LMFDB - Embedded newform 2667.2.a.l.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2667,2,Mod(1,2667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2667, 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("2667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2667 = 3 \cdot 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2667.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:	$21.2961022191$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4 x^{12} - 10 x^{11} + 53 x^{10} + 19 x^{9} - 242 x^{8} + 61 x^{7} + 467 x^{6} - 211 x^{5} + \cdots - 8 $ x^13 - 4x^12 - 10x^11 + 53x^10 + 19x^9 - 242x^8 + 61x^7 + 467x^6 - 211x^5 - 372x^4 + 146x^3 + 116x^2 - 12x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$2.70878$ of defining polynomial
Character	$\chi$	$=$	2667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.70878 q^{2} -1.00000 q^{3} +5.33747 q^{4} +2.87857 q^{5} -2.70878 q^{6} +1.00000 q^{7} +9.04047 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.70878 q^{2} -1.00000 q^{3} +5.33747 q^{4} +2.87857 q^{5} -2.70878 q^{6} +1.00000 q^{7} +9.04047 q^{8} +1.00000 q^{9} +7.79741 q^{10} -1.50105 q^{11} -5.33747 q^{12} +5.43745 q^{13} +2.70878 q^{14} -2.87857 q^{15} +13.8137 q^{16} +1.68422 q^{17} +2.70878 q^{18} -3.30288 q^{19} +15.3643 q^{20} -1.00000 q^{21} -4.06601 q^{22} -5.07189 q^{23} -9.04047 q^{24} +3.28617 q^{25} +14.7288 q^{26} -1.00000 q^{27} +5.33747 q^{28} -8.28010 q^{29} -7.79741 q^{30} -9.29635 q^{31} +19.3372 q^{32} +1.50105 q^{33} +4.56218 q^{34} +2.87857 q^{35} +5.33747 q^{36} -7.22083 q^{37} -8.94677 q^{38} -5.43745 q^{39} +26.0237 q^{40} -2.03090 q^{41} -2.70878 q^{42} +0.859629 q^{43} -8.01182 q^{44} +2.87857 q^{45} -13.7386 q^{46} -6.92288 q^{47} -13.8137 q^{48} +1.00000 q^{49} +8.90151 q^{50} -1.68422 q^{51} +29.0223 q^{52} +8.32870 q^{53} -2.70878 q^{54} -4.32088 q^{55} +9.04047 q^{56} +3.30288 q^{57} -22.4289 q^{58} +8.94067 q^{59} -15.3643 q^{60} +9.99896 q^{61} -25.1817 q^{62} +1.00000 q^{63} +24.7529 q^{64} +15.6521 q^{65} +4.06601 q^{66} -15.7116 q^{67} +8.98949 q^{68} +5.07189 q^{69} +7.79741 q^{70} +5.53761 q^{71} +9.04047 q^{72} +6.56437 q^{73} -19.5596 q^{74} -3.28617 q^{75} -17.6290 q^{76} -1.50105 q^{77} -14.7288 q^{78} -9.27964 q^{79} +39.7637 q^{80} +1.00000 q^{81} -5.50124 q^{82} +7.17857 q^{83} -5.33747 q^{84} +4.84815 q^{85} +2.32854 q^{86} +8.28010 q^{87} -13.5702 q^{88} +9.76491 q^{89} +7.79741 q^{90} +5.43745 q^{91} -27.0711 q^{92} +9.29635 q^{93} -18.7525 q^{94} -9.50758 q^{95} -19.3372 q^{96} -9.08877 q^{97} +2.70878 q^{98} -1.50105 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 4 q^{2} - 13 q^{3} + 10 q^{4} + 12 q^{5} - 4 q^{6} + 13 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 4 * q^2 - 13 * q^3 + 10 * q^4 + 12 * q^5 - 4 * q^6 + 13 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 4 q^{2} - 13 q^{3} + 10 q^{4} + 12 q^{5} - 4 q^{6} + 13 q^{7} + 9 q^{8} + 13 q^{9} + 6 q^{10} + 3 q^{11} - 10 q^{12} + 21 q^{13} + 4 q^{14} - 12 q^{15} + 8 q^{16} + 17 q^{17} + 4 q^{18} + 5 q^{19} + 29 q^{20} - 13 q^{21} + q^{22} + 4 q^{23} - 9 q^{24} + q^{25} + 22 q^{26} - 13 q^{27} + 10 q^{28} + 21 q^{29} - 6 q^{30} - 7 q^{31} + 12 q^{32} - 3 q^{33} + 2 q^{34} + 12 q^{35} + 10 q^{36} + 7 q^{37} - 9 q^{38} - 21 q^{39} + 29 q^{40} + 21 q^{41} - 4 q^{42} - 9 q^{43} - 2 q^{44} + 12 q^{45} - 28 q^{46} + 23 q^{47} - 8 q^{48} + 13 q^{49} + 15 q^{50} - 17 q^{51} + 15 q^{52} + 31 q^{53} - 4 q^{54} - 8 q^{55} + 9 q^{56} - 5 q^{57} - 25 q^{58} + 28 q^{59} - 29 q^{60} + 29 q^{61} - 3 q^{62} + 13 q^{63} + 9 q^{64} + 30 q^{65} - q^{66} - 18 q^{67} + 34 q^{68} - 4 q^{69} + 6 q^{70} + 10 q^{71} + 9 q^{72} + 24 q^{73} - 19 q^{74} - q^{75} + 3 q^{77} - 22 q^{78} - 28 q^{79} + 26 q^{80} + 13 q^{81} + 18 q^{82} + 26 q^{83} - 10 q^{84} + 20 q^{85} - 2 q^{86} - 21 q^{87} - 17 q^{88} + 44 q^{89} + 6 q^{90} + 21 q^{91} + 6 q^{92} + 7 q^{93} - 9 q^{94} - 2 q^{95} - 12 q^{96} + 17 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 - 13 * q^3 + 10 * q^4 + 12 * q^5 - 4 * q^6 + 13 * q^7 + 9 * q^8 + 13 * q^9 + 6 * q^10 + 3 * q^11 - 10 * q^12 + 21 * q^13 + 4 * q^14 - 12 * q^15 + 8 * q^16 + 17 * q^17 + 4 * q^18 + 5 * q^19 + 29 * q^20 - 13 * q^21 + q^22 + 4 * q^23 - 9 * q^24 + q^25 + 22 * q^26 - 13 * q^27 + 10 * q^28 + 21 * q^29 - 6 * q^30 - 7 * q^31 + 12 * q^32 - 3 * q^33 + 2 * q^34 + 12 * q^35 + 10 * q^36 + 7 * q^37 - 9 * q^38 - 21 * q^39 + 29 * q^40 + 21 * q^41 - 4 * q^42 - 9 * q^43 - 2 * q^44 + 12 * q^45 - 28 * q^46 + 23 * q^47 - 8 * q^48 + 13 * q^49 + 15 * q^50 - 17 * q^51 + 15 * q^52 + 31 * q^53 - 4 * q^54 - 8 * q^55 + 9 * q^56 - 5 * q^57 - 25 * q^58 + 28 * q^59 - 29 * q^60 + 29 * q^61 - 3 * q^62 + 13 * q^63 + 9 * q^64 + 30 * q^65 - q^66 - 18 * q^67 + 34 * q^68 - 4 * q^69 + 6 * q^70 + 10 * q^71 + 9 * q^72 + 24 * q^73 - 19 * q^74 - q^75 + 3 * q^77 - 22 * q^78 - 28 * q^79 + 26 * q^80 + 13 * q^81 + 18 * q^82 + 26 * q^83 - 10 * q^84 + 20 * q^85 - 2 * q^86 - 21 * q^87 - 17 * q^88 + 44 * q^89 + 6 * q^90 + 21 * q^91 + 6 * q^92 + 7 * q^93 - 9 * q^94 - 2 * q^95 - 12 * q^96 + 17 * q^97 + 4 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.70878	1.91539	0.957697	−	0.287777i	$-0.0929163\pi$
$2$	2.70878	1.91539	0.957697	+	0.287777i	$0.0929163\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.33747	2.66874
$5$	2.87857	1.28734	0.643668	−	0.765305i	$-0.277412\pi$
$5$	2.87857	1.28734	0.643668	+	0.765305i	$0.277412\pi$
$6$	−2.70878	−1.10585
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	9.04047	3.19629
$9$	1.00000	0.333333
$10$	7.79741	2.46576
$11$	−1.50105	−0.452584	−0.226292	−	0.974060i	$-0.572660\pi$
$11$	−1.50105	−0.452584	−0.226292	+	0.974060i	$0.572660\pi$
$12$	−5.33747	−1.54080
$13$	5.43745	1.50808	0.754039	−	0.656830i	$-0.228103\pi$
$13$	5.43745	1.50808	0.754039	+	0.656830i	$0.228103\pi$
$14$	2.70878	0.723951
$15$	−2.87857	−0.743244
$16$	13.8137	3.45342
$17$	1.68422	0.408484	0.204242	−	0.978920i	$-0.434527\pi$
$17$	1.68422	0.408484	0.204242	+	0.978920i	$0.434527\pi$
$18$	2.70878	0.638465
$19$	−3.30288	−0.757733	−0.378867	−	0.925451i	$-0.623686\pi$
$19$	−3.30288	−0.757733	−0.378867	+	0.925451i	$0.623686\pi$
$20$	15.3643	3.43556
$21$	−1.00000	−0.218218
$22$	−4.06601	−0.866877
$23$	−5.07189	−1.05756	−0.528781	−	0.848758i	$-0.677351\pi$
$23$	−5.07189	−1.05756	−0.528781	+	0.848758i	$0.677351\pi$
$24$	−9.04047	−1.84538
$25$	3.28617	0.657235
$26$	14.7288	2.88856
$27$	−1.00000	−0.192450
$28$	5.33747	1.00869
$29$	−8.28010	−1.53758	−0.768788	−	0.639504i	$-0.779140\pi$
$29$	−8.28010	−1.53758	−0.768788	+	0.639504i	$0.779140\pi$
$30$	−7.79741	−1.42361
$31$	−9.29635	−1.66967	−0.834837	−	0.550498i	$-0.814438\pi$
$31$	−9.29635	−1.66967	−0.834837	+	0.550498i	$0.814438\pi$
$32$	19.3372	3.41837
$33$	1.50105	0.261299
$34$	4.56218	0.782408
$35$	2.87857	0.486567
$36$	5.33747	0.889579
$37$	−7.22083	−1.18710	−0.593548	−	0.804798i	$-0.702273\pi$
$37$	−7.22083	−1.18710	−0.593548	+	0.804798i	$0.702273\pi$
$38$	−8.94677	−1.45136
$39$	−5.43745	−0.870689
$40$	26.0237	4.11470
$41$	−2.03090	−0.317173	−0.158586	−	0.987345i	$-0.550694\pi$
$41$	−2.03090	−0.317173	−0.158586	+	0.987345i	$0.550694\pi$
$42$	−2.70878	−0.417973
$43$	0.859629	0.131092	0.0655461	−	0.997850i	$-0.479121\pi$
$43$	0.859629	0.131092	0.0655461	+	0.997850i	$0.479121\pi$
$44$	−8.01182	−1.20783
$45$	2.87857	0.429112
$46$	−13.7386	−2.02565
$47$	−6.92288	−1.00981	−0.504903	−	0.863176i	$-0.668472\pi$
$47$	−6.92288	−1.00981	−0.504903	+	0.863176i	$0.668472\pi$
$48$	−13.8137	−1.99383
$49$	1.00000	0.142857
$50$	8.90151	1.25886
$51$	−1.68422	−0.235838
$52$	29.0223	4.02466
$53$	8.32870	1.14404	0.572018	−	0.820241i	$-0.306161\pi$
$53$	8.32870	1.14404	0.572018	+	0.820241i	$0.306161\pi$
$54$	−2.70878	−0.368618
$55$	−4.32088	−0.582628
$56$	9.04047	1.20808
$57$	3.30288	0.437477
$58$	−22.4289	−2.94506
$59$	8.94067	1.16398	0.581988	−	0.813197i	$-0.302275\pi$
$59$	8.94067	1.16398	0.581988	+	0.813197i	$0.302275\pi$
$60$	−15.3643	−1.98352
$61$	9.99896	1.28024	0.640118	−	0.768277i	$-0.278886\pi$
$61$	9.99896	1.28024	0.640118	+	0.768277i	$0.278886\pi$
$62$	−25.1817	−3.19808
$63$	1.00000	0.125988
$64$	24.7529	3.09411
$65$	15.6521	1.94140
$66$	4.06601	0.500491
$67$	−15.7116	−1.91947	−0.959736	−	0.280903i	$-0.909366\pi$
$67$	−15.7116	−1.91947	−0.959736	+	0.280903i	$0.909366\pi$
$68$	8.98949	1.09014
$69$	5.07189	0.610584
$70$	7.79741	0.931969
$71$	5.53761	0.657194	0.328597	−	0.944470i	$-0.393424\pi$
$71$	5.53761	0.657194	0.328597	+	0.944470i	$0.393424\pi$
$72$	9.04047	1.06543
$73$	6.56437	0.768302	0.384151	−	0.923270i	$-0.374494\pi$
$73$	6.56437	0.768302	0.384151	+	0.923270i	$0.374494\pi$
$74$	−19.5596	−2.27376
$75$	−3.28617	−0.379455
$76$	−17.6290	−2.02219
$77$	−1.50105	−0.171061
$78$	−14.7288	−1.66771
$79$	−9.27964	−1.04404	−0.522021	−	0.852933i	$-0.674822\pi$
$79$	−9.27964	−1.04404	−0.522021	+	0.852933i	$0.674822\pi$
$80$	39.7637	4.44571
$81$	1.00000	0.111111
$82$	−5.50124	−0.607511
$83$	7.17857	0.787950	0.393975	−	0.919121i	$-0.371100\pi$
$83$	7.17857	0.787950	0.393975	+	0.919121i	$0.371100\pi$
$84$	−5.33747	−0.582366
$85$	4.84815	0.525856
$86$	2.32854	0.251093
$87$	8.28010	0.887720
$88$	−13.5702	−1.44659
$89$	9.76491	1.03508	0.517539	−	0.855660i	$-0.326848\pi$
$89$	9.76491	1.03508	0.517539	+	0.855660i	$0.326848\pi$
$90$	7.79741	0.821919
$91$	5.43745	0.570000
$92$	−27.0711	−2.82235
$93$	9.29635	0.963986
$94$	−18.7525	−1.93418
$95$	−9.50758	−0.975457
$96$	−19.3372	−1.97360
$97$	−9.08877	−0.922825	−0.461412	−	0.887186i	$-0.652657\pi$
$97$	−9.08877	−0.922825	−0.461412	+	0.887186i	$0.652657\pi$
$98$	2.70878	0.273628
$99$	−1.50105	−0.150861
$100$	17.5399	1.75399
$101$	−2.25398	−0.224279	−0.112140	−	0.993692i	$-0.535770\pi$
$101$	−2.25398	−0.224279	−0.112140	+	0.993692i	$0.535770\pi$
$102$	−4.56218	−0.451723
$103$	17.1074	1.68564	0.842820	−	0.538195i	$-0.180894\pi$
$103$	17.1074	1.68564	0.842820	+	0.538195i	$0.180894\pi$
$104$	49.1571	4.82025
$105$	−2.87857	−0.280920
$106$	22.5606	2.19128
$107$	−3.37485	−0.326259	−0.163130	−	0.986605i	$-0.552159\pi$
$107$	−3.37485	−0.326259	−0.163130	+	0.986605i	$0.552159\pi$
$108$	−5.33747	−0.513599
$109$	8.18665	0.784139	0.392069	−	0.919936i	$-0.371759\pi$
$109$	8.18665	0.784139	0.392069	+	0.919936i	$0.371759\pi$
$110$	−11.7043	−1.11596
$111$	7.22083	0.685371
$112$	13.8137	1.30527
$113$	−13.4635	−1.26654	−0.633269	−	0.773932i	$-0.718287\pi$
$113$	−13.4635	−1.26654	−0.633269	+	0.773932i	$0.718287\pi$
$114$	8.94677	0.837942
$115$	−14.5998	−1.36144
$116$	−44.1948	−4.10338
$117$	5.43745	0.502693
$118$	24.2183	2.22947
$119$	1.68422	0.154392
$120$	−26.0237	−2.37562
$121$	−8.74685	−0.795168
$122$	27.0850	2.45216
$123$	2.03090	0.183120
$124$	−49.6190	−4.45592
$125$	−4.93337	−0.441254
$126$	2.70878	0.241317
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	28.3756	2.50808
$129$	−0.859629	−0.0756861
$130$	42.3980	3.71855
$131$	−0.496098	−0.0433443	−0.0216721	−	0.999765i	$-0.506899\pi$
$131$	−0.496098	−0.0433443	−0.0216721	+	0.999765i	$0.506899\pi$
$132$	8.01182	0.697339
$133$	−3.30288	−0.286396
$134$	−42.5591	−3.67655
$135$	−2.87857	−0.247748
$136$	15.2262	1.30563
$137$	20.7815	1.77548	0.887741	−	0.460343i	$-0.152274\pi$
$137$	20.7815	1.77548	0.887741	+	0.460343i	$0.152274\pi$
$138$	13.7386	1.16951
$139$	0.210195	0.0178285	0.00891424	−	0.999960i	$-0.497162\pi$
$139$	0.210195	0.0178285	0.00891424	+	0.999960i	$0.497162\pi$
$140$	15.3643	1.29852
$141$	6.92288	0.583012
$142$	15.0002	1.25879
$143$	−8.16189	−0.682531
$144$	13.8137	1.15114
$145$	−23.8349	−1.97938
$146$	17.7814	1.47160
$147$	−1.00000	−0.0824786
$148$	−38.5410	−3.16805
$149$	−9.61526	−0.787713	−0.393857	−	0.919172i	$-0.628859\pi$
$149$	−9.61526	−0.787713	−0.393857	+	0.919172i	$0.628859\pi$
$150$	−8.90151	−0.726806
$151$	4.39942	0.358020	0.179010	−	0.983847i	$-0.442711\pi$
$151$	4.39942	0.358020	0.179010	+	0.983847i	$0.442711\pi$
$152$	−29.8596	−2.42194
$153$	1.68422	0.136161
$154$	−4.06601	−0.327649
$155$	−26.7602	−2.14943
$156$	−29.0223	−2.32364
$157$	−1.08882	−0.0868971	−0.0434486	−	0.999056i	$-0.513834\pi$
$157$	−1.08882	−0.0868971	−0.0434486	+	0.999056i	$0.513834\pi$
$158$	−25.1365	−1.99975
$159$	−8.32870	−0.660509
$160$	55.6636	4.40060
$161$	−5.07189	−0.399721
$162$	2.70878	0.212822
$163$	−13.7282	−1.07528	−0.537638	−	0.843176i	$-0.680683\pi$
$163$	−13.7282	−1.07528	−0.537638	+	0.843176i	$0.680683\pi$
$164$	−10.8398	−0.846450
$165$	4.32088	0.336380
$166$	19.4451	1.50924
$167$	10.7070	0.828536	0.414268	−	0.910155i	$-0.364038\pi$
$167$	10.7070	0.828536	0.414268	+	0.910155i	$0.364038\pi$
$168$	−9.04047	−0.697488
$169$	16.5659	1.27430
$170$	13.1326	1.00722
$171$	−3.30288	−0.252578
$172$	4.58825	0.349851
$173$	−5.28100	−0.401507	−0.200754	−	0.979642i	$-0.564339\pi$
$173$	−5.28100	−0.401507	−0.200754	+	0.979642i	$0.564339\pi$
$174$	22.4289	1.70033
$175$	3.28617	0.248411
$176$	−20.7350	−1.56296
$177$	−8.94067	−0.672022
$178$	26.4510	1.98258
$179$	−3.05114	−0.228053	−0.114026	−	0.993478i	$-0.536375\pi$
$179$	−3.05114	−0.228053	−0.114026	+	0.993478i	$0.536375\pi$
$180$	15.3643	1.14519
$181$	19.8363	1.47442	0.737209	−	0.675664i	$-0.236143\pi$
$181$	19.8363	1.47442	0.737209	+	0.675664i	$0.236143\pi$
$182$	14.7288	1.09177
$183$	−9.99896	−0.739144
$184$	−45.8523	−3.38027
$185$	−20.7857	−1.52819
$186$	25.1817	1.84641
$187$	−2.52810	−0.184873
$188$	−36.9507	−2.69491
$189$	−1.00000	−0.0727393
$190$	−25.7539	−1.86839
$191$	26.8779	1.94482	0.972410	−	0.233280i	$-0.0749459\pi$
$191$	26.8779	1.94482	0.972410	+	0.233280i	$0.0749459\pi$
$192$	−24.7529	−1.78639
$193$	11.4021	0.820739	0.410369	−	0.911919i	$-0.365400\pi$
$193$	11.4021	0.820739	0.410369	+	0.911919i	$0.365400\pi$
$194$	−24.6194	−1.76757
$195$	−15.6521	−1.12087
$196$	5.33747	0.381248
$197$	−11.0512	−0.787368	−0.393684	−	0.919246i	$-0.628800\pi$
$197$	−11.0512	−0.787368	−0.393684	+	0.919246i	$0.628800\pi$
$198$	−4.06601	−0.288959
$199$	4.37619	0.310220	0.155110	−	0.987897i	$-0.450427\pi$
$199$	4.37619	0.310220	0.155110	+	0.987897i	$0.450427\pi$
$200$	29.7086	2.10071
$201$	15.7116	1.10821
$202$	−6.10553	−0.429583
$203$	−8.28010	−0.581149
$204$	−8.98949	−0.629390
$205$	−5.84608	−0.408308
$206$	46.3401	3.22867
$207$	−5.07189	−0.352521
$208$	75.1112	5.20803
$209$	4.95779	0.342938
$210$	−7.79741	−0.538072
$211$	−4.47388	−0.307994	−0.153997	−	0.988071i	$-0.549215\pi$
$211$	−4.47388	−0.307994	−0.153997	+	0.988071i	$0.549215\pi$
$212$	44.4542	3.05313
$213$	−5.53761	−0.379431
$214$	−9.14172	−0.624915
$215$	2.47450	0.168760
$216$	−9.04047	−0.615126
$217$	−9.29635	−0.631077
$218$	22.1758	1.50193
$219$	−6.56437	−0.443579
$220$	−23.0626	−1.55488
$221$	9.15787	0.616025
$222$	19.5596	1.31276
$223$	24.4884	1.63986	0.819932	−	0.572461i	$-0.194011\pi$
$223$	24.4884	1.63986	0.819932	+	0.572461i	$0.194011\pi$
$224$	19.3372	1.29202
$225$	3.28617	0.219078
$226$	−36.4696	−2.42592
$227$	−0.513152	−0.0340591	−0.0170296	−	0.999855i	$-0.505421\pi$
$227$	−0.513152	−0.0340591	−0.0170296	+	0.999855i	$0.505421\pi$
$228$	17.6290	1.16751
$229$	−19.6982	−1.30169	−0.650847	−	0.759209i	$-0.725586\pi$
$229$	−19.6982	−1.30169	−0.650847	+	0.759209i	$0.725586\pi$
$230$	−39.5476	−2.60769
$231$	1.50105	0.0987619
$232$	−74.8560	−4.91454
$233$	−1.36091	−0.0891564	−0.0445782	−	0.999006i	$-0.514194\pi$
$233$	−1.36091	−0.0891564	−0.0445782	+	0.999006i	$0.514194\pi$
$234$	14.7288	0.962855
$235$	−19.9280	−1.29996
$236$	47.7206	3.10635
$237$	9.27964	0.602777
$238$	4.56218	0.295722
$239$	25.4879	1.64867	0.824336	−	0.566100i	$-0.191549\pi$
$239$	25.4879	1.64867	0.824336	+	0.566100i	$0.191549\pi$
$240$	−39.7637	−2.56673
$241$	23.9835	1.54492	0.772458	−	0.635066i	$-0.219027\pi$
$241$	23.9835	1.54492	0.772458	+	0.635066i	$0.219027\pi$
$242$	−23.6933	−1.52306
$243$	−1.00000	−0.0641500
$244$	53.3692	3.41661
$245$	2.87857	0.183905
$246$	5.50124	0.350746
$247$	−17.9593	−1.14272
$248$	−84.0434	−5.33676
$249$	−7.17857	−0.454923
$250$	−13.3634	−0.845176
$251$	10.4969	0.662558	0.331279	−	0.943533i	$-0.392520\pi$
$251$	10.4969	0.662558	0.331279	+	0.943533i	$0.392520\pi$
$252$	5.33747	0.336229
$253$	7.61316	0.478635
$254$	−2.70878	−0.169964
$255$	−4.84815	−0.303603
$256$	27.3575	1.70984
$257$	3.96662	0.247431	0.123716	−	0.992318i	$-0.460519\pi$
$257$	3.96662	0.247431	0.123716	+	0.992318i	$0.460519\pi$
$258$	−2.32854	−0.144969
$259$	−7.22083	−0.448680
$260$	83.5426	5.18109
$261$	−8.28010	−0.512525
$262$	−1.34382	−0.0830214
$263$	−5.02765	−0.310018	−0.155009	−	0.987913i	$-0.549541\pi$
$263$	−5.02765	−0.310018	−0.155009	+	0.987913i	$0.549541\pi$
$264$	13.5702	0.835189
$265$	23.9748	1.47276
$266$	−8.94677	−0.548562
$267$	−9.76491	−0.597603
$268$	−83.8600	−5.12257
$269$	16.7702	1.02250	0.511249	−	0.859432i	$-0.329183\pi$
$269$	16.7702	1.02250	0.511249	+	0.859432i	$0.329183\pi$
$270$	−7.79741	−0.474535
$271$	−24.8503	−1.50955	−0.754773	−	0.655986i	$-0.772253\pi$
$271$	−24.8503	−1.50955	−0.754773	+	0.655986i	$0.772253\pi$
$272$	23.2653	1.41067
$273$	−5.43745	−0.329090
$274$	56.2924	3.40075
$275$	−4.93271	−0.297454
$276$	27.0711	1.62949
$277$	−5.45207	−0.327583	−0.163791	−	0.986495i	$-0.552372\pi$
$277$	−5.45207	−0.327583	−0.163791	+	0.986495i	$0.552372\pi$
$278$	0.569371	0.0341486
$279$	−9.29635	−0.556558
$280$	26.0237	1.55521
$281$	−9.96730	−0.594600	−0.297300	−	0.954784i	$-0.596086\pi$
$281$	−9.96730	−0.594600	−0.297300	+	0.954784i	$0.596086\pi$
$282$	18.7525	1.11670
$283$	−6.38116	−0.379320	−0.189660	−	0.981850i	$-0.560739\pi$
$283$	−6.38116	−0.379320	−0.189660	+	0.981850i	$0.560739\pi$
$284$	29.5569	1.75388
$285$	9.50758	0.563181
$286$	−22.1087	−1.30732
$287$	−2.03090	−0.119880
$288$	19.3372	1.13946
$289$	−14.1634	−0.833141
$290$	−64.5633	−3.79129
$291$	9.08877	0.532793
$292$	35.0372	2.05040
$293$	−26.0774	−1.52346	−0.761728	−	0.647896i	$-0.775649\pi$
$293$	−26.0774	−1.52346	−0.761728	+	0.647896i	$0.775649\pi$
$294$	−2.70878	−0.157979
$295$	25.7364	1.49843
$296$	−65.2797	−3.79431
$297$	1.50105	0.0870998
$298$	−26.0456	−1.50878
$299$	−27.5781	−1.59489
$300$	−17.5399	−1.01266
$301$	0.859629	0.0495482
$302$	11.9171	0.685750
$303$	2.25398	0.129488
$304$	−45.6250	−2.61677
$305$	28.7827	1.64809
$306$	4.56218	0.260803
$307$	−6.03900	−0.344664	−0.172332	−	0.985039i	$-0.555130\pi$
$307$	−6.03900	−0.344664	−0.172332	+	0.985039i	$0.555130\pi$
$308$	−8.01182	−0.456516
$309$	−17.1074	−0.973205
$310$	−72.4874	−4.11701
$311$	−27.0222	−1.53229	−0.766144	−	0.642669i	$-0.777827\pi$
$311$	−27.0222	−1.53229	−0.766144	+	0.642669i	$0.777827\pi$
$312$	−49.1571	−2.78297
$313$	−24.2532	−1.37087	−0.685435	−	0.728134i	$-0.740388\pi$
$313$	−24.2532	−1.37087	−0.685435	+	0.728134i	$0.740388\pi$
$314$	−2.94937	−0.166442
$315$	2.87857	0.162189
$316$	−49.5298	−2.78627
$317$	8.83443	0.496191	0.248095	−	0.968736i	$-0.420195\pi$
$317$	8.83443	0.496191	0.248095	+	0.968736i	$0.420195\pi$
$318$	−22.5606	−1.26514
$319$	12.4288	0.695882
$320$	71.2530	3.98317
$321$	3.37485	0.188366
$322$	−13.7386	−0.765623
$323$	−5.56279	−0.309522
$324$	5.33747	0.296526
$325$	17.8684	0.991161
$326$	−37.1867	−2.05958
$327$	−8.18665	−0.452723
$328$	−18.3603	−1.01378
$329$	−6.92288	−0.381671
$330$	11.7043	0.644301
$331$	−16.9974	−0.934261	−0.467130	−	0.884188i	$-0.654712\pi$
$331$	−16.9974	−0.934261	−0.467130	+	0.884188i	$0.654712\pi$
$332$	38.3154	2.10283
$333$	−7.22083	−0.395699
$334$	29.0030	1.58697
$335$	−45.2268	−2.47101
$336$	−13.8137	−0.753598
$337$	12.4361	0.677435	0.338718	−	0.940888i	$-0.390007\pi$
$337$	12.4361	0.677435	0.338718	+	0.940888i	$0.390007\pi$
$338$	44.8733	2.44078
$339$	13.4635	0.731236
$340$	25.8769	1.40337
$341$	13.9543	0.755667
$342$	−8.94677	−0.483786
$343$	1.00000	0.0539949
$344$	7.77146	0.419009
$345$	14.5998	0.786027
$346$	−14.3051	−0.769045
$347$	10.2559	0.550567	0.275283	−	0.961363i	$-0.411228\pi$
$347$	10.2559	0.550567	0.275283	+	0.961363i	$0.411228\pi$
$348$	44.1948	2.36909
$349$	28.0536	1.50167	0.750836	−	0.660488i	$-0.229651\pi$
$349$	28.0536	1.50167	0.750836	+	0.660488i	$0.229651\pi$
$350$	8.90151	0.475806
$351$	−5.43745	−0.290230
$352$	−29.0262	−1.54710
$353$	−0.120411	−0.00640881	−0.00320440	−	0.999995i	$-0.501020\pi$
$353$	−0.120411	−0.00640881	−0.00320440	+	0.999995i	$0.501020\pi$
$354$	−24.2183	−1.28719
$355$	15.9404	0.846029
$356$	52.1199	2.76235
$357$	−1.68422	−0.0891385
$358$	−8.26485	−0.436811
$359$	15.5091	0.818542	0.409271	−	0.912413i	$-0.365783\pi$
$359$	15.5091	0.818542	0.409271	+	0.912413i	$0.365783\pi$
$360$	26.0237	1.37157
$361$	−8.09097	−0.425840
$362$	53.7320	2.82409
$363$	8.74685	0.459090
$364$	29.0223	1.52118
$365$	18.8960	0.989063
$366$	−27.0850	−1.41575
$367$	0.278621	0.0145439	0.00727195	−	0.999974i	$-0.497685\pi$
$367$	0.278621	0.0145439	0.00727195	+	0.999974i	$0.497685\pi$
$368$	−70.0615	−3.65221
$369$	−2.03090	−0.105724
$370$	−56.3038	−2.92709
$371$	8.32870	0.432405
$372$	49.6190	2.57263
$373$	25.5201	1.32138	0.660691	−	0.750658i	$-0.270263\pi$
$373$	25.5201	1.32138	0.660691	+	0.750658i	$0.270263\pi$
$374$	−6.84807	−0.354105
$375$	4.93337	0.254758
$376$	−62.5861	−3.22763
$377$	−45.0226	−2.31878
$378$	−2.70878	−0.139324
$379$	−10.1849	−0.523161	−0.261580	−	0.965182i	$-0.584244\pi$
$379$	−10.1849	−0.523161	−0.261580	+	0.965182i	$0.584244\pi$
$380$	−50.7465	−2.60324
$381$	1.00000	0.0512316
$382$	72.8063	3.72510
$383$	−27.7594	−1.41844	−0.709220	−	0.704987i	$-0.750953\pi$
$383$	−27.7594	−1.41844	−0.709220	+	0.704987i	$0.750953\pi$
$384$	−28.3756	−1.44804
$385$	−4.32088	−0.220213
$386$	30.8857	1.57204
$387$	0.859629	0.0436974
$388$	−48.5111	−2.46278
$389$	26.1982	1.32830	0.664151	−	0.747598i	$-0.268793\pi$
$389$	26.1982	1.32830	0.664151	+	0.747598i	$0.268793\pi$
$390$	−42.3980	−2.14691
$391$	−8.54219	−0.431997
$392$	9.04047	0.456613
$393$	0.496098	0.0250248
$394$	−29.9353	−1.50812
$395$	−26.7121	−1.34403
$396$	−8.01182	−0.402609
$397$	8.93868	0.448620	0.224310	−	0.974518i	$-0.427987\pi$
$397$	8.93868	0.448620	0.224310	+	0.974518i	$0.427987\pi$
$398$	11.8541	0.594193
$399$	3.30288	0.165351
$400$	45.3942	2.26971
$401$	−35.2875	−1.76217	−0.881086	−	0.472956i	$-0.843187\pi$
$401$	−35.2875	−1.76217	−0.881086	+	0.472956i	$0.843187\pi$
$402$	42.5591	2.12266
$403$	−50.5484	−2.51800
$404$	−12.0306	−0.598542
$405$	2.87857	0.143037
$406$	−22.4289	−1.11313
$407$	10.8388	0.537261
$408$	−15.2262	−0.753807
$409$	−6.33933	−0.313460	−0.156730	−	0.987642i	$-0.550095\pi$
$409$	−6.33933	−0.313460	−0.156730	+	0.987642i	$0.550095\pi$
$410$	−15.8357	−0.782070
$411$	−20.7815	−1.02507
$412$	91.3102	4.49853
$413$	8.94067	0.439942
$414$	−13.7386	−0.675216
$415$	20.6640	1.01436
$416$	105.145	5.15517
$417$	−0.210195	−0.0102933
$418$	13.4296	0.656861
$419$	36.2997	1.77335	0.886677	−	0.462388i	$-0.153007\pi$
$419$	36.2997	1.77335	0.886677	+	0.462388i	$0.153007\pi$
$420$	−15.3643	−0.749701
$421$	−8.45931	−0.412282	−0.206141	−	0.978522i	$-0.566091\pi$
$421$	−8.45931	−0.412282	−0.206141	+	0.978522i	$0.566091\pi$
$422$	−12.1187	−0.589931
$423$	−6.92288	−0.336602
$424$	75.2954	3.65667
$425$	5.53465	0.268470
$426$	−15.0002	−0.726760
$427$	9.99896	0.483884
$428$	−18.0132	−0.870700
$429$	8.16189	0.394060
$430$	6.70288	0.323242
$431$	−29.6930	−1.43026	−0.715130	−	0.698991i	$-0.753633\pi$
$431$	−29.6930	−1.43026	−0.715130	+	0.698991i	$0.753633\pi$
$432$	−13.8137	−0.664611
$433$	29.0121	1.39423	0.697116	−	0.716958i	$-0.254466\pi$
$433$	29.0121	1.39423	0.697116	+	0.716958i	$0.254466\pi$
$434$	−25.1817	−1.20876
$435$	23.8349	1.14279
$436$	43.6960	2.09266
$437$	16.7519	0.801350
$438$	−17.7814	−0.849630
$439$	−15.1917	−0.725058	−0.362529	−	0.931972i	$-0.618087\pi$
$439$	−15.1917	−0.725058	−0.362529	+	0.931972i	$0.618087\pi$
$440$	−39.0628	−1.86225
$441$	1.00000	0.0476190
$442$	24.8066	1.17993
$443$	21.9474	1.04275	0.521377	−	0.853327i	$-0.325419\pi$
$443$	21.9474	1.04275	0.521377	+	0.853327i	$0.325419\pi$
$444$	38.5410	1.82907
$445$	28.1090	1.33249
$446$	66.3336	3.14099
$447$	9.61526	0.454786
$448$	24.7529	1.16947
$449$	10.5308	0.496979	0.248490	−	0.968635i	$-0.420066\pi$
$449$	10.5308	0.496979	0.248490	+	0.968635i	$0.420066\pi$
$450$	8.90151	0.419621
$451$	3.04848	0.143547
$452$	−71.8610	−3.38006
$453$	−4.39942	−0.206703
$454$	−1.39002	−0.0652366
$455$	15.6521	0.733781
$456$	29.8596	1.39830
$457$	−26.7062	−1.24926	−0.624632	−	0.780920i	$-0.714751\pi$
$457$	−26.7062	−1.24926	−0.624632	+	0.780920i	$0.714751\pi$
$458$	−53.3580	−2.49326
$459$	−1.68422	−0.0786127
$460$	−77.9260	−3.63332
$461$	5.08320	0.236748	0.118374	−	0.992969i	$-0.462232\pi$
$461$	5.08320	0.236748	0.118374	+	0.992969i	$0.462232\pi$
$462$	4.06601	0.189168
$463$	−2.56483	−0.119198	−0.0595988	−	0.998222i	$-0.518982\pi$
$463$	−2.56483	−0.119198	−0.0595988	+	0.998222i	$0.518982\pi$
$464$	−114.379	−5.30990
$465$	26.7602	1.24097
$466$	−3.68641	−0.170770
$467$	−38.3764	−1.77585	−0.887925	−	0.459989i	$-0.847853\pi$
$467$	−38.3764	−1.77585	−0.887925	+	0.459989i	$0.847853\pi$
$468$	29.0223	1.34155
$469$	−15.7116	−0.725492
$470$	−53.9805	−2.48994
$471$	1.08882	0.0501701
$472$	80.8279	3.72041
$473$	−1.29035	−0.0593302
$474$	25.1365	1.15456
$475$	−10.8538	−0.498009
$476$	8.98949	0.412033
$477$	8.32870	0.381345
$478$	69.0409	3.15786
$479$	−9.38202	−0.428675	−0.214338	−	0.976760i	$-0.568759\pi$
$479$	−9.38202	−0.428675	−0.214338	+	0.976760i	$0.568759\pi$
$480$	−55.6636	−2.54069
$481$	−39.2629	−1.79023
$482$	64.9661	2.95912
$483$	5.07189	0.230779
$484$	−46.6861	−2.12209
$485$	−26.1627	−1.18799
$486$	−2.70878	−0.122873
$487$	30.0828	1.36318	0.681591	−	0.731733i	$-0.261288\pi$
$487$	30.0828	1.36318	0.681591	+	0.731733i	$0.261288\pi$
$488$	90.3953	4.09200
$489$	13.7282	0.620811
$490$	7.79741	0.352251
$491$	39.3902	1.77765	0.888827	−	0.458244i	$-0.151521\pi$
$491$	39.3902	1.77765	0.888827	+	0.458244i	$0.151521\pi$
$492$	10.8398	0.488698
$493$	−13.9455	−0.628075
$494$	−48.6476	−2.18876
$495$	−4.32088	−0.194209
$496$	−128.417	−5.76609
$497$	5.53761	0.248396
$498$	−19.4451	−0.871357
$499$	19.4929	0.872624	0.436312	−	0.899795i	$-0.356284\pi$
$499$	19.4929	0.872624	0.436312	+	0.899795i	$0.356284\pi$
$500$	−26.3317	−1.17759
$501$	−10.7070	−0.478355
$502$	28.4337	1.26906
$503$	−25.0033	−1.11484	−0.557421	−	0.830230i	$-0.688209\pi$
$503$	−25.0033	−1.11484	−0.557421	+	0.830230i	$0.688209\pi$
$504$	9.04047	0.402695
$505$	−6.48824	−0.288723
$506$	20.6224	0.916776
$507$	−16.5659	−0.735716
$508$	−5.33747	−0.236812
$509$	0.817857	0.0362509	0.0181254	−	0.999836i	$-0.494230\pi$
$509$	0.817857	0.0362509	0.0181254	+	0.999836i	$0.494230\pi$
$510$	−13.1326	−0.581520
$511$	6.56437	0.290391
$512$	17.3540	0.766947
$513$	3.30288	0.145826
$514$	10.7447	0.473928
$515$	49.2448	2.16999
$516$	−4.58825	−0.201986
$517$	10.3916	0.457022
$518$	−19.5596	−0.859400
$519$	5.28100	0.231810
$520$	141.502	6.20529
$521$	23.7258	1.03945	0.519723	−	0.854335i	$-0.326035\pi$
$521$	23.7258	1.03945	0.519723	+	0.854335i	$0.326035\pi$
$522$	−22.4289	−0.981688
$523$	−12.8646	−0.562530	−0.281265	−	0.959630i	$-0.590754\pi$
$523$	−12.8646	−0.562530	−0.281265	+	0.959630i	$0.590754\pi$
$524$	−2.64791	−0.115674
$525$	−3.28617	−0.143420
$526$	−13.6188	−0.593807
$527$	−15.6571	−0.682035
$528$	20.7350	0.902377
$529$	2.72405	0.118437
$530$	64.9423	2.82091
$531$	8.94067	0.387992
$532$	−17.6290	−0.764316
$533$	−11.0429	−0.478321
$534$	−26.4510	−1.14464
$535$	−9.71475	−0.420005
$536$	−142.040	−6.13519
$537$	3.05114	0.131666
$538$	45.4268	1.95849
$539$	−1.50105	−0.0646548
$540$	−15.3643	−0.661174
$541$	−27.7136	−1.19150	−0.595751	−	0.803170i	$-0.703145\pi$
$541$	−27.7136	−1.19150	−0.595751	+	0.803170i	$0.703145\pi$
$542$	−67.3139	−2.89138
$543$	−19.8363	−0.851256
$544$	32.5682	1.39635
$545$	23.5658	1.00945
$546$	−14.7288	−0.630336
$547$	41.1078	1.75764	0.878821	−	0.477152i	$-0.158331\pi$
$547$	41.1078	1.75764	0.878821	+	0.477152i	$0.158331\pi$
$548$	110.921	4.73829
$549$	9.99896	0.426745
$550$	−13.3616	−0.569742
$551$	27.3482	1.16507
$552$	45.8523	1.95160
$553$	−9.27964	−0.394610
$554$	−14.7684	−0.627451
$555$	20.7857	0.882303
$556$	1.12191	0.0475795
$557$	−1.86702	−0.0791083	−0.0395541	−	0.999217i	$-0.512594\pi$
$557$	−1.86702	−0.0791083	−0.0395541	+	0.999217i	$0.512594\pi$
$558$	−25.1817	−1.06603
$559$	4.67419	0.197697
$560$	39.7637	1.68032
$561$	2.52810	0.106737
$562$	−26.9992	−1.13889
$563$	−8.31194	−0.350306	−0.175153	−	0.984541i	$-0.556042\pi$
$563$	−8.31194	−0.350306	−0.175153	+	0.984541i	$0.556042\pi$
$564$	36.9507	1.55591
$565$	−38.7556	−1.63046
$566$	−17.2851	−0.726548
$567$	1.00000	0.0419961
$568$	50.0626	2.10058
$569$	36.1817	1.51681	0.758407	−	0.651781i	$-0.225978\pi$
$569$	36.1817	1.51681	0.758407	+	0.651781i	$0.225978\pi$
$570$	25.7539	1.07871
$571$	12.8415	0.537398	0.268699	−	0.963224i	$-0.413406\pi$
$571$	12.8415	0.537398	0.268699	+	0.963224i	$0.413406\pi$
$572$	−43.5639	−1.82150
$573$	−26.8779	−1.12284
$574$	−5.50124	−0.229617
$575$	−16.6671	−0.695066
$576$	24.7529	1.03137
$577$	−4.22429	−0.175860	−0.0879298	−	0.996127i	$-0.528025\pi$
$577$	−4.22429	−0.175860	−0.0879298	+	0.996127i	$0.528025\pi$
$578$	−38.3655	−1.59579
$579$	−11.4021	−0.473854
$580$	−127.218	−5.28244
$581$	7.17857	0.297817
$582$	24.6194	1.02051
$583$	−12.5018	−0.517772
$584$	59.3451	2.45572
$585$	15.6521	0.647134
$586$	−70.6378	−2.91802
$587$	−11.3497	−0.468454	−0.234227	−	0.972182i	$-0.575256\pi$
$587$	−11.3497	−0.468454	−0.234227	+	0.972182i	$0.575256\pi$
$588$	−5.33747	−0.220114
$589$	30.7047	1.26517
$590$	69.7141	2.87008
$591$	11.0512	0.454587
$592$	−99.7462	−4.09955
$593$	−40.4494	−1.66106	−0.830528	−	0.556977i	$-0.811961\pi$
$593$	−40.4494	−1.66106	−0.830528	+	0.556977i	$0.811961\pi$
$594$	4.06601	0.166830
$595$	4.84815	0.198755
$596$	−51.3212	−2.10220
$597$	−4.37619	−0.179105
$598$	−74.7031	−3.05484
$599$	25.7241	1.05106	0.525530	−	0.850775i	$-0.323867\pi$
$599$	25.7241	1.05106	0.525530	+	0.850775i	$0.323867\pi$
$600$	−29.7086	−1.21285
$601$	−7.07077	−0.288423	−0.144211	−	0.989547i	$-0.546065\pi$
$601$	−7.07077	−0.288423	−0.144211	+	0.989547i	$0.546065\pi$
$602$	2.32854	0.0949044
$603$	−15.7116	−0.639824
$604$	23.4818	0.955461
$605$	−25.1784	−1.02365
$606$	6.10553	0.248020
$607$	−23.7490	−0.963940	−0.481970	−	0.876188i	$-0.660079\pi$
$607$	−23.7490	−0.963940	−0.481970	+	0.876188i	$0.660079\pi$
$608$	−63.8686	−2.59021
$609$	8.28010	0.335526
$610$	77.9660	3.15675
$611$	−37.6428	−1.52287
$612$	8.98949	0.363379
$613$	−36.8791	−1.48953	−0.744767	−	0.667325i	$-0.767439\pi$
$613$	−36.8791	−1.48953	−0.744767	+	0.667325i	$0.767439\pi$
$614$	−16.3583	−0.660167
$615$	5.84608	0.235737
$616$	−13.5702	−0.546759
$617$	42.2547	1.70111	0.850555	−	0.525886i	$-0.176266\pi$
$617$	42.2547	1.70111	0.850555	+	0.525886i	$0.176266\pi$
$618$	−46.3401	−1.86407
$619$	32.0800	1.28941	0.644703	−	0.764433i	$-0.276981\pi$
$619$	32.0800	1.28941	0.644703	+	0.764433i	$0.276981\pi$
$620$	−142.832	−5.73627
$621$	5.07189	0.203528
$622$	−73.1971	−2.93494
$623$	9.76491	0.391223
$624$	−75.1112	−3.00686
$625$	−30.6319	−1.22528
$626$	−65.6964	−2.62576
$627$	−4.95779	−0.197995
$628$	−5.81154	−0.231906
$629$	−12.1615	−0.484910
$630$	7.79741	0.310656
$631$	−12.8436	−0.511294	−0.255647	−	0.966770i	$-0.582288\pi$
$631$	−12.8436	−0.511294	−0.255647	+	0.966770i	$0.582288\pi$
$632$	−83.8924	−3.33706
$633$	4.47388	0.177821
$634$	23.9305	0.950401
$635$	−2.87857	−0.114233
$636$	−44.4542	−1.76272
$637$	5.43745	0.215440
$638$	33.6670	1.33289
$639$	5.53761	0.219065
$640$	81.6813	3.22874
$641$	−20.1359	−0.795322	−0.397661	−	0.917532i	$-0.630178\pi$
$641$	−20.1359	−0.795322	−0.397661	+	0.917532i	$0.630178\pi$
$642$	9.14172	0.360795
$643$	36.9635	1.45770	0.728848	−	0.684675i	$-0.240056\pi$
$643$	36.9635	1.45770	0.728848	+	0.684675i	$0.240056\pi$
$644$	−27.0711	−1.06675
$645$	−2.47450	−0.0974335
$646$	−15.0684	−0.592856
$647$	12.1948	0.479426	0.239713	−	0.970844i	$-0.422947\pi$
$647$	12.1948	0.479426	0.239713	+	0.970844i	$0.422947\pi$
$648$	9.04047	0.355143
$649$	−13.4204	−0.526797
$650$	48.4015	1.89846
$651$	9.29635	0.364353
$652$	−73.2740	−2.86963
$653$	−11.5419	−0.451669	−0.225834	−	0.974166i	$-0.572511\pi$
$653$	−11.5419	−0.451669	−0.225834	+	0.974166i	$0.572511\pi$
$654$	−22.1758	−0.867143
$655$	−1.42805	−0.0557987
$656$	−28.0541	−1.09533
$657$	6.56437	0.256101
$658$	−18.7525	−0.731050
$659$	13.9433	0.543156	0.271578	−	0.962416i	$-0.412455\pi$
$659$	13.9433	0.543156	0.271578	+	0.962416i	$0.412455\pi$
$660$	23.0626	0.897710
$661$	−46.7279	−1.81751	−0.908753	−	0.417335i	$-0.862964\pi$
$661$	−46.7279	−1.81751	−0.908753	+	0.417335i	$0.862964\pi$
$662$	−46.0421	−1.78948
$663$	−9.15787	−0.355662
$664$	64.8976	2.51852
$665$	−9.50758	−0.368688
$666$	−19.5596	−0.757920
$667$	41.9957	1.62608
$668$	57.1486	2.21114
$669$	−24.4884	−0.946776
$670$	−122.509	−4.73295
$671$	−15.0089	−0.579414
$672$	−19.3372	−0.745950
$673$	−46.4878	−1.79197	−0.895986	−	0.444083i	$-0.853530\pi$
$673$	−46.4878	−1.79197	−0.895986	+	0.444083i	$0.853530\pi$
$674$	33.6865	1.29756
$675$	−3.28617	−0.126485
$676$	88.4199	3.40077
$677$	−17.3432	−0.666555	−0.333278	−	0.942829i	$-0.608155\pi$
$677$	−17.3432	−0.666555	−0.333278	+	0.942829i	$0.608155\pi$
$678$	36.4696	1.40061
$679$	−9.08877	−0.348795
$680$	43.8296	1.68079
$681$	0.513152	0.0196640
$682$	37.7991	1.44740
$683$	16.4433	0.629185	0.314593	−	0.949227i	$-0.398132\pi$
$683$	16.4433	0.629185	0.314593	+	0.949227i	$0.398132\pi$
$684$	−17.6290	−0.674064
$685$	59.8210	2.28564
$686$	2.70878	0.103422
$687$	19.6982	0.751533
$688$	11.8746	0.452717
$689$	45.2869	1.72529
$690$	39.5476	1.50555
$691$	−8.28341	−0.315116	−0.157558	−	0.987510i	$-0.550362\pi$
$691$	−8.28341	−0.315116	−0.157558	+	0.987510i	$0.550362\pi$
$692$	−28.1872	−1.07152
$693$	−1.50105	−0.0570202
$694$	27.7810	1.05455
$695$	0.605061	0.0229513
$696$	74.8560	2.83741
$697$	−3.42048	−0.129560
$698$	75.9908	2.87630
$699$	1.36091	0.0514745
$700$	17.5399	0.662945
$701$	−24.0456	−0.908190	−0.454095	−	0.890953i	$-0.650037\pi$
$701$	−24.0456	−0.908190	−0.454095	+	0.890953i	$0.650037\pi$
$702$	−14.7288	−0.555904
$703$	23.8495	0.899503
$704$	−37.1554	−1.40035
$705$	19.9280	0.750532
$706$	−0.326165	−0.0122754
$707$	−2.25398	−0.0847696
$708$	−47.7206	−1.79345
$709$	−16.4417	−0.617480	−0.308740	−	0.951146i	$-0.599907\pi$
$709$	−16.4417	−0.617480	−0.308740	+	0.951146i	$0.599907\pi$
$710$	43.1790	1.62048
$711$	−9.27964	−0.348014
$712$	88.2794	3.30841
$713$	47.1500	1.76578
$714$	−4.56218	−0.170735
$715$	−23.4946	−0.878648
$716$	−16.2854	−0.608612
$717$	−25.4879	−0.951862
$718$	42.0108	1.56783
$719$	−12.7441	−0.475276	−0.237638	−	0.971354i	$-0.576373\pi$
$719$	−12.7441	−0.475276	−0.237638	+	0.971354i	$0.576373\pi$
$720$	39.7637	1.48190
$721$	17.1074	0.637112
$722$	−21.9166	−0.815653
$723$	−23.9835	−0.891957
$724$	105.876	3.93484
$725$	−27.2098	−1.01055
$726$	23.6933	0.879339
$727$	−51.9453	−1.92654	−0.963272	−	0.268528i	$-0.913463\pi$
$727$	−51.9453	−1.92654	−0.963272	+	0.268528i	$0.913463\pi$
$728$	49.1571	1.82188
$729$	1.00000	0.0370370
$730$	51.1851	1.89445
$731$	1.44781	0.0535491
$732$	−53.3692	−1.97258
$733$	25.2902	0.934115	0.467057	−	0.884227i	$-0.345314\pi$
$733$	25.2902	0.934115	0.467057	+	0.884227i	$0.345314\pi$
$734$	0.754722	0.0278573
$735$	−2.87857	−0.106178
$736$	−98.0763	−3.61514
$737$	23.5838	0.868722
$738$	−5.50124	−0.202504
$739$	−17.4581	−0.642207	−0.321103	−	0.947044i	$-0.604054\pi$
$739$	−17.4581	−0.642207	−0.321103	+	0.947044i	$0.604054\pi$
$740$	−110.943	−4.07835
$741$	17.9593	0.659750
$742$	22.5606	0.828226
$743$	21.0345	0.771680	0.385840	−	0.922566i	$-0.373912\pi$
$743$	21.0345	0.771680	0.385840	+	0.922566i	$0.373912\pi$
$744$	84.0434	3.08118
$745$	−27.6782	−1.01405
$746$	69.1283	2.53097
$747$	7.17857	0.262650
$748$	−13.4937	−0.493378
$749$	−3.37485	−0.123314
$750$	13.3634	0.487962
$751$	31.0063	1.13144	0.565718	−	0.824599i	$-0.308599\pi$
$751$	31.0063	1.13144	0.565718	+	0.824599i	$0.308599\pi$
$752$	−95.6305	−3.48729
$753$	−10.4969	−0.382528
$754$	−121.956	−4.44139
$755$	12.6641	0.460892
$756$	−5.33747	−0.194122
$757$	−2.88141	−0.104727	−0.0523633	−	0.998628i	$-0.516675\pi$
$757$	−2.88141	−0.104727	−0.0523633	+	0.998628i	$0.516675\pi$
$758$	−27.5885	−1.00206
$759$	−7.61316	−0.276340
$760$	−85.9531	−3.11785
$761$	52.1088	1.88894	0.944470	−	0.328597i	$-0.106576\pi$
$761$	52.1088	1.88894	0.944470	+	0.328597i	$0.106576\pi$
$762$	2.70878	0.0981286
$763$	8.18665	0.296377
$764$	143.460	5.19021
$765$	4.84815	0.175285
$766$	−75.1941	−2.71687
$767$	48.6144	1.75537
$768$	−27.3575	−0.987178
$769$	22.2692	0.803048	0.401524	−	0.915849i	$-0.368481\pi$
$769$	22.2692	0.803048	0.401524	+	0.915849i	$0.368481\pi$
$770$	−11.7043	−0.421794
$771$	−3.96662	−0.142854
$772$	60.8582	2.19034
$773$	33.9532	1.22121	0.610605	−	0.791935i	$-0.290926\pi$
$773$	33.9532	1.22121	0.610605	+	0.791935i	$0.290926\pi$
$774$	2.32854	0.0836978
$775$	−30.5494	−1.09737
$776$	−82.1668	−2.94962
$777$	7.22083	0.259046
$778$	70.9652	2.54422
$779$	6.70781	0.240332
$780$	−83.5426	−2.99131
$781$	−8.31224	−0.297435
$782$	−23.1389	−0.827445
$783$	8.28010	0.295907
$784$	13.8137	0.493346
$785$	−3.13424	−0.111866
$786$	1.34382	0.0479324
$787$	23.0039	0.820002	0.410001	−	0.912085i	$-0.365528\pi$
$787$	23.0039	0.820002	0.410001	+	0.912085i	$0.365528\pi$
$788$	−58.9857	−2.10128
$789$	5.02765	0.178989
$790$	−72.3572	−2.57435
$791$	−13.4635	−0.478706
$792$	−13.5702	−0.482196
$793$	54.3689	1.93069
$794$	24.2129	0.859284
$795$	−23.9748	−0.850297
$796$	23.3578	0.827895
$797$	−3.18430	−0.112794	−0.0563968	−	0.998408i	$-0.517961\pi$
$797$	−3.18430	−0.112794	−0.0563968	+	0.998408i	$0.517961\pi$
$798$	8.94677	0.316712
$799$	−11.6597	−0.412490
$800$	63.5455	2.24667
$801$	9.76491	0.345026
$802$	−95.5859	−3.37526
$803$	−9.85346	−0.347721
$804$	83.8600	2.95752
$805$	−14.5998	−0.514575
$806$	−136.924	−4.82296
$807$	−16.7702	−0.590340
$808$	−20.3770	−0.716862
$809$	0.519198	0.0182540	0.00912701	−	0.999958i	$-0.497095\pi$
$809$	0.519198	0.0182540	0.00912701	+	0.999958i	$0.497095\pi$
$810$	7.79741	0.273973
$811$	17.7425	0.623023	0.311511	−	0.950242i	$-0.399165\pi$
$811$	17.7425	0.623023	0.311511	+	0.950242i	$0.399165\pi$
$812$	−44.1948	−1.55093
$813$	24.8503	0.871537
$814$	29.3600	1.02907
$815$	−39.5176	−1.38424
$816$	−23.2653	−0.814449
$817$	−2.83925	−0.0993329
$818$	−17.1718	−0.600399
$819$	5.43745	0.190000
$820$	−31.2033	−1.08967
$821$	13.1810	0.460021	0.230011	−	0.973188i	$-0.426124\pi$
$821$	13.1810	0.460021	0.230011	+	0.973188i	$0.426124\pi$
$822$	−56.2924	−1.96342
$823$	16.7749	0.584736	0.292368	−	0.956306i	$-0.405557\pi$
$823$	16.7749	0.584736	0.292368	+	0.956306i	$0.405557\pi$
$824$	154.659	5.38780
$825$	4.93271	0.171735
$826$	24.2183	0.842662
$827$	8.15970	0.283740	0.141870	−	0.989885i	$-0.454688\pi$
$827$	8.15970	0.283740	0.141870	+	0.989885i	$0.454688\pi$
$828$	−27.0711	−0.940785
$829$	−4.84768	−0.168367	−0.0841834	−	0.996450i	$-0.526828\pi$
$829$	−4.84768	−0.168367	−0.0841834	+	0.996450i	$0.526828\pi$
$830$	55.9742	1.94289
$831$	5.45207	0.189130
$832$	134.593	4.66616
$833$	1.68422	0.0583548
$834$	−0.569371	−0.0197157
$835$	30.8210	1.06660
$836$	26.4621	0.915211
$837$	9.29635	0.321329
$838$	98.3277	3.39667
$839$	35.2043	1.21539	0.607693	−	0.794172i	$-0.292095\pi$
$839$	35.2043	1.21539	0.607693	+	0.794172i	$0.292095\pi$
$840$	−26.0237	−0.897901
$841$	39.5600	1.36414
$842$	−22.9144	−0.789682
$843$	9.96730	0.343292
$844$	−23.8792	−0.821956
$845$	47.6861	1.64045
$846$	−18.7525	−0.644726
$847$	−8.74685	−0.300545
$848$	115.050	3.95083
$849$	6.38116	0.219001
$850$	14.9921	0.514226
$851$	36.6232	1.25543
$852$	−29.5569	−1.01260
$853$	−30.9868	−1.06097	−0.530484	−	0.847695i	$-0.677990\pi$
$853$	−30.9868	−1.06097	−0.530484	+	0.847695i	$0.677990\pi$
$854$	27.0850	0.926828
$855$	−9.50758	−0.325152
$856$	−30.5102	−1.04282
$857$	30.4958	1.04172	0.520858	−	0.853643i	$-0.325612\pi$
$857$	30.4958	1.04172	0.520858	+	0.853643i	$0.325612\pi$
$858$	22.1087	0.754780
$859$	−24.8062	−0.846376	−0.423188	−	0.906042i	$-0.639089\pi$
$859$	−24.8062	−0.846376	−0.423188	+	0.906042i	$0.639089\pi$
$860$	13.2076	0.450376
$861$	2.03090	0.0692127
$862$	−80.4317	−2.73951
$863$	45.5391	1.55017	0.775084	−	0.631858i	$-0.217707\pi$
$863$	45.5391	1.55017	0.775084	+	0.631858i	$0.217707\pi$
$864$	−19.3372	−0.657866
$865$	−15.2017	−0.516875
$866$	78.5873	2.67050
$867$	14.1634	0.481014
$868$	−49.6190	−1.68418
$869$	13.9292	0.472516
$870$	64.5633	2.18890
$871$	−85.4308	−2.89471
$872$	74.0112	2.50633
$873$	−9.08877	−0.307608
$874$	45.3770	1.53490
$875$	−4.93337	−0.166778
$876$	−35.0372	−1.18380
$877$	38.0252	1.28402	0.642010	−	0.766697i	$-0.278101\pi$
$877$	38.0252	1.28402	0.642010	+	0.766697i	$0.278101\pi$
$878$	−41.1508	−1.38877
$879$	26.0774	0.879568
$880$	−59.6873	−2.01206
$881$	−18.1199	−0.610476	−0.305238	−	0.952276i	$-0.598736\pi$
$881$	−18.1199	−0.610476	−0.305238	+	0.952276i	$0.598736\pi$
$882$	2.70878	0.0912093
$883$	−40.1982	−1.35278	−0.676388	−	0.736546i	$-0.736456\pi$
$883$	−40.1982	−1.35278	−0.676388	+	0.736546i	$0.736456\pi$
$884$	48.8799	1.64401
$885$	−25.7364	−0.865118
$886$	59.4507	1.99728
$887$	43.6325	1.46504	0.732518	−	0.680748i	$-0.238345\pi$
$887$	43.6325	1.46504	0.732518	+	0.680748i	$0.238345\pi$
$888$	65.2797	2.19064
$889$	−1.00000	−0.0335389
$890$	76.1410	2.55225
$891$	−1.50105	−0.0502871
$892$	130.706	4.37637
$893$	22.8655	0.765164
$894$	26.0456	0.871095
$895$	−8.78291	−0.293580
$896$	28.3756	0.947964
$897$	27.5781	0.920807
$898$	28.5256	0.951911
$899$	76.9747	2.56725
$900$	17.5399	0.584662
$901$	14.0274	0.467320
$902$	8.25764	0.274949
$903$	−0.859629	−0.0286067
$904$	−121.716	−4.04822
$905$	57.1001	1.89807
$906$	−11.9171	−0.395918
$907$	−14.8276	−0.492341	−0.246170	−	0.969227i	$-0.579172\pi$
$907$	−14.8276	−0.492341	−0.246170	+	0.969227i	$0.579172\pi$
$908$	−2.73894	−0.0908948
$909$	−2.25398	−0.0747598
$910$	42.3980	1.40548
$911$	48.2909	1.59995	0.799975	−	0.600034i	$-0.204846\pi$
$911$	48.2909	1.59995	0.799975	+	0.600034i	$0.204846\pi$
$912$	45.6250	1.51079
$913$	−10.7754	−0.356613
$914$	−72.3411	−2.39283
$915$	−28.7827	−0.951527
$916$	−105.139	−3.47388
$917$	−0.496098	−0.0163826
$918$	−4.56218	−0.150574
$919$	−46.0061	−1.51760	−0.758801	−	0.651322i	$-0.774215\pi$
$919$	−46.0061	−1.51760	−0.758801	+	0.651322i	$0.774215\pi$
$920$	−131.989	−4.35155
$921$	6.03900	0.198992
$922$	13.7693	0.453466
$923$	30.1105	0.991099
$924$	8.01182	0.263570
$925$	−23.7289	−0.780201
$926$	−6.94754	−0.228310
$927$	17.1074	0.561880
$928$	−160.114	−5.25601
$929$	15.8115	0.518759	0.259379	−	0.965776i	$-0.416482\pi$
$929$	15.8115	0.518759	0.259379	+	0.965776i	$0.416482\pi$
$930$	72.4874	2.37696
$931$	−3.30288	−0.108248
$932$	−7.26384	−0.237935
$933$	27.0222	0.884667
$934$	−103.953	−3.40145
$935$	−7.27732	−0.237994
$936$	49.1571	1.60675
$937$	22.8913	0.747825	0.373913	−	0.927464i	$-0.378016\pi$
$937$	22.8913	0.747825	0.373913	+	0.927464i	$0.378016\pi$
$938$	−42.5591	−1.38960
$939$	24.2532	0.791472
$940$	−106.365	−3.46925
$941$	58.6620	1.91233	0.956163	−	0.292836i	$-0.0945989\pi$
$941$	58.6620	1.91233	0.956163	+	0.292836i	$0.0945989\pi$
$942$	2.94937	0.0960955
$943$	10.3005	0.335430
$944$	123.504	4.01970
$945$	−2.87857	−0.0936399
$946$	−3.49526	−0.113641
$947$	−35.5721	−1.15594	−0.577969	−	0.816058i	$-0.696155\pi$
$947$	−35.5721	−1.15594	−0.577969	+	0.816058i	$0.696155\pi$
$948$	49.5298	1.60865
$949$	35.6935	1.15866
$950$	−29.4007	−0.953883
$951$	−8.83443	−0.286476
$952$	15.2262	0.493483
$953$	−56.3625	−1.82576	−0.912880	−	0.408229i	$-0.866147\pi$
$953$	−56.3625	−1.82576	−0.912880	+	0.408229i	$0.866147\pi$
$954$	22.5606	0.730426
$955$	77.3701	2.50364
$956$	136.041	4.39987
$957$	−12.4288	−0.401768
$958$	−25.4138	−0.821082
$959$	20.7815	0.671069
$960$	−71.2530	−2.29968
$961$	55.4221	1.78781
$962$	−106.354	−3.42901
$963$	−3.37485	−0.108753
$964$	128.012	4.12297
$965$	32.8217	1.05657
$966$	13.7386	0.442033
$967$	−32.3294	−1.03964	−0.519822	−	0.854275i	$-0.674002\pi$
$967$	−32.3294	−1.03964	−0.519822	+	0.854275i	$0.674002\pi$
$968$	−79.0756	−2.54159
$969$	5.56279	0.178702
$970$	−70.8688	−2.27546
$971$	18.2980	0.587210	0.293605	−	0.955927i	$-0.405145\pi$
$971$	18.2980	0.587210	0.293605	+	0.955927i	$0.405145\pi$
$972$	−5.33747	−0.171200
$973$	0.210195	0.00673853
$974$	81.4876	2.61103
$975$	−17.8684	−0.572247
$976$	138.122	4.42119
$977$	35.5195	1.13637	0.568185	−	0.822901i	$-0.307646\pi$
$977$	35.5195	1.13637	0.568185	+	0.822901i	$0.307646\pi$
$978$	37.1867	1.18910
$979$	−14.6576	−0.468460
$980$	15.3643	0.490795
$981$	8.18665	0.261380
$982$	106.699	3.40491
$983$	19.4569	0.620578	0.310289	−	0.950642i	$-0.399574\pi$
$983$	19.4569	0.620578	0.310289	+	0.950642i	$0.399574\pi$
$984$	18.3603	0.585304
$985$	−31.8118	−1.01361
$986$	−37.7753	−1.20301
$987$	6.92288	0.220358
$988$	−95.8571	−3.04962
$989$	−4.35994	−0.138638
$990$	−11.7043	−0.371987
$991$	39.5095	1.25506	0.627531	−	0.778592i	$-0.284066\pi$
$991$	39.5095	1.25506	0.627531	+	0.778592i	$0.284066\pi$
$992$	−179.766	−5.70757
$993$	16.9974	0.539396
$994$	15.0002	0.475776
$995$	12.5972	0.399357
$996$	−38.3154	−1.21407
$997$	−48.2009	−1.52654	−0.763269	−	0.646080i	$-0.776407\pi$
$997$	−48.2009	−1.52654	−0.763269	+	0.646080i	$0.776407\pi$
$998$	52.8020	1.67142
$999$	7.22083	0.228457

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.l.1.13	✓	13
3.2	odd	2		8001.2.a.o.1.1		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.l.1.13	✓	13	1.1	even	1	trivial
8001.2.a.o.1.1		13	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:	\( N \)	\(=\)	\( 2667 = 3 \cdot 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2667.a (trivial)

\(f(q)\)	\(=\)	\(q+2.70878 q^{2} -1.00000 q^{3} +5.33747 q^{4} +2.87857 q^{5} -2.70878 q^{6} +1.00000 q^{7} +9.04047 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.70878 q^{2} -1.00000 q^{3} +5.33747 q^{4} +2.87857 q^{5} -2.70878 q^{6} +1.00000 q^{7} +9.04047 q^{8} +1.00000 q^{9} +7.79741 q^{10} -1.50105 q^{11} -5.33747 q^{12} +5.43745 q^{13} +2.70878 q^{14} -2.87857 q^{15} +13.8137 q^{16} +1.68422 q^{17} +2.70878 q^{18} -3.30288 q^{19} +15.3643 q^{20} -1.00000 q^{21} -4.06601 q^{22} -5.07189 q^{23} -9.04047 q^{24} +3.28617 q^{25} +14.7288 q^{26} -1.00000 q^{27} +5.33747 q^{28} -8.28010 q^{29} -7.79741 q^{30} -9.29635 q^{31} +19.3372 q^{32} +1.50105 q^{33} +4.56218 q^{34} +2.87857 q^{35} +5.33747 q^{36} -7.22083 q^{37} -8.94677 q^{38} -5.43745 q^{39} +26.0237 q^{40} -2.03090 q^{41} -2.70878 q^{42} +0.859629 q^{43} -8.01182 q^{44} +2.87857 q^{45} -13.7386 q^{46} -6.92288 q^{47} -13.8137 q^{48} +1.00000 q^{49} +8.90151 q^{50} -1.68422 q^{51} +29.0223 q^{52} +8.32870 q^{53} -2.70878 q^{54} -4.32088 q^{55} +9.04047 q^{56} +3.30288 q^{57} -22.4289 q^{58} +8.94067 q^{59} -15.3643 q^{60} +9.99896 q^{61} -25.1817 q^{62} +1.00000 q^{63} +24.7529 q^{64} +15.6521 q^{65} +4.06601 q^{66} -15.7116 q^{67} +8.98949 q^{68} +5.07189 q^{69} +7.79741 q^{70} +5.53761 q^{71} +9.04047 q^{72} +6.56437 q^{73} -19.5596 q^{74} -3.28617 q^{75} -17.6290 q^{76} -1.50105 q^{77} -14.7288 q^{78} -9.27964 q^{79} +39.7637 q^{80} +1.00000 q^{81} -5.50124 q^{82} +7.17857 q^{83} -5.33747 q^{84} +4.84815 q^{85} +2.32854 q^{86} +8.28010 q^{87} -13.5702 q^{88} +9.76491 q^{89} +7.79741 q^{90} +5.43745 q^{91} -27.0711 q^{92} +9.29635 q^{93} -18.7525 q^{94} -9.50758 q^{95} -19.3372 q^{96} -9.08877 q^{97} +2.70878 q^{98} -1.50105 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} - 13 q^{3} + 10 q^{4} + 12 q^{5} - 4 q^{6} + 13 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 4 * q^2 - 13 * q^3 + 10 * q^4 + 12 * q^5 - 4 * q^6 + 13 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 4 q^{2} - 13 q^{3} + 10 q^{4} + 12 q^{5} - 4 q^{6} + 13 q^{7} + 9 q^{8} + 13 q^{9} + 6 q^{10} + 3 q^{11} - 10 q^{12} + 21 q^{13} + 4 q^{14} - 12 q^{15} + 8 q^{16} + 17 q^{17} + 4 q^{18} + 5 q^{19} + 29 q^{20} - 13 q^{21} + q^{22} + 4 q^{23} - 9 q^{24} + q^{25} + 22 q^{26} - 13 q^{27} + 10 q^{28} + 21 q^{29} - 6 q^{30} - 7 q^{31} + 12 q^{32} - 3 q^{33} + 2 q^{34} + 12 q^{35} + 10 q^{36} + 7 q^{37} - 9 q^{38} - 21 q^{39} + 29 q^{40} + 21 q^{41} - 4 q^{42} - 9 q^{43} - 2 q^{44} + 12 q^{45} - 28 q^{46} + 23 q^{47} - 8 q^{48} + 13 q^{49} + 15 q^{50} - 17 q^{51} + 15 q^{52} + 31 q^{53} - 4 q^{54} - 8 q^{55} + 9 q^{56} - 5 q^{57} - 25 q^{58} + 28 q^{59} - 29 q^{60} + 29 q^{61} - 3 q^{62} + 13 q^{63} + 9 q^{64} + 30 q^{65} - q^{66} - 18 q^{67} + 34 q^{68} - 4 q^{69} + 6 q^{70} + 10 q^{71} + 9 q^{72} + 24 q^{73} - 19 q^{74} - q^{75} + 3 q^{77} - 22 q^{78} - 28 q^{79} + 26 q^{80} + 13 q^{81} + 18 q^{82} + 26 q^{83} - 10 q^{84} + 20 q^{85} - 2 q^{86} - 21 q^{87} - 17 q^{88} + 44 q^{89} + 6 q^{90} + 21 q^{91} + 6 q^{92} + 7 q^{93} - 9 q^{94} - 2 q^{95} - 12 q^{96} + 17 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 - 13 * q^3 + 10 * q^4 + 12 * q^5 - 4 * q^6 + 13 * q^7 + 9 * q^8 + 13 * q^9 + 6 * q^10 + 3 * q^11 - 10 * q^12 + 21 * q^13 + 4 * q^14 - 12 * q^15 + 8 * q^16 + 17 * q^17 + 4 * q^18 + 5 * q^19 + 29 * q^20 - 13 * q^21 + q^22 + 4 * q^23 - 9 * q^24 + q^25 + 22 * q^26 - 13 * q^27 + 10 * q^28 + 21 * q^29 - 6 * q^30 - 7 * q^31 + 12 * q^32 - 3 * q^33 + 2 * q^34 + 12 * q^35 + 10 * q^36 + 7 * q^37 - 9 * q^38 - 21 * q^39 + 29 * q^40 + 21 * q^41 - 4 * q^42 - 9 * q^43 - 2 * q^44 + 12 * q^45 - 28 * q^46 + 23 * q^47 - 8 * q^48 + 13 * q^49 + 15 * q^50 - 17 * q^51 + 15 * q^52 + 31 * q^53 - 4 * q^54 - 8 * q^55 + 9 * q^56 - 5 * q^57 - 25 * q^58 + 28 * q^59 - 29 * q^60 + 29 * q^61 - 3 * q^62 + 13 * q^63 + 9 * q^64 + 30 * q^65 - q^66 - 18 * q^67 + 34 * q^68 - 4 * q^69 + 6 * q^70 + 10 * q^71 + 9 * q^72 + 24 * q^73 - 19 * q^74 - q^75 + 3 * q^77 - 22 * q^78 - 28 * q^79 + 26 * q^80 + 13 * q^81 + 18 * q^82 + 26 * q^83 - 10 * q^84 + 20 * q^85 - 2 * q^86 - 21 * q^87 - 17 * q^88 + 44 * q^89 + 6 * q^90 + 21 * q^91 + 6 * q^92 + 7 * q^93 - 9 * q^94 - 2 * q^95 - 12 * q^96 + 17 * q^97 + 4 * q^98 + 3 * q^99

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