	−2.14604
$222$	−8.79680	−0.590402
$223$	−2.92914	−0.196150	−0.0980748	−	0.995179i	$-0.531268\pi$
$223$	−2.92914	−0.196150	−0.0980748	+	0.995179i	$0.531268\pi$
$224$	0.0521532	0.00348463
$225$	−3.53293	−0.235528
$226$	−17.1860	−1.14319
$227$	−14.9020	−0.989078	−0.494539	−	0.869156i	$-0.664663\pi$
$227$	−14.9020	−0.989078	−0.494539	+	0.869156i	$0.664663\pi$
$228$	−11.2341	−0.743994
$229$	11.0974	0.733339	0.366670	−	0.930351i	$-0.380498\pi$
$229$	11.0974	0.733339	0.366670	+	0.930351i	$0.380498\pi$
$230$	2.96824	0.195720
$231$	3.50660	0.230718
$232$	4.91461	0.322660
$233$	11.2169	0.734845	0.367423	−	0.930054i	$-0.380240\pi$
$233$	11.2169	0.734845	0.367423	+	0.930054i	$0.380240\pi$
$234$	−16.2126	−1.05985
$235$	1.87503	0.122314
$236$	0.446511	0.0290654
$237$	5.76461	0.374452
$238$	11.4803	0.744159
$239$	18.4791	1.19531	0.597655	−	0.801753i	$-0.296099\pi$
$239$	18.4791	1.19531	0.597655	+	0.801753i	$0.296099\pi$
$240$	4.88470	0.315306
$241$	−7.35820	−0.473984	−0.236992	−	0.971512i	$-0.576161\pi$
$241$	−7.35820	−0.473984	−0.236992	+	0.971512i	$0.576161\pi$
$242$	4.97299	0.319676
$243$	1.00000	0.0641500
$244$	−28.5290	−1.82638
$245$	−7.33551	−0.468649
$246$	28.9240	1.84413
$247$	18.5551	1.18063
$248$	−4.32397	−0.274572
$249$	−11.4558	−0.725980
$250$	−25.3278	−1.60187
$251$	−22.0099	−1.38925	−0.694627	−	0.719370i	$-0.744430\pi$
$251$	−22.0099	−1.38925	−0.694627	+	0.719370i	$0.744430\pi$
$252$	3.89117	0.245120
$253$	3.60961	0.226934
$254$	39.4309	2.47411
$255$	5.84090	0.365772
$256$	−32.0430	−2.00269
$257$	−13.2471	−0.826328	−0.413164	−	0.910657i	$-0.635576\pi$
$257$	−13.2471	−0.826328	−0.413164	+	0.910657i	$0.635576\pi$
$258$	−27.3993	−1.70580
$259$	−3.48720	−0.216684
$260$	−32.0966	−1.99055
$261$	1.00000	0.0618984
$262$	10.1924	0.629686
$263$	11.0930	0.684026	0.342013	−	0.939695i	$-0.388891\pi$
$263$	11.0930	0.684026	0.342013	+	0.939695i	$0.388891\pi$
$264$	17.7398	1.09181
$265$	2.71727	0.166921
$266$	−6.67703	−0.409395
$267$	3.39528	0.207788
$268$	24.6650	1.50666
$269$	−15.7762	−0.961894	−0.480947	−	0.876750i	$-0.659707\pi$
$269$	−15.7762	−0.961894	−0.480947	+	0.876750i	$0.659707\pi$
$270$	2.96824	0.180642
$271$	−4.31111	−0.261881	−0.130941	−	0.991390i	$-0.541800\pi$
$271$	−4.31111	−0.261881	−0.130941	+	0.991390i	$0.541800\pi$
$272$	19.4476	1.17918
$273$	−6.42697	−0.388978
$274$	22.1092	1.33567
$275$	−12.7525	−0.769004
$276$	4.00547	0.241101
$277$	0.634824	0.0381429	0.0190714	−	0.999818i	$-0.493929\pi$
$277$	0.634824	0.0381429	0.0190714	+	0.999818i	$0.493929\pi$
$278$	−7.18604	−0.430990
$279$	−0.879818	−0.0526733
$280$	5.78285	0.345591
$281$	27.9614	1.66804	0.834018	−	0.551738i	$-0.186035\pi$
$281$	27.9614	1.66804	0.834018	+	0.551738i	$0.186035\pi$
$282$	3.79364	0.225908
$283$	−18.1799	−1.08068	−0.540340	−	0.841447i	$-0.681704\pi$
$283$	−18.1799	−1.08068	−0.540340	+	0.841447i	$0.681704\pi$
$284$	11.0021	0.652852
$285$	−3.39711	−0.201227
$286$	−58.5212	−3.46043
$287$	11.4660	0.676816
$288$	0.0536852	0.00316343
$289$	6.25456	0.367915
$290$	2.96824	0.174301
$291$	−7.46502	−0.437607
$292$	19.6816	1.15178
$293$	−8.26939	−0.483103	−0.241551	−	0.970388i	$-0.577656\pi$
$293$	−8.26939	−0.483103	−0.241551	+	0.970388i	$0.577656\pi$
$294$	−14.8415	−0.865574
$295$	0.135022	0.00786129
$296$	−17.6417	−1.02540
$297$	3.60961	0.209451
$298$	45.6811	2.64624
$299$	−6.61576	−0.382599
$300$	−14.1510	−0.817010
$301$	−10.8616	−0.626050
$302$	23.8191	1.37064
$303$	0.796755	0.0457724
$304$	−11.3108	−0.648722
$305$	−8.62700	−0.493981
$306$	11.8176	0.675564
$307$	21.5875	1.23207	0.616033	−	0.787721i	$-0.288739\pi$
$307$	21.5875	1.23207	0.616033	+	0.787721i	$0.288739\pi$
$308$	14.0456	0.800322
$309$	−0.447276	−0.0254446
$310$	−2.61151	−0.148324
$311$	29.4192	1.66821	0.834104	−	0.551607i	$-0.185985\pi$
$311$	29.4192	1.66821	0.834104	+	0.551607i	$0.185985\pi$
$312$	−32.5139	−1.84074
$313$	11.2268	0.634574	0.317287	−	0.948329i	$-0.397228\pi$
$313$	11.2268	0.634574	0.317287	+	0.948329i	$0.397228\pi$
$314$	18.8990	1.06653
$315$	1.17666	0.0662975
$316$	23.0900	1.29891
$317$	31.0877	1.74606	0.873030	−	0.487666i	$-0.162152\pi$
$317$	31.0877	1.74606	0.873030	+	0.487666i	$0.162152\pi$
$318$	5.49770	0.308296
$319$	3.60961	0.202099
$320$	−9.61004	−0.537218
$321$	−12.7827	−0.713460
$322$	2.38067	0.132670
$323$	−13.5250	−0.752552
$324$	4.00547	0.222526
$325$	23.3730	1.29650
$326$	−29.1776	−1.61600
$327$	7.60998	0.420833
$328$	58.0062	3.20286
$329$	1.50387	0.0829108
$330$	10.7142	0.589797
$331$	19.1328	1.05164	0.525818	−	0.850597i	$-0.323759\pi$
$331$	19.1328	1.05164	0.525818	+	0.850597i	$0.323759\pi$
$332$	−45.8858	−2.51831
$333$	−3.58964	−0.196711
$334$	14.4047	0.788189
$335$	7.45855	0.407504
$336$	3.91776	0.213731
$337$	−19.3409	−1.05357	−0.526783	−	0.850000i	$-0.676602\pi$
$337$	−19.3409	−1.05357	−0.526783	+	0.850000i	$0.676602\pi$
$338$	75.4009	4.10127
$339$	−7.01294	−0.380891
$340$	23.3956	1.26880
$341$	−3.17580	−0.171979
$342$	−6.87317	−0.371658
$343$	−12.6837	−0.684854
$344$	−54.9484	−2.96262
$345$	1.21123	0.0652103
$346$	−21.0343	−1.13081
$347$	−26.3935	−1.41688	−0.708438	−	0.705773i	$-0.750600\pi$
$347$	−26.3935	−1.41688	−0.708438	+	0.705773i	$0.750600\pi$
$348$	4.00547	0.214716
$349$	−13.3300	−0.713541	−0.356770	−	0.934192i	$-0.616122\pi$
$349$	−13.3300	−0.713541	−0.356770	+	0.934192i	$0.616122\pi$
$350$	−8.41074	−0.449573
$351$	−6.61576	−0.353123
$352$	0.193783	0.0103287
$353$	−11.0751	−0.589468	−0.294734	−	0.955579i	$-0.595231\pi$
$353$	−11.0751	−0.589468	−0.294734	+	0.955579i	$0.595231\pi$
$354$	0.273182	0.0145195
$355$	3.32695	0.176576
$356$	13.5997	0.720781
$357$	4.68469	0.247940
$358$	−45.9543	−2.42876
$359$	4.23971	0.223763	0.111882	−	0.993722i	$-0.464312\pi$
$359$	4.23971	0.223763	0.111882	+	0.993722i	$0.464312\pi$
$360$	5.95272	0.313736
$361$	−11.1338	−0.585987
$362$	−42.3252	−2.22456
$363$	2.02929	0.106510
$364$	−25.7430	−1.34930
$365$	5.95160	0.311521
$366$	−17.4545	−0.912361
$367$	13.6881	0.714516	0.357258	−	0.934006i	$-0.383712\pi$
$367$	13.6881	0.714516	0.357258	+	0.934006i	$0.383712\pi$
$368$	4.03285	0.210227
$369$	11.8028	0.614429
$370$	−10.6549	−0.553923
$371$	2.17939	0.113148
$372$	−3.52408	−0.182715
$373$	−30.5174	−1.58013	−0.790064	−	0.613024i	$-0.789953\pi$
$373$	−30.5174	−1.58013	−0.790064	+	0.613024i	$0.789953\pi$
$374$	42.6568	2.20573
$375$	−10.3353	−0.533714
$376$	7.60803	0.392354
$377$	−6.61576	−0.340729
$378$	2.38067	0.122449
$379$	−18.7133	−0.961237	−0.480618	−	0.876930i	$-0.659588\pi$
$379$	−18.7133	−0.961237	−0.480618	+	0.876930i	$0.659588\pi$
$380$	−13.6070	−0.698025
$381$	16.0903	0.824329
$382$	26.5208	1.35692
$383$	26.8095	1.36990	0.684951	−	0.728589i	$-0.259824\pi$
$383$	26.8095	1.36990	0.684951	+	0.728589i	$0.259824\pi$
$384$	−19.5508	−0.997697
$385$	4.24730	0.216462
$386$	−24.5736	−1.25076
$387$	−11.1806	−0.568343
$388$	−29.9009	−1.51799
$389$	26.1690	1.32682	0.663410	−	0.748256i	$-0.269108\pi$
$389$	26.1690	1.32682	0.663410	+	0.748256i	$0.269108\pi$
$390$	−19.6372	−0.994367
$391$	4.82230	0.243874
$392$	−29.7642	−1.50332
$393$	4.15912	0.209800
$394$	47.2239	2.37911
$395$	6.98226	0.351316
$396$	14.4582	0.726551
$397$	19.8435	0.995914	0.497957	−	0.867202i	$-0.334084\pi$
$397$	19.8435	0.995914	0.497957	+	0.867202i	$0.334084\pi$
$398$	−64.6246	−3.23934
$399$	−2.72465	−0.136403
$400$	−14.2477	−0.712387
$401$	−0.873341	−0.0436125	−0.0218063	−	0.999762i	$-0.506942\pi$
$401$	−0.873341	−0.0436125	−0.0218063	+	0.999762i	$0.506942\pi$
$402$	15.0904	0.752643
$403$	5.82066	0.289948
$404$	3.19138	0.158777
$405$	1.21123	0.0601864
$406$	2.38067	0.118151
$407$	−12.9572	−0.642265
$408$	23.6997	1.17331
$409$	−35.4908	−1.75491	−0.877455	−	0.479660i	$-0.840760\pi$
$409$	−35.4908	−1.75491	−0.877455	+	0.479660i	$0.840760\pi$
$410$	35.0336	1.73018
$411$	9.02194	0.445020
$412$	−1.79155	−0.0882633
$413$	0.108294	0.00532881
$414$	2.45061	0.120441
$415$	−13.8756	−0.681125
$416$	−0.355169	−0.0174136
$417$	−2.93235	−0.143598
$418$	−24.8095	−1.21347
$419$	−25.3204	−1.23698	−0.618492	−	0.785791i	$-0.712256\pi$
$419$	−25.3204	−1.23698	−0.618492	+	0.785791i	$0.712256\pi$
$420$	4.71309	0.229975
$421$	−2.35782	−0.114913	−0.0574566	−	0.998348i	$-0.518299\pi$
$421$	−2.35782	−0.114913	−0.0574566	+	0.998348i	$0.518299\pi$
$422$	19.6212	0.955143
$423$	1.54804	0.0752684
$424$	11.0255	0.535444
$425$	−17.0368	−0.826407
$426$	6.73123	0.326129
$427$	−6.91927	−0.334847
$428$	−51.2006	−2.47488
$429$	−23.8803	−1.15295
$430$	−33.1868	−1.60041
$431$	26.6339	1.28291	0.641455	−	0.767161i	$-0.278331\pi$
$431$	26.6339	1.28291	0.641455	+	0.767161i	$0.278331\pi$
$432$	4.03285	0.194030
$433$	30.9755	1.48859	0.744294	−	0.667852i	$-0.232786\pi$
$433$	30.9755	1.48859	0.744294	+	0.667852i	$0.232786\pi$
$434$	−2.09456	−0.100542
$435$	1.21123	0.0580740
$436$	30.4815	1.45980
$437$	−2.80468	−0.134166
$438$	12.0415	0.575366
$439$	14.0374	0.669970	0.334985	−	0.942224i	$-0.391269\pi$
$439$	14.0374	0.669970	0.334985	+	0.942224i	$0.391269\pi$
$440$	21.4870	1.02435
$441$	−6.05626	−0.288393
$442$	−78.1821	−3.71874
$443$	33.4135	1.58752	0.793762	−	0.608229i	$-0.208120\pi$
$443$	33.4135	1.58752	0.793762	+	0.608229i	$0.208120\pi$
$444$	−14.3782	−0.682359
$445$	4.11246	0.194949
$446$	−7.17817	−0.339896
$447$	18.6407	0.881677
$448$	−7.70772	−0.364155
$449$	7.37954	0.348262	0.174131	−	0.984722i	$-0.444288\pi$
$449$	7.37954	0.348262	0.174131	+	0.984722i	$0.444288\pi$
$450$	−8.65781	−0.408133
$451$	42.6035	2.00612
$452$	−28.0901	−1.32125
$453$	9.71968	0.456670
$454$	−36.5188	−1.71391
$455$	−7.78453	−0.364944
$456$	−13.7839	−0.645492
$457$	−31.2019	−1.45956	−0.729781	−	0.683681i	$-0.760378\pi$
$457$	−31.2019	−1.45956	−0.729781	+	0.683681i	$0.760378\pi$
$458$	27.1954	1.27076
$459$	4.82230	0.225086
$460$	4.85154	0.226204
$461$	40.8683	1.90343	0.951714	−	0.306986i	$-0.0993205\pi$
$461$	40.8683	1.90343	0.951714	+	0.306986i	$0.0993205\pi$
$462$	8.59331	0.399797
$463$	−9.18712	−0.426962	−0.213481	−	0.976947i	$-0.568480\pi$
$463$	−9.18712	−0.426962	−0.213481	+	0.976947i	$0.568480\pi$
$464$	4.03285	0.187220
$465$	−1.06566	−0.0494188
$466$	27.4883	1.27337
$467$	−15.8601	−0.733917	−0.366958	−	0.930237i	$-0.619601\pi$
$467$	−15.8601	−0.733917	−0.366958	+	0.930237i	$0.619601\pi$
$468$	−26.4992	−1.22493
$469$	5.98212	0.276229
$470$	4.59497	0.211950
$471$	7.71197	0.355349
$472$	0.547859	0.0252172
$473$	−40.3577	−1.85565
$474$	14.1268	0.648865
$475$	9.90873	0.454644
$476$	18.7644	0.860063
$477$	2.24340	0.102718
$478$	45.2849	2.07128
$479$	−16.4171	−0.750115	−0.375057	−	0.927002i	$-0.622377\pi$
$479$	−16.4171	−0.750115	−0.375057	+	0.927002i	$0.622377\pi$
$480$	0.0650251	0.00296797
$481$	23.7482	1.08282
$482$	−18.0321	−0.821338
$483$	0.971463	0.0442031
$484$	8.12825	0.369466
$485$	−9.04184	−0.410569
$486$	2.45061	0.111162
$487$	35.6972	1.61759	0.808797	−	0.588088i	$-0.200119\pi$
$487$	35.6972	1.61759	0.808797	+	0.588088i	$0.200119\pi$
$488$	−35.0044	−1.58458
$489$	−11.9063	−0.538421
$490$	−17.9764	−0.812093
$491$	34.2249	1.54455	0.772273	−	0.635290i	$-0.219120\pi$
$491$	34.2249	1.54455	0.772273	+	0.635290i	$0.219120\pi$
$492$	47.2757	2.13135
$493$	4.82230	0.217185
$494$	45.4712	2.04585
$495$	4.37206	0.196510
$496$	−3.54817	−0.159318
$497$	2.66838	0.119693
$498$	−28.0736	−1.25801
$499$	30.1196	1.34834	0.674169	−	0.738577i	$-0.264502\pi$
$499$	30.1196	1.34834	0.674169	+	0.738577i	$0.264502\pi$
$500$	−41.3978	−1.85137
$501$	5.87801	0.262610
$502$	−53.9376	−2.40735
$503$	8.55512	0.381454	0.190727	−	0.981643i	$-0.438915\pi$
$503$	8.55512	0.381454	0.190727	+	0.981643i	$0.438915\pi$
$504$	4.77437	0.212667
$505$	0.965052	0.0429442
$506$	8.84573	0.393241
$507$	30.7683	1.36647
$508$	64.4491	2.85946
$509$	−6.87162	−0.304579	−0.152290	−	0.988336i	$-0.548665\pi$
$509$	−6.87162	−0.304579	−0.152290	+	0.988336i	$0.548665\pi$
$510$	14.3138	0.633824
$511$	4.77347	0.211166
$512$	−39.4233	−1.74228
$513$	−2.80468	−0.123830
$514$	−32.4633	−1.43189
$515$	−0.541753	−0.0238725
$516$	−44.7836	−1.97149
$517$	5.58783	0.245752
$518$	−8.54576	−0.375479
$519$	−8.58330	−0.376765
$520$	−39.3818	−1.72700
$521$	−19.3761	−0.848881	−0.424440	−	0.905456i	$-0.639529\pi$
$521$	−19.3761	−0.848881	−0.424440	+	0.905456i	$0.639529\pi$
$522$	2.45061	0.107260
$523$	0.309818	0.0135474	0.00677370	−	0.999977i	$-0.497844\pi$
$523$	0.309818	0.0135474	0.00677370	+	0.999977i	$0.497844\pi$
$524$	16.6592	0.727761
$525$	−3.43211	−0.149789
$526$	27.1847	1.18531
$527$	−4.24274	−0.184817
$528$	14.5570	0.633512
$529$	1.00000	0.0434783
$530$	6.65897	0.289247
$531$	0.111475	0.00483762
$532$	−10.9135	−0.473160
$533$	−78.0845	−3.38221
$534$	8.32049	0.360063
$535$	−15.4827	−0.669378
$536$	30.2634	1.30718
$537$	−18.7522	−0.809219
$538$	−38.6613	−1.66681
$539$	−21.8607	−0.941609
$540$	4.85154	0.208777
$541$	10.5011	0.451478	0.225739	−	0.974188i	$-0.427520\pi$
$541$	10.5011	0.451478	0.225739	+	0.974188i	$0.427520\pi$
$542$	−10.5648	−0.453799
$543$	−17.2713	−0.741183
$544$	0.258886	0.0110997
$545$	9.21742	0.394831
$546$	−15.7500	−0.674036
$547$	−35.2453	−1.50698	−0.753489	−	0.657460i	$-0.771631\pi$
$547$	−35.2453	−1.50698	−0.753489	+	0.657460i	$0.771631\pi$
$548$	36.1371	1.54370
$549$	−7.12252	−0.303982
$550$	−31.2513	−1.33256
$551$	−2.80468	−0.119483
$552$	4.91461	0.209180
$553$	5.60011	0.238141
$554$	1.55570	0.0660955
$555$	−4.34787	−0.184557
$556$	−11.7455	−0.498118
$557$	−36.6005	−1.55081	−0.775407	−	0.631462i	$-0.782455\pi$
$557$	−36.6005	−1.55081	−0.775407	+	0.631462i	$0.782455\pi$
$558$	−2.15609	−0.0912744
$559$	73.9683	3.12852
$560$	4.74530	0.200526
$561$	17.4066	0.734908
$562$	68.5223	2.89044
$563$	44.7796	1.88724	0.943618	−	0.331037i	$-0.107398\pi$
$563$	44.7796	1.88724	0.943618	+	0.331037i	$0.107398\pi$
$564$	6.20064	0.261094
$565$	−8.49427	−0.357357
$566$	−44.5517	−1.87265
$567$	0.971463	0.0407976
$568$	13.4993	0.566417
$569$	7.11731	0.298373	0.149187	−	0.988809i	$-0.452335\pi$
$569$	7.11731	0.298373	0.149187	+	0.988809i	$0.452335\pi$
$570$	−8.32498	−0.348695
$571$	0.486328	0.0203522	0.0101761	−	0.999948i	$-0.496761\pi$
$571$	0.486328	0.0203522	0.0101761	+	0.999948i	$0.496761\pi$
$572$	−95.6519	−3.99941
$573$	10.8221	0.452102
$574$	28.0986	1.17281
$575$	−3.53293	−0.147333
$576$	−7.93413	−0.330589
$577$	17.2741	0.719129	0.359565	−	0.933120i	$-0.382925\pi$
$577$	17.2741	0.719129	0.359565	+	0.933120i	$0.382925\pi$
$578$	15.3275	0.637538
$579$	−10.0276	−0.416731
$580$	4.85154	0.201449
$581$	−11.1289	−0.461703
$582$	−18.2938	−0.758303
$583$	8.09782	0.335377
$584$	24.1489	0.999288
$585$	−8.01320	−0.331305
$586$	−20.2650	−0.837140
$587$	−32.8644	−1.35646	−0.678230	−	0.734850i	$-0.737253\pi$
$587$	−32.8644	−1.35646	−0.678230	+	0.734850i	$0.737253\pi$
$588$	−24.2582	−1.00039
$589$	2.46761	0.101676
$590$	0.330886	0.0136224
$591$	19.2703	0.792675
$592$	−14.4765	−0.594979
$593$	−27.4183	−1.12594	−0.562968	−	0.826479i	$-0.690341\pi$
$593$	−27.4183	−1.12594	−0.562968	+	0.826479i	$0.690341\pi$
$594$	8.84573	0.362945
$595$	5.67422	0.232621
$596$	74.6649	3.05839
$597$	−26.3709	−1.07929
$598$	−16.2126	−0.662983
$599$	19.4591	0.795076	0.397538	−	0.917586i	$-0.369865\pi$
$599$	19.4591	0.795076	0.397538	+	0.917586i	$0.369865\pi$
$600$	−17.3630	−0.708840
$601$	−36.0765	−1.47159	−0.735796	−	0.677203i	$-0.763192\pi$
$601$	−36.0765	−1.47159	−0.735796	+	0.677203i	$0.763192\pi$
$602$	−26.6174	−1.08484
$603$	6.15784	0.250767
$604$	38.9319	1.58412
$605$	2.45793	0.0999291
$606$	1.95253	0.0793162
$607$	9.87912	0.400981	0.200491	−	0.979696i	$-0.435746\pi$
$607$	9.87912	0.400981	0.200491	+	0.979696i	$0.435746\pi$
$608$	−0.150570	−0.00610642
$609$	0.971463	0.0393657
$610$	−21.1414	−0.855989
$611$	−10.2415	−0.414326
$612$	19.3156	0.780785
$613$	−29.1959	−1.17921	−0.589605	−	0.807692i	$-0.700717\pi$
$613$	−29.1959	−1.17921	−0.589605	+	0.807692i	$0.700717\pi$
$614$	52.9025	2.13497
$615$	14.2959	0.576466
$616$	17.2336	0.694362
$617$	11.1507	0.448911	0.224456	−	0.974484i	$-0.427940\pi$
$617$	11.1507	0.448911	0.224456	+	0.974484i	$0.427940\pi$
$618$	−1.09610	−0.0440915
$619$	18.2017	0.731589	0.365795	−	0.930696i	$-0.380797\pi$
$619$	18.2017	0.731589	0.365795	+	0.930696i	$0.380797\pi$
$620$	−4.26847	−0.171426
$621$	1.00000	0.0401286
$622$	72.0948	2.89074
$623$	3.29839	0.132147
$624$	−26.6803	−1.06807
$625$	5.14619	0.205848
$626$	27.5124	1.09962
$627$	−10.1238	−0.404306
$628$	30.8901	1.23265
$629$	−17.3103	−0.690208
$630$	2.88354	0.114883
$631$	28.7794	1.14569	0.572844	−	0.819664i	$-0.305840\pi$
$631$	28.7794	1.14569	0.572844	+	0.819664i	$0.305840\pi$
$632$	28.3308	1.12694
$633$	8.00666	0.318236
$634$	76.1838	3.02564
$635$	19.4890	0.773397
$636$	8.98589	0.356314
$637$	40.0668	1.58750
$638$	8.84573	0.350206
$639$	2.74676	0.108660
$640$	−23.6805	−0.936053
$641$	46.7463	1.84637	0.923184	−	0.384358i	$-0.125577\pi$
$641$	46.7463	1.84637	0.923184	+	0.384358i	$0.125577\pi$
$642$	−31.3253	−1.23631
$643$	−16.3867	−0.646228	−0.323114	−	0.946360i	$-0.604730\pi$
$643$	−16.3867	−0.646228	−0.323114	+	0.946360i	$0.604730\pi$
$644$	3.89117	0.153333
$645$	−13.5423	−0.533227
$646$	−33.1445	−1.30405
$647$	3.45161	0.135697	0.0678485	−	0.997696i	$-0.478387\pi$
$647$	3.45161	0.135697	0.0678485	+	0.997696i	$0.478387\pi$
$648$	4.91461	0.193064
$649$	0.402383	0.0157949
$650$	57.2780	2.24663
$651$	−0.854711	−0.0334988
$652$	−47.6903	−1.86770
$653$	22.1264	0.865874	0.432937	−	0.901424i	$-0.357477\pi$
$653$	22.1264	0.865874	0.432937	+	0.901424i	$0.357477\pi$
$654$	18.6491	0.729236
$655$	5.03764	0.196837
$656$	47.5988	1.85842
$657$	4.91369	0.191701
$658$	3.68538	0.143671
$659$	−8.83575	−0.344192	−0.172096	−	0.985080i	$-0.555054\pi$
$659$	−8.83575	−0.344192	−0.172096	+	0.985080i	$0.555054\pi$
$660$	17.5122	0.681660
$661$	6.69279	0.260319	0.130160	−	0.991493i	$-0.458451\pi$
$661$	6.69279	0.260319	0.130160	+	0.991493i	$0.458451\pi$
$662$	46.8870	1.82232
$663$	−31.9032	−1.23902
$664$	−56.3007	−2.18489
$665$	−3.30017	−0.127975
$666$	−8.79680	−0.340869
$667$	1.00000	0.0387202
$668$	23.5442	0.910952
$669$	−2.92914	−0.113247
$670$	18.2780	0.706140
$671$	−25.7095	−0.992505
$672$	0.0521532	0.00201185
$673$	20.8594	0.804071	0.402035	−	0.915624i	$-0.368303\pi$
$673$	20.8594	0.804071	0.402035	+	0.915624i	$0.368303\pi$
$674$	−47.3969	−1.82566
$675$	−3.53293	−0.135982
$676$	123.241	4.74005
$677$	−20.5616	−0.790248	−0.395124	−	0.918628i	$-0.629298\pi$
$677$	−20.5616	−0.790248	−0.395124	+	0.918628i	$0.629298\pi$
$678$	−17.1860	−0.660023
$679$	−7.25199	−0.278306
$680$	28.7058	1.10082
$681$	−14.9020	−0.571044
$682$	−7.78263	−0.298012
$683$	33.8369	1.29473	0.647366	−	0.762180i	$-0.275871\pi$
$683$	33.8369	1.29473	0.647366	+	0.762180i	$0.275871\pi$
$684$	−11.2341	−0.429545
$685$	10.9276	0.417523
$686$	−31.0827	−1.18674
$687$	11.0974	0.423394
$688$	−45.0897	−1.71903
$689$	−14.8418	−0.565428
$690$	2.96824	0.112999
$691$	22.3353	0.849674	0.424837	−	0.905270i	$-0.360331\pi$
$691$	22.3353	0.849674	0.424837	+	0.905270i	$0.360331\pi$
$692$	−34.3801	−1.30694
$693$	3.50660	0.133205
$694$	−64.6800	−2.45522
$695$	−3.55175	−0.134726
$696$	4.91461	0.186288
$697$	56.9166	2.15587
$698$	−32.6667	−1.23645
$699$	11.2169	0.424263
$700$	−13.7472	−0.519595
$701$	−31.9852	−1.20806	−0.604031	−	0.796961i	$-0.706440\pi$
$701$	−31.9852	−1.20806	−0.604031	+	0.796961i	$0.706440\pi$
$702$	−16.2126	−0.611906
$703$	10.0678	0.379714
$704$	−28.6391	−1.07938
$705$	1.87503	0.0706178
$706$	−27.1407	−1.02145
$707$	0.774018	0.0291099
$708$	0.446511	0.0167809
$709$	42.6363	1.60124	0.800619	−	0.599174i	$-0.204504\pi$
$709$	42.6363	1.60124	0.800619	+	0.599174i	$0.204504\pi$
$710$	8.15305	0.305979
$711$	5.76461	0.216190
$712$	16.6865	0.625352
$713$	−0.879818	−0.0329494
$714$	11.4803	0.429640
$715$	−28.9245	−1.08172
$716$	−75.1115	−2.80705
$717$	18.4791	0.690113
$718$	10.3899	0.387746
$719$	5.03168	0.187650	0.0938250	−	0.995589i	$-0.470091\pi$
$719$	5.03168	0.187650	0.0938250	+	0.995589i	$0.470091\pi$
$720$	4.88470	0.182042
$721$	−0.434512	−0.0161821
$722$	−27.2845	−1.01542
$723$	−7.35820	−0.273655
$724$	−69.1797	−2.57104
$725$	−3.53293	−0.131210
$726$	4.97299	0.184565
$727$	−0.687407	−0.0254945	−0.0127473	−	0.999919i	$-0.504058\pi$
$727$	−0.687407	−0.0254945	−0.0127473	+	0.999919i	$0.504058\pi$
$728$	−31.5861	−1.17066
$729$	1.00000	0.0370370
$730$	14.5850	0.539816
$731$	−53.9163	−1.99416
$732$	−28.5290	−1.05446
$733$	29.8891	1.10398	0.551989	−	0.833851i	$-0.313869\pi$
$733$	29.8891	1.10398	0.551989	+	0.833851i	$0.313869\pi$
$734$	33.5443	1.23814
$735$	−7.33551	−0.270574
$736$	0.0536852	0.00197886
$737$	22.2274	0.818757
$738$	28.9240	1.06471
$739$	8.44047	0.310488	0.155244	−	0.987876i	$-0.450384\pi$
$739$	8.44047	0.310488	0.155244	+	0.987876i	$0.450384\pi$
$740$	−17.4153	−0.640198
$741$	18.5551	0.681639
$742$	5.34081	0.196067
$743$	−41.2959	−1.51500	−0.757500	−	0.652835i	$-0.773579\pi$
$743$	−41.2959	−1.51500	−0.757500	+	0.652835i	$0.773579\pi$
$744$	−4.32397	−0.158524
$745$	22.5782	0.827201
$746$	−74.7860	−2.73811
$747$	−11.4558	−0.419145
$748$	69.7217	2.54928
$749$	−12.4179	−0.453741
$750$	−25.3278	−0.924841
$751$	23.1167	0.843540	0.421770	−	0.906703i	$-0.361409\pi$
$751$	23.1167	0.843540	0.421770	+	0.906703i	$0.361409\pi$
$752$	6.24301	0.227659
$753$	−22.0099	−0.802086
$754$	−16.2126	−0.590429
$755$	11.7728	0.428454
$756$	3.89117	0.141520
$757$	−21.5153	−0.781988	−0.390994	−	0.920393i	$-0.627869\pi$
$757$	−21.5153	−0.781988	−0.390994	+	0.920393i	$0.627869\pi$
$758$	−45.8589	−1.66567
$759$	3.60961	0.131021
$760$	−16.6955	−0.605609
$761$	8.35122	0.302732	0.151366	−	0.988478i	$-0.451633\pi$
$761$	8.35122	0.302732	0.151366	+	0.988478i	$0.451633\pi$
$762$	39.4309	1.42843
$763$	7.39281	0.267638
$764$	43.3478	1.56827
$765$	5.84090	0.211178
$766$	65.6995	2.37382
$767$	−0.737494	−0.0266294
$768$	−32.0430	−1.15625
$769$	−48.6804	−1.75546	−0.877731	−	0.479154i	$-0.840944\pi$
$769$	−48.6804	−1.75546	−0.877731	+	0.479154i	$0.840944\pi$
$770$	10.4085	0.375095
$771$	−13.2471	−0.477081
$772$	−40.1651	−1.44557
$773$	35.2809	1.26896	0.634482	−	0.772937i	$-0.281213\pi$
$773$	35.2809	1.26896	0.634482	+	0.772937i	$0.281213\pi$
$774$	−27.3993	−0.984847
$775$	3.10833	0.111655
$776$	−36.6877	−1.31701
$777$	−3.48720	−0.125103
$778$	64.1299	2.29917
$779$	−33.1031	−1.18604
$780$	−32.0966	−1.14924
$781$	9.91474	0.354777
$782$	11.8176	0.422595
$783$	1.00000	0.0357371
$784$	−24.4240	−0.872284
$785$	9.34096	0.333393
$786$	10.1924	0.363549
$787$	18.7092	0.666909	0.333455	−	0.942766i	$-0.391786\pi$
$787$	18.7092	0.666909	0.333455	+	0.942766i	$0.391786\pi$
$788$	77.1866	2.74966
$789$	11.0930	0.394922
$790$	17.1108	0.608774
$791$	−6.81282	−0.242236
$792$	17.7398	0.630358
$793$	47.1209	1.67331
$794$	48.6285	1.72576
$795$	2.71727	0.0963718
$796$	−105.628	−3.74388
$797$	−11.0424	−0.391141	−0.195571	−	0.980690i	$-0.562656\pi$
$797$	−11.0424	−0.391141	−0.195571	+	0.980690i	$0.562656\pi$
$798$	−6.67703	−0.236364
$799$	7.46512	0.264097
$800$	−0.189666	−0.00670570
$801$	3.39528	0.119966
$802$	−2.14021	−0.0755736
$803$	17.7365	0.625907
$804$	24.6650	0.869869
$805$	1.17666	0.0414720
$806$	14.2642	0.502433
$807$	−15.7762	−0.555350
$808$	3.91574	0.137755
$809$	−13.3665	−0.469941	−0.234970	−	0.972003i	$-0.575499\pi$
$809$	−13.3665	−0.469941	−0.234970	+	0.972003i	$0.575499\pi$
$810$	2.96824	0.104293
$811$	20.6937	0.726654	0.363327	−	0.931662i	$-0.381641\pi$
$811$	20.6937	0.726654	0.363327	+	0.931662i	$0.381641\pi$
$812$	3.89117	0.136553
$813$	−4.31111	−0.151197
$814$	−31.7530	−1.11294
$815$	−14.4212	−0.505154
$816$	19.4476	0.680802
$817$	31.3581	1.09708
$818$	−86.9741	−3.04098
$819$	−6.42697	−0.224576
$820$	57.2617	1.99967
$821$	37.8007	1.31925	0.659626	−	0.751594i	$-0.270715\pi$
$821$	37.8007	1.31925	0.659626	+	0.751594i	$0.270715\pi$
$822$	22.1092	0.771148
$823$	−35.3953	−1.23380	−0.616902	−	0.787040i	$-0.711612\pi$
$823$	−35.3953	−1.23380	−0.616902	+	0.787040i	$0.711612\pi$
$824$	−2.19819	−0.0765775
$825$	−12.7525	−0.443985
$826$	0.265387	0.00923398
$827$	50.9326	1.77110	0.885549	−	0.464545i	$-0.153782\pi$
$827$	50.9326	1.77110	0.885549	+	0.464545i	$0.153782\pi$
$828$	4.00547	0.139200
$829$	15.8607	0.550865	0.275432	−	0.961320i	$-0.411179\pi$
$829$	15.8607	0.550865	0.275432	+	0.961320i	$0.411179\pi$
$830$	−34.0035	−1.18028
$831$	0.634824	0.0220218
$832$	52.4903	1.81977
$833$	−29.2051	−1.01190
$834$	−7.18604	−0.248832
$835$	7.11961	0.246384
$836$	−40.5506	−1.40247
$837$	−0.879818	−0.0304110
$838$	−62.0504	−2.14350
$839$	44.4147	1.53336	0.766682	−	0.642027i	$-0.221906\pi$
$839$	44.4147	1.53336	0.766682	+	0.642027i	$0.221906\pi$
$840$	5.78285	0.199527
$841$	1.00000	0.0344828
$842$	−5.77809	−0.199126
$843$	27.9614	0.963040
$844$	32.0704	1.10391
$845$	37.2674	1.28204
$846$	3.79364	0.130428
$847$	1.97138	0.0677374
$848$	9.04730	0.310686
$849$	−18.1799	−0.623931
$850$	−41.7505	−1.43203
$851$	−3.58964	−0.123051
$852$	11.0021	0.376925
$853$	−57.4686	−1.96769	−0.983844	−	0.179027i	$-0.942705\pi$
$853$	−57.4686	−1.96769	−0.983844	+	0.179027i	$0.942705\pi$
$854$	−16.9564	−0.580236
$855$	−3.39711	−0.116179
$856$	−62.8220	−2.14721
$857$	30.6152	1.04580	0.522898	−	0.852396i	$-0.324851\pi$
$857$	30.6152	1.04580	0.522898	+	0.852396i	$0.324851\pi$
$858$	−58.5212	−1.99788
$859$	−1.13987	−0.0388920	−0.0194460	−	0.999811i	$-0.506190\pi$
$859$	−1.13987	−0.0388920	−0.0194460	+	0.999811i	$0.506190\pi$
$860$	−54.2432	−1.84968
$861$	11.4660	0.390760
$862$	65.2692	2.22308
$863$	−44.0565	−1.49970	−0.749851	−	0.661607i	$-0.769875\pi$
$863$	−44.0565	−1.49970	−0.749851	+	0.661607i	$0.769875\pi$
$864$	0.0536852	0.00182641
$865$	−10.3963	−0.353486
$866$	75.9088	2.57949
$867$	6.25456	0.212416
$868$	−3.42352	−0.116202
$869$	20.8080	0.705863
$870$	2.96824	0.100633
$871$	−40.7388	−1.38038
$872$	37.4001	1.26653
$873$	−7.46502	−0.252653
$874$	−6.87317	−0.232488
$875$	−10.0404	−0.339427
$876$	19.6816	0.664980
$877$	−17.3140	−0.584652	−0.292326	−	0.956319i	$-0.594429\pi$
$877$	−17.3140	−0.584652	−0.292326	+	0.956319i	$0.594429\pi$
$878$	34.4002	1.16095
$879$	−8.26939	−0.278920
$880$	17.6319	0.594370
$881$	−38.0049	−1.28042	−0.640209	−	0.768201i	$-0.721152\pi$
$881$	−38.0049	−1.28042	−0.640209	+	0.768201i	$0.721152\pi$
$882$	−14.8415	−0.499739
$883$	7.68227	0.258529	0.129264	−	0.991610i	$-0.458738\pi$
$883$	7.68227	0.258529	0.129264	+	0.991610i	$0.458738\pi$
$884$	−127.787	−4.29795
$885$	0.135022	0.00453872
$886$	81.8833	2.75092
$887$	45.7949	1.53764	0.768821	−	0.639465i	$-0.220844\pi$
$887$	45.7949	1.53764	0.768821	+	0.639465i	$0.220844\pi$
$888$	−17.6417	−0.592017
$889$	15.6311	0.524250
$890$	10.0780	0.337816
$891$	3.60961	0.120927
$892$	−11.7326	−0.392836
$893$	−4.34177	−0.145292
$894$	45.6811	1.52781
$895$	−22.7132	−0.759220
$896$	−18.9929	−0.634508
$897$	−6.61576	−0.220894
$898$	18.0843	0.603482
$899$	−0.879818	−0.0293436
$900$	−14.1510	−0.471701
$901$	10.8184	0.360412
$902$	104.404	3.47629
$903$	−10.8616	−0.361450
$904$	−34.4659	−1.14632
$905$	−20.9195	−0.695388
$906$	23.8191	0.791337
$907$	−7.34775	−0.243978	−0.121989	−	0.992531i	$-0.538927\pi$
$907$	−7.34775	−0.243978	−0.121989	+	0.992531i	$0.538927\pi$
$908$	−59.6893	−1.98086
$909$	0.796755	0.0264267
$910$	−19.0768	−0.632390
$911$	8.12967	0.269348	0.134674	−	0.990890i	$-0.457001\pi$
$911$	8.12967	0.269348	0.134674	+	0.990890i	$0.457001\pi$
$912$	−11.3108	−0.374540
$913$	−41.3509	−1.36851
$914$	−76.4635	−2.52919
$915$	−8.62700	−0.285200
$916$	44.4504	1.46868
$917$	4.04043	0.133427
$918$	11.8176	0.390037
$919$	16.4766	0.543514	0.271757	−	0.962366i	$-0.412395\pi$
$919$	16.4766	0.543514	0.271757	+	0.962366i	$0.412395\pi$
$920$	5.95272	0.196255
$921$	21.5875	0.711333
$922$	100.152	3.29834
$923$	−18.1719	−0.598136
$924$	14.0456	0.462066
$925$	12.6819	0.416979
$926$	−22.5140	−0.739857
$927$	−0.447276	−0.0146905
$928$	0.0536852	0.00176230
$929$	54.4912	1.78780	0.893898	−	0.448270i	$-0.147960\pi$
$929$	54.4912	1.78780	0.893898	+	0.448270i	$0.147960\pi$
$930$	−2.61151	−0.0856349
$931$	16.9859	0.556690
$932$	44.9291	1.47170
$933$	29.4192	0.963140
$934$	−38.8668	−1.27176
$935$	21.0834	0.689501
$936$	−32.5139	−1.06275
$937$	48.2496	1.57624	0.788122	−	0.615519i	$-0.211054\pi$
$937$	48.2496	1.57624	0.788122	+	0.615519i	$0.211054\pi$
$938$	14.6598	0.478660
$939$	11.2268	0.366372
$940$	7.51039	0.244962
$941$	5.22563	0.170351	0.0851753	−	0.996366i	$-0.472855\pi$
$941$	5.22563	0.170351	0.0851753	+	0.996366i	$0.472855\pi$
$942$	18.8990	0.615763
$943$	11.8028	0.384352
$944$	0.449563	0.0146320
$945$	1.17666	0.0382769
$946$	−98.9007	−3.21554
$947$	30.3485	0.986192	0.493096	−	0.869975i	$-0.335865\pi$
$947$	30.3485	0.986192	0.493096	+	0.869975i	$0.335865\pi$
$948$	23.0900	0.749927
$949$	−32.5078	−1.05525
$950$	24.2824	0.787825
$951$	31.0877	1.00809
$952$	23.0234	0.746194
$953$	−46.2230	−1.49731	−0.748654	−	0.662960i	$-0.769300\pi$
$953$	−46.2230	−1.49731	−0.748654	+	0.662960i	$0.769300\pi$
$954$	5.49770	0.177995
$955$	13.1081	0.424168
$956$	74.0173	2.39389
$957$	3.60961	0.116682
$958$	−40.2317	−1.29983
$959$	8.76449	0.283020
$960$	−9.61004	−0.310163
$961$	−30.2259	−0.975030
$962$	58.1975	1.87636
$963$	−12.7827	−0.411916
$964$	−29.4731	−0.949263
$965$	−12.1457	−0.390983
$966$	2.38067	0.0765969
$967$	8.43018	0.271096	0.135548	−	0.990771i	$-0.456720\pi$
$967$	8.43018	0.271096	0.135548	+	0.990771i	$0.456720\pi$
$968$	9.97317	0.320550
$969$	−13.5250	−0.434486
$970$	−22.1580	−0.711450
$971$	−18.9726	−0.608861	−0.304430	−	0.952535i	$-0.598466\pi$
$971$	−18.9726	−0.608861	−0.304430	+	0.952535i	$0.598466\pi$
$972$	4.00547	0.128475
$973$	−2.84867	−0.0913243
$974$	87.4797	2.80303
$975$	23.3730	0.748535
$976$	−28.7240	−0.919434
$977$	−28.2590	−0.904085	−0.452042	−	0.891996i	$-0.649304\pi$
$977$	−28.2590	−0.904085	−0.452042	+	0.891996i	$0.649304\pi$
$978$	−29.1776	−0.932998
$979$	12.2556	0.391692
$980$	−29.3822	−0.938579
$981$	7.60998	0.242968
$982$	83.8717	2.67645
$983$	−20.4747	−0.653043	−0.326522	−	0.945190i	$-0.605877\pi$
$983$	−20.4747	−0.653043	−0.326522	+	0.945190i	$0.605877\pi$
$984$	58.0062	1.84917
$985$	23.3407	0.743698
$986$	11.8176	0.376348
$987$	1.50387	0.0478686
$988$	74.3219	2.36449
$989$	−11.1806	−0.355523
$990$	10.7142	0.340520
$991$	−28.5762	−0.907753	−0.453877	−	0.891065i	$-0.649959\pi$
$991$	−28.5762	−0.907753	−0.453877	+	0.891065i	$0.649959\pi$
$992$	−0.0472332	−0.00149966
$993$	19.1328	0.607162
$994$	6.53914	0.207409
$995$	−31.9412	−1.01260
$996$	−45.8858	−1.45395
$997$	−16.8259	−0.532881	−0.266441	−	0.963851i	$-0.585848\pi$
$997$	−16.8259	−0.532881	−0.266441	+	0.963851i	$0.585848\pi$
$998$	73.8113	2.33646
$999$	−3.58964	−0.113571

Twists

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

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

\(f(q)\)	\(=\)	\(q+2.45061 q^{2} +1.00000 q^{3} +4.00547 q^{4} +1.21123 q^{5} +2.45061 q^{6} +0.971463 q^{7} +4.91461 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.45061 q^{2} +1.00000 q^{3} +4.00547 q^{4} +1.21123 q^{5} +2.45061 q^{6} +0.971463 q^{7} +4.91461 q^{8} +1.00000 q^{9} +2.96824 q^{10} +3.60961 q^{11} +4.00547 q^{12} -6.61576 q^{13} +2.38067 q^{14} +1.21123 q^{15} +4.03285 q^{16} +4.82230 q^{17} +2.45061 q^{18} -2.80468 q^{19} +4.85154 q^{20} +0.971463 q^{21} +8.84573 q^{22} +1.00000 q^{23} +4.91461 q^{24} -3.53293 q^{25} -16.2126 q^{26} +1.00000 q^{27} +3.89117 q^{28} +1.00000 q^{29} +2.96824 q^{30} -0.879818 q^{31} +0.0536852 q^{32} +3.60961 q^{33} +11.8176 q^{34} +1.17666 q^{35} +4.00547 q^{36} -3.58964 q^{37} -6.87317 q^{38} -6.61576 q^{39} +5.95272 q^{40} +11.8028 q^{41} +2.38067 q^{42} -11.1806 q^{43} +14.4582 q^{44} +1.21123 q^{45} +2.45061 q^{46} +1.54804 q^{47} +4.03285 q^{48} -6.05626 q^{49} -8.65781 q^{50} +4.82230 q^{51} -26.4992 q^{52} +2.24340 q^{53} +2.45061 q^{54} +4.37206 q^{55} +4.77437 q^{56} -2.80468 q^{57} +2.45061 q^{58} +0.111475 q^{59} +4.85154 q^{60} -7.12252 q^{61} -2.15609 q^{62} +0.971463 q^{63} -7.93413 q^{64} -8.01320 q^{65} +8.84573 q^{66} +6.15784 q^{67} +19.3156 q^{68} +1.00000 q^{69} +2.88354 q^{70} +2.74676 q^{71} +4.91461 q^{72} +4.91369 q^{73} -8.79680 q^{74} -3.53293 q^{75} -11.2341 q^{76} +3.50660 q^{77} -16.2126 q^{78} +5.76461 q^{79} +4.88470 q^{80} +1.00000 q^{81} +28.9240 q^{82} -11.4558 q^{83} +3.89117 q^{84} +5.84090 q^{85} -27.3993 q^{86} +1.00000 q^{87} +17.7398 q^{88} +3.39528 q^{89} +2.96824 q^{90} -6.42697 q^{91} +4.00547 q^{92} -0.879818 q^{93} +3.79364 q^{94} -3.39711 q^{95} +0.0536852 q^{96} -7.46502 q^{97} -14.8415 q^{98} +3.60961 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9}+O(q^{10}) \) 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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