LMFDB - Embedded newform 139.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [139,2,Mod(1,139)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(139, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("139.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	139.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:	$1.10992058810$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 11x^{5} + 8x^{4} + 35x^{3} - 10x^{2} - 32x - 8 $ x^7 - x^6 - 11x^5 + 8x^4 + 35x^3 - 10x^2 - 32*x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.48318$ of defining polynomial
Character	$\chi$	$=$	139.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48318 q^{2} +1.56460 q^{3} +4.16616 q^{4} +3.76669 q^{5} -3.88518 q^{6} -3.67776 q^{7} -5.37897 q^{8} -0.552027 q^{9} +O(q^{10})$	\(q-2.48318 q^{2} +1.56460 q^{3} +4.16616 q^{4} +3.76669 q^{5} -3.88518 q^{6} -3.67776 q^{7} -5.37897 q^{8} -0.552027 q^{9} -9.35335 q^{10} +5.01926 q^{11} +6.51838 q^{12} +1.93452 q^{13} +9.13252 q^{14} +5.89336 q^{15} +5.02459 q^{16} -0.320577 q^{17} +1.37078 q^{18} -2.85843 q^{19} +15.6926 q^{20} -5.75422 q^{21} -12.4637 q^{22} -1.64820 q^{23} -8.41593 q^{24} +9.18795 q^{25} -4.80375 q^{26} -5.55750 q^{27} -15.3221 q^{28} +8.72513 q^{29} -14.6343 q^{30} +1.09788 q^{31} -1.71901 q^{32} +7.85313 q^{33} +0.796050 q^{34} -13.8530 q^{35} -2.29983 q^{36} -4.88302 q^{37} +7.09798 q^{38} +3.02675 q^{39} -20.2609 q^{40} -9.59487 q^{41} +14.2887 q^{42} -5.85039 q^{43} +20.9111 q^{44} -2.07931 q^{45} +4.09278 q^{46} -6.33260 q^{47} +7.86147 q^{48} +6.52589 q^{49} -22.8153 q^{50} -0.501575 q^{51} +8.05953 q^{52} +6.55399 q^{53} +13.8003 q^{54} +18.9060 q^{55} +19.7825 q^{56} -4.47230 q^{57} -21.6660 q^{58} -6.51771 q^{59} +24.5527 q^{60} -10.3143 q^{61} -2.72623 q^{62} +2.03022 q^{63} -5.78057 q^{64} +7.28674 q^{65} -19.5007 q^{66} -0.221404 q^{67} -1.33558 q^{68} -2.57878 q^{69} +34.3994 q^{70} -4.41910 q^{71} +2.96933 q^{72} -1.92636 q^{73} +12.1254 q^{74} +14.3755 q^{75} -11.9087 q^{76} -18.4596 q^{77} -7.51595 q^{78} +16.5019 q^{79} +18.9261 q^{80} -7.03919 q^{81} +23.8257 q^{82} -11.1705 q^{83} -23.9730 q^{84} -1.20751 q^{85} +14.5276 q^{86} +13.6513 q^{87} -26.9984 q^{88} +5.44197 q^{89} +5.16330 q^{90} -7.11469 q^{91} -6.86668 q^{92} +1.71774 q^{93} +15.7249 q^{94} -10.7668 q^{95} -2.68957 q^{96} +3.46235 q^{97} -16.2049 q^{98} -2.77077 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + q^{2} - 2 q^{3} + 9 q^{4} + 11 q^{5} - 7 q^{6} - 5 q^{7} + 6 q^{8} + 13 q^{9}+O(q^{10}) $ 7 * q + q^2 - 2 * q^3 + 9 * q^4 + 11 * q^5 - 7 * q^6 - 5 * q^7 + 6 * q^8 + 13 * q^9	\( 7 q + q^{2} - 2 q^{3} + 9 q^{4} + 11 q^{5} - 7 q^{6} - 5 q^{7} + 6 q^{8} + 13 q^{9} - 4 q^{10} + 2 q^{11} - 8 q^{12} + 6 q^{13} + 7 q^{14} - 3 q^{15} + 5 q^{16} + 5 q^{17} - 10 q^{18} - 10 q^{19} + 12 q^{20} - 5 q^{21} - 18 q^{22} - q^{23} - 21 q^{24} + 14 q^{25} - 8 q^{26} - 11 q^{27} - 28 q^{28} + 30 q^{29} - 41 q^{30} - 20 q^{31} - 12 q^{32} - 20 q^{33} - 17 q^{34} - 7 q^{35} + 2 q^{36} + 6 q^{37} + 6 q^{38} + 11 q^{39} - 22 q^{40} + 19 q^{41} + 6 q^{42} - 12 q^{43} + 25 q^{44} + 27 q^{45} + 22 q^{46} - 3 q^{47} + 15 q^{48} - 8 q^{49} + 12 q^{50} + 23 q^{51} - 8 q^{52} + 38 q^{53} - 7 q^{54} + 7 q^{55} + 21 q^{56} - 19 q^{57} - 21 q^{58} - 14 q^{59} - 8 q^{60} + 4 q^{61} - q^{62} - 18 q^{63} - 16 q^{64} + 10 q^{65} + 18 q^{66} + 9 q^{67} - 25 q^{68} + 9 q^{69} + 20 q^{70} + 24 q^{71} + 41 q^{72} - 5 q^{73} + 9 q^{74} - 21 q^{75} + 3 q^{76} - 13 q^{77} + 20 q^{78} + 8 q^{79} + 11 q^{80} + 39 q^{81} + 56 q^{82} - 9 q^{83} - q^{84} - 22 q^{85} + 39 q^{86} - 25 q^{87} - 29 q^{88} + 10 q^{89} + 72 q^{90} + 7 q^{91} + 29 q^{92} - 15 q^{93} - 36 q^{94} - 21 q^{95} - 11 q^{96} - 5 q^{97} - 49 q^{98} - 31 q^{99}+O(q^{100}) \) 7 * q + q^2 - 2 * q^3 + 9 * q^4 + 11 * q^5 - 7 * q^6 - 5 * q^7 + 6 * q^8 + 13 * q^9 - 4 * q^10 + 2 * q^11 - 8 * q^12 + 6 * q^13 + 7 * q^14 - 3 * q^15 + 5 * q^16 + 5 * q^17 - 10 * q^18 - 10 * q^19 + 12 * q^20 - 5 * q^21 - 18 * q^22 - q^23 - 21 * q^24 + 14 * q^25 - 8 * q^26 - 11 * q^27 - 28 * q^28 + 30 * q^29 - 41 * q^30 - 20 * q^31 - 12 * q^32 - 20 * q^33 - 17 * q^34 - 7 * q^35 + 2 * q^36 + 6 * q^37 + 6 * q^38 + 11 * q^39 - 22 * q^40 + 19 * q^41 + 6 * q^42 - 12 * q^43 + 25 * q^44 + 27 * q^45 + 22 * q^46 - 3 * q^47 + 15 * q^48 - 8 * q^49 + 12 * q^50 + 23 * q^51 - 8 * q^52 + 38 * q^53 - 7 * q^54 + 7 * q^55 + 21 * q^56 - 19 * q^57 - 21 * q^58 - 14 * q^59 - 8 * q^60 + 4 * q^61 - q^62 - 18 * q^63 - 16 * q^64 + 10 * q^65 + 18 * q^66 + 9 * q^67 - 25 * q^68 + 9 * q^69 + 20 * q^70 + 24 * q^71 + 41 * q^72 - 5 * q^73 + 9 * q^74 - 21 * q^75 + 3 * q^76 - 13 * q^77 + 20 * q^78 + 8 * q^79 + 11 * q^80 + 39 * q^81 + 56 * q^82 - 9 * q^83 - q^84 - 22 * q^85 + 39 * q^86 - 25 * q^87 - 29 * q^88 + 10 * q^89 + 72 * q^90 + 7 * q^91 + 29 * q^92 - 15 * q^93 - 36 * q^94 - 21 * q^95 - 11 * q^96 - 5 * q^97 - 49 * q^98 - 31 * 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 $

$2$	−2.48318	−1.75587	−0.877935	−	0.478779i	$-0.841079\pi$
$2$	−2.48318	−1.75587	−0.877935	+	0.478779i	$0.841079\pi$
$3$	1.56460	0.903322	0.451661	−	0.892190i	$-0.350832\pi$
$3$	1.56460	0.903322	0.451661	+	0.892190i	$0.350832\pi$
$4$	4.16616	2.08308
$5$	3.76669	1.68451	0.842257	−	0.539076i	$-0.181226\pi$
$5$	3.76669	1.68451	0.842257	+	0.539076i	$0.181226\pi$
$6$	−3.88518	−1.58612
$7$	−3.67776	−1.39006	−0.695031	−	0.718980i	$-0.744609\pi$
$7$	−3.67776	−1.39006	−0.695031	+	0.718980i	$0.744609\pi$
$8$	−5.37897	−1.90175
$9$	−0.552027	−0.184009
$10$	−9.35335	−2.95779
$11$	5.01926	1.51336	0.756682	−	0.653783i	$-0.226819\pi$
$11$	5.01926	1.51336	0.756682	+	0.653783i	$0.226819\pi$
$12$	6.51838	1.88169
$13$	1.93452	0.536539	0.268270	−	0.963344i	$-0.413548\pi$
$13$	1.93452	0.536539	0.268270	+	0.963344i	$0.413548\pi$
$14$	9.13252	2.44077
$15$	5.89336	1.52166
$16$	5.02459	1.25615
$17$	−0.320577	−0.0777514	−0.0388757	−	0.999244i	$-0.512378\pi$
$17$	−0.320577	−0.0777514	−0.0388757	+	0.999244i	$0.512378\pi$
$18$	1.37078	0.323096
$19$	−2.85843	−0.655768	−0.327884	−	0.944718i	$-0.606336\pi$
$19$	−2.85843	−0.655768	−0.327884	+	0.944718i	$0.606336\pi$
$20$	15.6926	3.50898
$21$	−5.75422	−1.25567
$22$	−12.4637	−2.65727
$23$	−1.64820	−0.343674	−0.171837	−	0.985125i	$-0.554970\pi$
$23$	−1.64820	−0.343674	−0.171837	+	0.985125i	$0.554970\pi$
$24$	−8.41593	−1.71789
$25$	9.18795	1.83759
$26$	−4.80375	−0.942094
$27$	−5.55750	−1.06954
$28$	−15.3221	−2.89561
$29$	8.72513	1.62022	0.810108	−	0.586280i	$-0.199408\pi$
$29$	8.72513	1.62022	0.810108	+	0.586280i	$0.199408\pi$
$30$	−14.6343	−2.67184
$31$	1.09788	0.197185	0.0985924	−	0.995128i	$-0.468566\pi$
$31$	1.09788	0.197185	0.0985924	+	0.995128i	$0.468566\pi$
$32$	−1.71901	−0.303882
$33$	7.85313	1.36705
$34$	0.796050	0.136521
$35$	−13.8530	−2.34158
$36$	−2.29983	−0.383306
$37$	−4.88302	−0.802763	−0.401382	−	0.915911i	$-0.631470\pi$
$37$	−4.88302	−0.802763	−0.401382	+	0.915911i	$0.631470\pi$
$38$	7.09798	1.15144
$39$	3.02675	0.484668
$40$	−20.2609	−3.20353
$41$	−9.59487	−1.49847	−0.749233	−	0.662306i	$-0.769578\pi$
$41$	−9.59487	−1.49847	−0.749233	+	0.662306i	$0.769578\pi$
$42$	14.2887	2.20480
$43$	−5.85039	−0.892176	−0.446088	−	0.894989i	$-0.647183\pi$
$43$	−5.85039	−0.892176	−0.446088	+	0.894989i	$0.647183\pi$
$44$	20.9111	3.15246
$45$	−2.07931	−0.309966
$46$	4.09278	0.603447
$47$	−6.33260	−0.923704	−0.461852	−	0.886957i	$-0.652815\pi$
$47$	−6.33260	−0.923704	−0.461852	+	0.886957i	$0.652815\pi$
$48$	7.86147	1.13471
$49$	6.52589	0.932270
$50$	−22.8153	−3.22657
$51$	−0.501575	−0.0702346
$52$	8.05953	1.11766
$53$	6.55399	0.900259	0.450130	−	0.892963i	$-0.351378\pi$
$53$	6.55399	0.900259	0.450130	+	0.892963i	$0.351378\pi$
$54$	13.8003	1.87798
$55$	18.9060	2.54928
$56$	19.7825	2.64355
$57$	−4.47230	−0.592370
$58$	−21.6660	−2.84489
$59$	−6.51771	−0.848534	−0.424267	−	0.905537i	$-0.639468\pi$
$59$	−6.51771	−0.848534	−0.424267	+	0.905537i	$0.639468\pi$
$60$	24.5527	3.16974
$61$	−10.3143	−1.32062	−0.660308	−	0.750995i	$-0.729574\pi$
$61$	−10.3143	−1.32062	−0.660308	+	0.750995i	$0.729574\pi$
$62$	−2.72623	−0.346231
$63$	2.03022	0.255784
$64$	−5.78057	−0.722571
$65$	7.28674	0.903808
$66$	−19.5007	−2.40037
$67$	−0.221404	−0.0270488	−0.0135244	−	0.999909i	$-0.504305\pi$
$67$	−0.221404	−0.0270488	−0.0135244	+	0.999909i	$0.504305\pi$
$68$	−1.33558	−0.161963
$69$	−2.57878	−0.310448
$70$	34.3994	4.11151
$71$	−4.41910	−0.524451	−0.262225	−	0.965007i	$-0.584456\pi$
$71$	−4.41910	−0.524451	−0.262225	+	0.965007i	$0.584456\pi$
$72$	2.96933	0.349939
$73$	−1.92636	−0.225464	−0.112732	−	0.993625i	$-0.535960\pi$
$73$	−1.92636	−0.225464	−0.112732	+	0.993625i	$0.535960\pi$
$74$	12.1254	1.40955
$75$	14.3755	1.65994
$76$	−11.9087	−1.36602
$77$	−18.4596	−2.10367
$78$	−7.51595	−0.851014
$79$	16.5019	1.85661	0.928305	−	0.371820i	$-0.121266\pi$
$79$	16.5019	1.85661	0.928305	+	0.371820i	$0.121266\pi$
$80$	18.9261	2.11600
$81$	−7.03919	−0.782132
$82$	23.8257	2.63111
$83$	−11.1705	−1.22612	−0.613061	−	0.790036i	$-0.710062\pi$
$83$	−11.1705	−1.22612	−0.613061	+	0.790036i	$0.710062\pi$
$84$	−23.9730	−2.61567
$85$	−1.20751	−0.130973
$86$	14.5276	1.56655
$87$	13.6513	1.46358
$88$	−26.9984	−2.87804
$89$	5.44197	0.576848	0.288424	−	0.957503i	$-0.406869\pi$
$89$	5.44197	0.576848	0.288424	+	0.957503i	$0.406869\pi$
$90$	5.16330	0.544260
$91$	−7.11469	−0.745822
$92$	−6.86668	−0.715901
$93$	1.71774	0.178121
$94$	15.7249	1.62190
$95$	−10.7668	−1.10465
$96$	−2.68957	−0.274503
$97$	3.46235	0.351548	0.175774	−	0.984431i	$-0.443757\pi$
$97$	3.46235	0.351548	0.175774	+	0.984431i	$0.443757\pi$
$98$	−16.2049	−1.63695
$99$	−2.77077	−0.278473
$100$	38.2785	3.82785
$101$	8.21196	0.817120	0.408560	−	0.912731i	$-0.366031\pi$
$101$	8.21196	0.817120	0.408560	+	0.912731i	$0.366031\pi$
$102$	1.24550	0.123323
$103$	−4.39161	−0.432718	−0.216359	−	0.976314i	$-0.569418\pi$
$103$	−4.39161	−0.432718	−0.216359	+	0.976314i	$0.569418\pi$
$104$	−10.4057	−1.02036
$105$	−21.6743	−2.11520
$106$	−16.2747	−1.58074
$107$	−1.46816	−0.141932	−0.0709660	−	0.997479i	$-0.522608\pi$
$107$	−1.46816	−0.141932	−0.0709660	+	0.997479i	$0.522608\pi$
$108$	−23.1535	−2.22794
$109$	−10.9449	−1.04833	−0.524166	−	0.851616i	$-0.675623\pi$
$109$	−10.9449	−1.04833	−0.524166	+	0.851616i	$0.675623\pi$
$110$	−46.9469	−4.47621
$111$	−7.63997	−0.725154
$112$	−18.4792	−1.74612
$113$	15.7092	1.47779	0.738897	−	0.673819i	$-0.235347\pi$
$113$	15.7092	1.47779	0.738897	+	0.673819i	$0.235347\pi$
$114$	11.1055	1.04013
$115$	−6.20826	−0.578924
$116$	36.3503	3.37504
$117$	−1.06791	−0.0987280
$118$	16.1846	1.48992
$119$	1.17900	0.108079
$120$	−31.7002	−2.89382
$121$	14.1930	1.29027
$122$	25.6123	2.31883
$123$	−15.0121	−1.35360
$124$	4.57394	0.410752
$125$	15.7747	1.41093
$126$	−5.04140	−0.449123
$127$	−8.77542	−0.778692	−0.389346	−	0.921091i	$-0.627299\pi$
$127$	−8.77542	−0.778692	−0.389346	+	0.921091i	$0.627299\pi$
$128$	17.7922	1.57262
$129$	−9.15352	−0.805923
$130$	−18.0942	−1.58697
$131$	4.17930	0.365147	0.182574	−	0.983192i	$-0.441557\pi$
$131$	4.17930	0.365147	0.182574	+	0.983192i	$0.441557\pi$
$132$	32.7174	2.84769
$133$	10.5126	0.911558
$134$	0.549785	0.0474942
$135$	−20.9334	−1.80166
$136$	1.72437	0.147864
$137$	−8.14588	−0.695950	−0.347975	−	0.937504i	$-0.613131\pi$
$137$	−8.14588	−0.695950	−0.347975	+	0.937504i	$0.613131\pi$
$138$	6.40356	0.545107
$139$	1.00000	0.0848189
$139$	1.00000	0.0848189
$140$	−57.7137	−4.87770
$141$	−9.90798	−0.834402
$142$	10.9734	0.920868
$143$	9.70986	0.811979
$144$	−2.77371	−0.231142
$145$	32.8649	2.72928
$146$	4.78350	0.395885
$147$	10.2104	0.842140
$148$	−20.3435	−1.67222
$149$	0.336484	0.0275658	0.0137829	−	0.999905i	$-0.495613\pi$
$149$	0.336484	0.0275658	0.0137829	+	0.999905i	$0.495613\pi$
$150$	−35.6968	−2.91463
$151$	17.6069	1.43283	0.716413	−	0.697677i	$-0.245783\pi$
$151$	17.6069	1.43283	0.716413	+	0.697677i	$0.245783\pi$
$152$	15.3754	1.24711
$153$	0.176967	0.0143070
$154$	45.8385	3.69377
$155$	4.13537	0.332161
$156$	12.6099	1.00960
$157$	5.49163	0.438280	0.219140	−	0.975693i	$-0.429675\pi$
$157$	5.49163	0.438280	0.219140	+	0.975693i	$0.429675\pi$
$158$	−40.9771	−3.25997
$159$	10.2544	0.813224
$160$	−6.47499	−0.511893
$161$	6.06168	0.477728
$162$	17.4795	1.37332
$163$	−3.37555	−0.264393	−0.132197	−	0.991224i	$-0.542203\pi$
$163$	−3.37555	−0.264393	−0.132197	+	0.991224i	$0.542203\pi$
$164$	−39.9738	−3.12143
$165$	29.5803	2.30282
$166$	27.7383	2.15291
$167$	2.95641	0.228774	0.114387	−	0.993436i	$-0.463510\pi$
$167$	2.95641	0.228774	0.114387	+	0.993436i	$0.463510\pi$
$168$	30.9517	2.38798
$169$	−9.25763	−0.712126
$170$	2.99847	0.229972
$171$	1.57793	0.120667
$172$	−24.3737	−1.85848
$173$	23.9199	1.81860	0.909298	−	0.416145i	$-0.136619\pi$
$173$	23.9199	1.81860	0.909298	+	0.416145i	$0.136619\pi$
$174$	−33.8987	−2.56985
$175$	−33.7910	−2.55436
$176$	25.2197	1.90101
$177$	−10.1976	−0.766500
$178$	−13.5134	−1.01287
$179$	0.981994	0.0733977	0.0366989	−	0.999326i	$-0.488316\pi$
$179$	0.981994	0.0733977	0.0366989	+	0.999326i	$0.488316\pi$
$180$	−8.66276	−0.645684
$181$	7.43082	0.552328	0.276164	−	0.961111i	$-0.410937\pi$
$181$	7.43082	0.552328	0.276164	+	0.961111i	$0.410937\pi$
$182$	17.6670	1.30957
$183$	−16.1378	−1.19294
$184$	8.86562	0.653582
$185$	−18.3928	−1.35227
$186$	−4.26545	−0.312758
$187$	−1.60906	−0.117666
$188$	−26.3826	−1.92415
$189$	20.4391	1.48673
$190$	26.7359	1.93962
$191$	14.4018	1.04208	0.521040	−	0.853532i	$-0.325544\pi$
$191$	14.4018	1.04208	0.521040	+	0.853532i	$0.325544\pi$
$192$	−9.04428	−0.652714
$193$	−10.7996	−0.777370	−0.388685	−	0.921371i	$-0.627071\pi$
$193$	−10.7996	−0.777370	−0.388685	+	0.921371i	$0.627071\pi$
$194$	−8.59762	−0.617273
$195$	11.4008	0.816430
$196$	27.1879	1.94199
$197$	23.3541	1.66391	0.831954	−	0.554844i	$-0.187222\pi$
$197$	23.3541	1.66391	0.831954	+	0.554844i	$0.187222\pi$
$198$	6.88030	0.488962
$199$	−19.1019	−1.35410	−0.677048	−	0.735939i	$-0.736741\pi$
$199$	−19.1019	−1.35410	−0.677048	+	0.735939i	$0.736741\pi$
$200$	−49.4217	−3.49464
$201$	−0.346409	−0.0244338
$202$	−20.3917	−1.43476
$203$	−32.0889	−2.25220
$204$	−2.08964	−0.146304
$205$	−36.1409	−2.52419
$206$	10.9051	0.759797
$207$	0.909852	0.0632391
$208$	9.72017	0.673973
$209$	−14.3472	−0.992416
$210$	53.8212	3.71402
$211$	−3.95125	−0.272015	−0.136008	−	0.990708i	$-0.543427\pi$
$211$	−3.95125	−0.272015	−0.136008	+	0.990708i	$0.543427\pi$
$212$	27.3050	1.87531
$213$	−6.91413	−0.473748
$214$	3.64569	0.249214
$215$	−22.0366	−1.50288
$216$	29.8936	2.03400
$217$	−4.03773	−0.274099
$218$	27.1781	1.84073
$219$	−3.01399	−0.203666
$220$	78.7655	5.31037
$221$	−0.620163	−0.0417167
$222$	18.9714	1.27328
$223$	8.53385	0.571469	0.285734	−	0.958309i	$-0.407762\pi$
$223$	8.53385	0.571469	0.285734	+	0.958309i	$0.407762\pi$
$224$	6.32211	0.422414
$225$	−5.07200	−0.338133
$226$	−39.0086	−2.59481
$227$	−6.89031	−0.457326	−0.228663	−	0.973506i	$-0.573435\pi$
$227$	−6.89031	−0.457326	−0.228663	+	0.973506i	$0.573435\pi$
$228$	−18.6323	−1.23396
$229$	5.62355	0.371615	0.185807	−	0.982586i	$-0.440510\pi$
$229$	5.62355	0.371615	0.185807	+	0.982586i	$0.440510\pi$
$230$	15.4162	1.01652
$231$	−28.8819	−1.90029
$232$	−46.9322	−3.08125
$233$	−1.43017	−0.0936935	−0.0468468	−	0.998902i	$-0.514917\pi$
$233$	−1.43017	−0.0936935	−0.0468468	+	0.998902i	$0.514917\pi$
$234$	2.65180	0.173354
$235$	−23.8529	−1.55599
$236$	−27.1539	−1.76757
$237$	25.8189	1.67712
$238$	−2.92768	−0.189773
$239$	11.4060	0.737796	0.368898	−	0.929470i	$-0.379735\pi$
$239$	11.4060	0.737796	0.368898	+	0.929470i	$0.379735\pi$
$240$	29.6117	1.91143
$241$	16.5641	1.06699	0.533493	−	0.845804i	$-0.320879\pi$
$241$	16.5641	1.06699	0.533493	+	0.845804i	$0.320879\pi$
$242$	−35.2436	−2.26555
$243$	5.65899	0.363025
$244$	−42.9712	−2.75095
$245$	24.5810	1.57042
$246$	37.2778	2.37674
$247$	−5.52968	−0.351845
$248$	−5.90545	−0.374997
$249$	−17.4774	−1.10758
$250$	−39.1714	−2.47742
$251$	7.14003	0.450674	0.225337	−	0.974281i	$-0.427652\pi$
$251$	7.14003	0.450674	0.225337	+	0.974281i	$0.427652\pi$
$252$	8.45823	0.532818
$253$	−8.27275	−0.520104
$254$	21.7909	1.36728
$255$	−1.88928	−0.118311
$256$	−32.6200	−2.03875
$257$	23.1376	1.44328	0.721641	−	0.692268i	$-0.243388\pi$
$257$	23.1376	1.44328	0.721641	+	0.692268i	$0.243388\pi$
$258$	22.7298	1.41510
$259$	17.9586	1.11589
$260$	30.3577	1.88271
$261$	−4.81651	−0.298134
$262$	−10.3779	−0.641151
$263$	28.9163	1.78306	0.891528	−	0.452966i	$-0.149634\pi$
$263$	28.9163	1.78306	0.891528	+	0.452966i	$0.149634\pi$
$264$	−42.2417	−2.59980
$265$	24.6868	1.51650
$266$	−26.1046	−1.60058
$267$	8.51451	0.521079
$268$	−0.922405	−0.0563449
$269$	4.15750	0.253487	0.126744	−	0.991936i	$-0.459547\pi$
$269$	4.15750	0.253487	0.126744	+	0.991936i	$0.459547\pi$
$270$	51.9813	3.16348
$271$	−7.73906	−0.470115	−0.235057	−	0.971982i	$-0.575528\pi$
$271$	−7.73906	−0.470115	−0.235057	+	0.971982i	$0.575528\pi$
$272$	−1.61077	−0.0976672
$273$	−11.1316	−0.673718
$274$	20.2277	1.22200
$275$	46.1167	2.78094
$276$	−10.7436	−0.646689
$277$	3.93125	0.236206	0.118103	−	0.993001i	$-0.462319\pi$
$277$	3.93125	0.236206	0.118103	+	0.993001i	$0.462319\pi$
$278$	−2.48318	−0.148931
$279$	−0.606059	−0.0362838
$280$	74.5146	4.45310
$281$	−13.5398	−0.807717	−0.403859	−	0.914821i	$-0.632331\pi$
$281$	−13.5398	−0.807717	−0.403859	+	0.914821i	$0.632331\pi$
$282$	24.6033	1.46510
$283$	19.1993	1.14128	0.570641	−	0.821200i	$-0.306695\pi$
$283$	19.1993	1.14128	0.570641	+	0.821200i	$0.306695\pi$
$284$	−18.4107	−1.09247
$285$	−16.8457	−0.997856
$286$	−24.1113	−1.42573
$287$	35.2876	2.08296
$288$	0.948942	0.0559169
$289$	−16.8972	−0.993955
$290$	−81.6093	−4.79226
$291$	5.41719	0.317561
$292$	−8.02554	−0.469659
$293$	−25.5252	−1.49120	−0.745598	−	0.666396i	$-0.767836\pi$
$293$	−25.5252	−1.49120	−0.745598	+	0.666396i	$0.767836\pi$
$294$	−25.3542	−1.47869
$295$	−24.5502	−1.42937
$296$	26.2656	1.52666
$297$	−27.8945	−1.61861
$298$	−0.835549	−0.0484020
$299$	−3.18848	−0.184395
$300$	59.8905	3.45778
$301$	21.5163	1.24018
$302$	−43.7209	−2.51586
$303$	12.8484	0.738123
$304$	−14.3624	−0.823742
$305$	−38.8509	−2.22460
$306$	−0.439441	−0.0251212
$307$	6.77909	0.386903	0.193452	−	0.981110i	$-0.438032\pi$
$307$	6.77909	0.386903	0.193452	+	0.981110i	$0.438032\pi$
$308$	−76.9058	−4.38211
$309$	−6.87111	−0.390884
$310$	−10.2688	−0.583231
$311$	−32.0482	−1.81729	−0.908643	−	0.417573i	$-0.862881\pi$
$311$	−32.0482	−1.81729	−0.908643	+	0.417573i	$0.862881\pi$
$312$	−16.2808	−0.921718
$313$	2.35936	0.133359	0.0666795	−	0.997774i	$-0.478760\pi$
$313$	2.35936	0.133359	0.0666795	+	0.997774i	$0.478760\pi$
$314$	−13.6367	−0.769563
$315$	7.64721	0.430871
$316$	68.7496	3.86747
$317$	8.05786	0.452574	0.226287	−	0.974061i	$-0.427341\pi$
$317$	8.05786	0.452574	0.226287	+	0.974061i	$0.427341\pi$
$318$	−25.4634	−1.42792
$319$	43.7937	2.45198
$320$	−21.7736	−1.21718
$321$	−2.29708	−0.128210
$322$	−15.0522	−0.838828
$323$	0.916347	0.0509869
$324$	−29.3264	−1.62924
$325$	17.7743	0.985939
$326$	8.38208	0.464241
$327$	−17.1244	−0.946981
$328$	51.6104	2.84971
$329$	23.2897	1.28400
$330$	−73.4531	−4.04346
$331$	−9.67255	−0.531651	−0.265826	−	0.964021i	$-0.585645\pi$
$331$	−9.67255	−0.531651	−0.265826	+	0.964021i	$0.585645\pi$
$332$	−46.5381	−2.55411
$333$	2.69556	0.147716
$334$	−7.34128	−0.401697
$335$	−0.833960	−0.0455641
$336$	−28.9126	−1.57731
$337$	−11.2077	−0.610521	−0.305261	−	0.952269i	$-0.598744\pi$
$337$	−11.2077	−0.610521	−0.305261	+	0.952269i	$0.598744\pi$
$338$	22.9883	1.25040
$339$	24.5786	1.33492
$340$	−5.03070	−0.272828
$341$	5.51054	0.298412
$342$	−3.91828	−0.211876
$343$	1.74367	0.0941491
$344$	31.4691	1.69670
$345$	−9.71345	−0.522955
$346$	−59.3973	−3.19322
$347$	2.42372	0.130112	0.0650561	−	0.997882i	$-0.479277\pi$
$347$	2.42372	0.130112	0.0650561	+	0.997882i	$0.479277\pi$
$348$	56.8737	3.04875
$349$	−19.8877	−1.06457	−0.532283	−	0.846567i	$-0.678666\pi$
$349$	−19.8877	−1.06457	−0.532283	+	0.846567i	$0.678666\pi$
$350$	83.9091	4.48513
$351$	−10.7511	−0.573851
$352$	−8.62818	−0.459883
$353$	2.50948	0.133566	0.0667831	−	0.997768i	$-0.478726\pi$
$353$	2.50948	0.133566	0.0667831	+	0.997768i	$0.478726\pi$
$354$	25.3225	1.34587
$355$	−16.6454	−0.883445
$356$	22.6721	1.20162
$357$	1.84467	0.0976303
$358$	−2.43847	−0.128877
$359$	−11.0468	−0.583029	−0.291515	−	0.956566i	$-0.594159\pi$
$359$	−11.0468	−0.583029	−0.291515	+	0.956566i	$0.594159\pi$
$360$	11.1846	0.589478
$361$	−10.8294	−0.569968
$362$	−18.4520	−0.969817
$363$	22.2063	1.16553
$364$	−29.6410	−1.55361
$365$	−7.25601	−0.379797
$366$	40.0731	2.09465
$367$	28.7068	1.49848	0.749242	−	0.662296i	$-0.230418\pi$
$367$	28.7068	1.49848	0.749242	+	0.662296i	$0.230418\pi$
$368$	−8.28154	−0.431705
$369$	5.29662	0.275731
$370$	45.6726	2.37441
$371$	−24.1040	−1.25142
$372$	7.15639	0.371042
$373$	36.5928	1.89470	0.947350	−	0.320199i	$-0.103750\pi$
$373$	36.5928	1.89470	0.947350	+	0.320199i	$0.103750\pi$
$374$	3.99558	0.206607
$375$	24.6811	1.27453
$376$	34.0628	1.75666
$377$	16.8789	0.869310
$378$	−50.7540	−2.61050
$379$	−2.73973	−0.140730	−0.0703652	−	0.997521i	$-0.522416\pi$
$379$	−2.73973	−0.140730	−0.0703652	+	0.997521i	$0.522416\pi$
$380$	−44.8563	−2.30108
$381$	−13.7300	−0.703410
$382$	−35.7623	−1.82976
$383$	38.8075	1.98297	0.991486	−	0.130216i	$-0.0415671\pi$
$383$	38.8075	1.98297	0.991486	+	0.130216i	$0.0415671\pi$
$384$	27.8377	1.42059
$385$	−69.5316	−3.54366
$386$	26.8172	1.36496
$387$	3.22957	0.164168
$388$	14.4247	0.732304
$389$	−28.4346	−1.44169	−0.720846	−	0.693095i	$-0.756247\pi$
$389$	−28.4346	−1.44169	−0.720846	+	0.693095i	$0.756247\pi$
$390$	−28.3103	−1.43355
$391$	0.528376	0.0267211
$392$	−35.1025	−1.77295
$393$	6.53893	0.329845
$394$	−57.9923	−2.92161
$395$	62.1576	3.12749
$396$	−11.5435	−0.580081
$397$	−14.3578	−0.720598	−0.360299	−	0.932837i	$-0.617325\pi$
$397$	−14.3578	−0.720598	−0.360299	+	0.932837i	$0.617325\pi$
$398$	47.4333	2.37762
$399$	16.4480	0.823431
$400$	46.1657	2.30828
$401$	−22.9135	−1.14425	−0.572123	−	0.820168i	$-0.693880\pi$
$401$	−22.9135	−1.14425	−0.572123	+	0.820168i	$0.693880\pi$
$402$	0.860194	0.0429026
$403$	2.12387	0.105797
$404$	34.2124	1.70213
$405$	−26.5144	−1.31751
$406$	79.6824	3.95457
$407$	−24.5091	−1.21487
$408$	2.69796	0.133569
$409$	10.2648	0.507560	0.253780	−	0.967262i	$-0.418326\pi$
$409$	10.2648	0.507560	0.253780	+	0.967262i	$0.418326\pi$
$410$	89.7442	4.43215
$411$	−12.7450	−0.628667
$412$	−18.2961	−0.901387
$413$	23.9706	1.17951
$414$	−2.25932	−0.111040
$415$	−42.0758	−2.06542
$416$	−3.32547	−0.163044
$417$	1.56460	0.0766188
$418$	35.6266	1.74255
$419$	−33.3063	−1.62712	−0.813559	−	0.581482i	$-0.802473\pi$
$419$	−33.3063	−1.62712	−0.813559	+	0.581482i	$0.802473\pi$
$420$	−90.2989	−4.40613
$421$	2.57798	0.125643	0.0628215	−	0.998025i	$-0.479990\pi$
$421$	2.57798	0.125643	0.0628215	+	0.998025i	$0.479990\pi$
$422$	9.81165	0.477624
$423$	3.49576	0.169970
$424$	−35.2537	−1.71207
$425$	−2.94545	−0.142875
$426$	17.1690	0.831840
$427$	37.9336	1.83574
$428$	−6.11658	−0.295656
$429$	15.1920	0.733479
$430$	54.7208	2.63887
$431$	33.9552	1.63556	0.817781	−	0.575529i	$-0.195204\pi$
$431$	33.9552	1.63556	0.817781	+	0.575529i	$0.195204\pi$
$432$	−27.9242	−1.34350
$433$	−27.5099	−1.32204	−0.661020	−	0.750368i	$-0.729876\pi$
$433$	−27.5099	−1.32204	−0.661020	+	0.750368i	$0.729876\pi$
$434$	10.0264	0.481282
$435$	51.4204	2.46542
$436$	−45.5982	−2.18376
$437$	4.71127	0.225370
$438$	7.48426	0.357612
$439$	−6.88770	−0.328732	−0.164366	−	0.986399i	$-0.552558\pi$
$439$	−6.88770	−0.328732	−0.164366	+	0.986399i	$0.552558\pi$
$440$	−101.695	−4.84810
$441$	−3.60247	−0.171546
$442$	1.53997	0.0732491
$443$	−26.6821	−1.26770	−0.633851	−	0.773455i	$-0.718527\pi$
$443$	−26.6821	−1.26770	−0.633851	+	0.773455i	$0.718527\pi$
$444$	−31.8294	−1.51055
$445$	20.4982	0.971708
$446$	−21.1911	−1.00343
$447$	0.526463	0.0249008
$448$	21.2595	1.00442
$449$	−21.2689	−1.00374	−0.501871	−	0.864942i	$-0.667355\pi$
$449$	−21.2689	−1.00374	−0.501871	+	0.864942i	$0.667355\pi$
$450$	12.5947	0.593718
$451$	−48.1591	−2.26772
$452$	65.4469	3.07837
$453$	27.5477	1.29430
$454$	17.1099	0.803005
$455$	−26.7988	−1.25635
$456$	24.0563	1.12654
$457$	15.5804	0.728823	0.364411	−	0.931238i	$-0.381270\pi$
$457$	15.5804	0.728823	0.364411	+	0.931238i	$0.381270\pi$
$458$	−13.9643	−0.652508
$459$	1.78161	0.0831584
$460$	−25.8646	−1.20595
$461$	−7.61982	−0.354890	−0.177445	−	0.984131i	$-0.556783\pi$
$461$	−7.61982	−0.354890	−0.177445	+	0.984131i	$0.556783\pi$
$462$	71.7189	3.33666
$463$	27.8633	1.29492	0.647459	−	0.762100i	$-0.275832\pi$
$463$	27.8633	1.29492	0.647459	+	0.762100i	$0.275832\pi$
$464$	43.8402	2.03523
$465$	6.47020	0.300048
$466$	3.55136	0.164514
$467$	20.6076	0.953607	0.476804	−	0.879010i	$-0.341795\pi$
$467$	20.6076	0.953607	0.476804	+	0.879010i	$0.341795\pi$
$468$	−4.44908	−0.205659
$469$	0.814270	0.0375995
$470$	59.2310	2.73212
$471$	8.59220	0.395908
$472$	35.0586	1.61370
$473$	−29.3646	−1.35019
$474$	−64.1128	−2.94480
$475$	−26.2631	−1.20503
$476$	4.91193	0.225138
$477$	−3.61798	−0.165656
$478$	−28.3232	−1.29547
$479$	8.70849	0.397901	0.198951	−	0.980010i	$-0.436247\pi$
$479$	8.70849	0.397901	0.198951	+	0.980010i	$0.436247\pi$
$480$	−10.1308	−0.462404
$481$	−9.44630	−0.430714
$482$	−41.1316	−1.87349
$483$	9.48411	0.431542
$484$	59.1302	2.68774
$485$	13.0416	0.592188
$486$	−14.0523	−0.637424
$487$	−0.792885	−0.0359291	−0.0179645	−	0.999839i	$-0.505719\pi$
$487$	−0.792885	−0.0359291	−0.0179645	+	0.999839i	$0.505719\pi$
$488$	55.4805	2.51148
$489$	−5.28138	−0.238832
$490$	−61.0389	−2.75746
$491$	−4.15362	−0.187450	−0.0937252	−	0.995598i	$-0.529878\pi$
$491$	−4.15362	−0.187450	−0.0937252	+	0.995598i	$0.529878\pi$
$492$	−62.5430	−2.81965
$493$	−2.79708	−0.125974
$494$	13.7312	0.617795
$495$	−10.4366	−0.469091
$496$	5.51639	0.247693
$497$	16.2524	0.729019
$498$	43.3994	1.94477
$499$	9.15019	0.409619	0.204809	−	0.978802i	$-0.434343\pi$
$499$	9.15019	0.409619	0.204809	+	0.978802i	$0.434343\pi$
$500$	65.7200	2.93909
$501$	4.62560	0.206656
$502$	−17.7299	−0.791326
$503$	−18.4456	−0.822450	−0.411225	−	0.911534i	$-0.634899\pi$
$503$	−18.4456	−0.822450	−0.411225	+	0.911534i	$0.634899\pi$
$504$	−10.9205	−0.486437
$505$	30.9319	1.37645
$506$	20.5427	0.913234
$507$	−14.4845	−0.643279
$508$	−36.5598	−1.62208
$509$	30.4642	1.35030	0.675152	−	0.737679i	$-0.264078\pi$
$509$	30.4642	1.35030	0.675152	+	0.737679i	$0.264078\pi$
$510$	4.69141	0.207739
$511$	7.08469	0.313408
$512$	45.4169	2.00716
$513$	15.8857	0.701371
$514$	−57.4546	−2.53421
$515$	−16.5418	−0.728920
$516$	−38.1351	−1.67880
$517$	−31.7849	−1.39790
$518$	−44.5942	−1.95936
$519$	37.4251	1.64278
$520$	−39.1951	−1.71882
$521$	10.4940	0.459749	0.229875	−	0.973220i	$-0.426168\pi$
$521$	10.4940	0.459749	0.229875	+	0.973220i	$0.426168\pi$
$522$	11.9602	0.523486
$523$	11.7187	0.512423	0.256211	−	0.966621i	$-0.417526\pi$
$523$	11.7187	0.512423	0.256211	+	0.966621i	$0.417526\pi$
$524$	17.4116	0.760631
$525$	−52.8695	−2.30741
$526$	−71.8043	−3.13081
$527$	−0.351955	−0.0153314
$528$	39.4588	1.71722
$529$	−20.2834	−0.881888
$530$	−61.3018	−2.66278
$531$	3.59795	0.156138
$532$	43.7972	1.89885
$533$	−18.5615	−0.803986
$534$	−21.1430	−0.914948
$535$	−5.53009	−0.239087
$536$	1.19092	0.0514401
$537$	1.53643	0.0663018
$538$	−10.3238	−0.445091
$539$	32.7551	1.41086
$540$	−87.2119	−3.75300
$541$	−3.46252	−0.148865	−0.0744326	−	0.997226i	$-0.523715\pi$
$541$	−3.46252	−0.148865	−0.0744326	+	0.997226i	$0.523715\pi$
$542$	19.2175	0.825460
$543$	11.6263	0.498930
$544$	0.551077	0.0236272
$545$	−41.2260	−1.76593
$546$	27.6418	1.18296
$547$	−17.5518	−0.750459	−0.375230	−	0.926932i	$-0.622436\pi$
$547$	−17.5518	−0.750459	−0.375230	+	0.926932i	$0.622436\pi$
$548$	−33.9371	−1.44972
$549$	5.69380	0.243005
$550$	−114.516	−4.88297
$551$	−24.9402	−1.06249
$552$	13.8711	0.590395
$553$	−60.6900	−2.58080
$554$	−9.76198	−0.414747
$555$	−28.7774	−1.22153
$556$	4.16616	0.176685
$557$	−38.0718	−1.61315	−0.806577	−	0.591129i	$-0.798682\pi$
$557$	−38.0718	−1.61315	−0.806577	+	0.591129i	$0.798682\pi$
$558$	1.50495	0.0637096
$559$	−11.3177	−0.478688
$560$	−69.6055	−2.94137
$561$	−2.51754	−0.106290
$562$	33.6217	1.41825
$563$	−37.7706	−1.59184	−0.795921	−	0.605400i	$-0.793013\pi$
$563$	−37.7706	−1.59184	−0.795921	+	0.605400i	$0.793013\pi$
$564$	−41.2783	−1.73813
$565$	59.1715	2.48937
$566$	−47.6753	−2.00394
$567$	25.8884	1.08721
$568$	23.7702	0.997375
$569$	18.5035	0.775709	0.387854	−	0.921721i	$-0.373216\pi$
$569$	18.5035	0.775709	0.387854	+	0.921721i	$0.373216\pi$
$570$	41.8310	1.75211
$571$	26.7650	1.12008	0.560040	−	0.828466i	$-0.310786\pi$
$571$	26.7650	1.12008	0.560040	+	0.828466i	$0.310786\pi$
$572$	40.4529	1.69142
$573$	22.5331	0.941335
$574$	−87.6253	−3.65741
$575$	−15.1436	−0.631532
$576$	3.19103	0.132960
$577$	−10.4962	−0.436961	−0.218480	−	0.975841i	$-0.570110\pi$
$577$	−10.4962	−0.436961	−0.218480	+	0.975841i	$0.570110\pi$
$578$	41.9588	1.74526
$579$	−16.8970	−0.702215
$580$	136.920	5.68531
$581$	41.0824	1.70438
$582$	−13.4518	−0.557597
$583$	32.8962	1.36242
$584$	10.3618	0.428776
$585$	−4.02247	−0.166309
$586$	63.3835	2.61835
$587$	−13.6306	−0.562596	−0.281298	−	0.959621i	$-0.590765\pi$
$587$	−13.6306	−0.562596	−0.281298	+	0.959621i	$0.590765\pi$
$588$	42.5382	1.75425
$589$	−3.13821	−0.129308
$590$	60.9625	2.50979
$591$	36.5398	1.50305
$592$	−24.5352	−1.00839
$593$	−19.8228	−0.814025	−0.407012	−	0.913423i	$-0.633429\pi$
$593$	−19.8228	−0.814025	−0.407012	+	0.913423i	$0.633429\pi$
$594$	69.2671	2.84206
$595$	4.44095	0.182061
$596$	1.40185	0.0574219
$597$	−29.8868	−1.22319
$598$	7.91756	0.323773
$599$	39.6002	1.61802	0.809010	−	0.587794i	$-0.200004\pi$
$599$	39.6002	1.61802	0.809010	+	0.587794i	$0.200004\pi$
$600$	−77.3251	−3.15679
$601$	7.01537	0.286163	0.143082	−	0.989711i	$-0.454299\pi$
$601$	7.01537	0.286163	0.143082	+	0.989711i	$0.454299\pi$
$602$	−53.4288	−2.17760
$603$	0.122221	0.00497722
$604$	73.3530	2.98469
$605$	53.4605	2.17348
$606$	−31.9049	−1.29605
$607$	−35.2836	−1.43212	−0.716058	−	0.698041i	$-0.754055\pi$
$607$	−35.2836	−1.43212	−0.716058	+	0.698041i	$0.754055\pi$
$608$	4.91368	0.199276
$609$	−50.2063	−2.03446
$610$	96.4737	3.90611
$611$	−12.2505	−0.495603
$612$	0.737275	0.0298026
$613$	29.2541	1.18156	0.590782	−	0.806831i	$-0.298819\pi$
$613$	29.2541	1.18156	0.590782	+	0.806831i	$0.298819\pi$
$614$	−16.8337	−0.679352
$615$	−56.5460	−2.28016
$616$	99.2936	4.00065
$617$	−7.71652	−0.310656	−0.155328	−	0.987863i	$-0.549643\pi$
$617$	−7.71652	−0.310656	−0.155328	+	0.987863i	$0.549643\pi$
$618$	17.0622	0.686341
$619$	−13.6849	−0.550041	−0.275021	−	0.961438i	$-0.588685\pi$
$619$	−13.6849	−0.550041	−0.275021	+	0.961438i	$0.588685\pi$
$620$	17.2286	0.691918
$621$	9.15988	0.367573
$622$	79.5813	3.19092
$623$	−20.0142	−0.801853
$624$	15.2082	0.608814
$625$	13.4787	0.539147
$626$	−5.85871	−0.234161
$627$	−22.4476	−0.896471
$628$	22.8790	0.912973
$629$	1.56538	0.0624160
$630$	−18.9894	−0.756555
$631$	6.67134	0.265582	0.132791	−	0.991144i	$-0.457606\pi$
$631$	6.67134	0.265582	0.132791	+	0.991144i	$0.457606\pi$
$632$	−88.7632	−3.53081
$633$	−6.18212	−0.245717
$634$	−20.0091	−0.794662
$635$	−33.0543	−1.31172
$636$	42.7214	1.69401
$637$	12.6245	0.500199
$638$	−108.747	−4.30535
$639$	2.43946	0.0965037
$640$	67.0177	2.64911
$641$	50.3780	1.98981	0.994905	−	0.100820i	$-0.0321465\pi$
$641$	50.3780	1.98981	0.994905	+	0.100820i	$0.0321465\pi$
$642$	5.70405	0.225121
$643$	20.6698	0.815136	0.407568	−	0.913175i	$-0.366377\pi$
$643$	20.6698	0.815136	0.407568	+	0.913175i	$0.366377\pi$
$644$	25.2540	0.995146
$645$	−34.4785	−1.35759
$646$	−2.27545	−0.0895264
$647$	31.4817	1.23767	0.618836	−	0.785520i	$-0.287604\pi$
$647$	31.4817	1.23767	0.618836	+	0.785520i	$0.287604\pi$
$648$	37.8635	1.48742
$649$	−32.7141	−1.28414
$650$	−44.1366	−1.73118
$651$	−6.31743	−0.247600
$652$	−14.0631	−0.550753
$653$	9.35717	0.366174	0.183087	−	0.983097i	$-0.441391\pi$
$653$	9.35717	0.366174	0.183087	+	0.983097i	$0.441391\pi$
$654$	42.5229	1.66278
$655$	15.7421	0.615096
$656$	−48.2103	−1.88230
$657$	1.06340	0.0414874
$658$	−57.8325	−2.25455
$659$	31.4427	1.22483	0.612416	−	0.790535i	$-0.290198\pi$
$659$	31.4427	1.22483	0.612416	+	0.790535i	$0.290198\pi$
$660$	123.236	4.79697
$661$	−20.2818	−0.788871	−0.394435	−	0.918924i	$-0.629060\pi$
$661$	−20.2818	−0.788871	−0.394435	+	0.918924i	$0.629060\pi$
$662$	24.0186	0.933511
$663$	−0.970307	−0.0376836
$664$	60.0858	2.33178
$665$	39.5977	1.53553
$666$	−6.69355	−0.259370
$667$	−14.3808	−0.556826
$668$	12.3169	0.476555
$669$	13.3521	0.516221
$670$	2.07087	0.0800047
$671$	−51.7704	−1.99857
$672$	9.89158	0.381576
$673$	11.5905	0.446782	0.223391	−	0.974729i	$-0.428287\pi$
$673$	11.5905	0.446782	0.223391	+	0.974729i	$0.428287\pi$
$674$	27.8307	1.07200
$675$	−51.0620	−1.96538
$676$	−38.5688	−1.48342
$677$	−34.8510	−1.33943	−0.669717	−	0.742617i	$-0.733584\pi$
$677$	−34.8510	−1.33943	−0.669717	+	0.742617i	$0.733584\pi$
$678$	−61.0329	−2.34395
$679$	−12.7337	−0.488674
$680$	6.49518	0.249079
$681$	−10.7806	−0.413113
$682$	−13.6836	−0.523974
$683$	12.7665	0.488497	0.244248	−	0.969713i	$-0.421459\pi$
$683$	12.7665	0.488497	0.244248	+	0.969713i	$0.421459\pi$
$684$	6.57391	0.251360
$685$	−30.6830	−1.17234
$686$	−4.32983	−0.165314
$687$	8.79861	0.335688
$688$	−29.3958	−1.12071
$689$	12.6788	0.483025
$690$	24.1202	0.918241
$691$	−3.25420	−0.123796	−0.0618978	−	0.998082i	$-0.519715\pi$
$691$	−3.25420	−0.123796	−0.0618978	+	0.998082i	$0.519715\pi$
$692$	99.6542	3.78828
$693$	10.1902	0.387094
$694$	−6.01853	−0.228460
$695$	3.76669	0.142879
$696$	−73.4301	−2.78336
$697$	3.07590	0.116508
$698$	49.3847	1.86924
$699$	−2.23764	−0.0846354
$700$	−140.779	−5.32095
$701$	−10.7274	−0.405168	−0.202584	−	0.979265i	$-0.564934\pi$
$701$	−10.7274	−0.405168	−0.202584	+	0.979265i	$0.564934\pi$
$702$	26.6969	1.00761
$703$	13.9578	0.526427
$704$	−29.0142	−1.09351
$705$	−37.3203	−1.40556
$706$	−6.23148	−0.234525
$707$	−30.2016	−1.13585
$708$	−42.4849	−1.59668
$709$	−30.3373	−1.13934	−0.569670	−	0.821873i	$-0.692929\pi$
$709$	−30.3373	−1.13934	−0.569670	+	0.821873i	$0.692929\pi$
$710$	41.3334	1.55122
$711$	−9.10950	−0.341633
$712$	−29.2722	−1.09702
$713$	−1.80953	−0.0677673
$714$	−4.58064	−0.171426
$715$	36.5740	1.36779
$716$	4.09115	0.152893
$717$	17.8459	0.666467
$718$	27.4312	1.02372
$719$	−16.5155	−0.615924	−0.307962	−	0.951399i	$-0.599647\pi$
$719$	−16.5155	−0.615924	−0.307962	+	0.951399i	$0.599647\pi$
$720$	−10.4477	−0.389363
$721$	16.1513	0.601504
$722$	26.8913	1.00079
$723$	25.9162	0.963833
$724$	30.9580	1.15054
$725$	80.1661	2.97729
$726$	−55.1422	−2.04652
$727$	−0.711471	−0.0263870	−0.0131935	−	0.999913i	$-0.504200\pi$
$727$	−0.711471	−0.0263870	−0.0131935	+	0.999913i	$0.504200\pi$
$728$	38.2697	1.41837
$729$	29.9716	1.11006
$730$	18.0180	0.666874
$731$	1.87550	0.0693680
$732$	−67.2328	−2.48500
$733$	−50.8654	−1.87876	−0.939378	−	0.342884i	$-0.888596\pi$
$733$	−50.8654	−1.87876	−0.939378	+	0.342884i	$0.888596\pi$
$734$	−71.2841	−2.63114
$735$	38.4594	1.41860
$736$	2.83328	0.104436
$737$	−1.11128	−0.0409347
$738$	−13.1525	−0.484148
$739$	34.1665	1.25684	0.628418	−	0.777876i	$-0.283703\pi$
$739$	34.1665	1.25684	0.628418	+	0.777876i	$0.283703\pi$
$740$	−76.6275	−2.81688
$741$	−8.65174	−0.317830
$742$	59.8544	2.19732
$743$	−42.4874	−1.55871	−0.779356	−	0.626581i	$-0.784454\pi$
$743$	−42.4874	−1.55871	−0.779356	+	0.626581i	$0.784454\pi$
$744$	−9.23967	−0.338743
$745$	1.26743	0.0464350
$746$	−90.8662	−3.32685
$747$	6.16642	0.225617
$748$	−6.70361	−0.245108
$749$	5.39952	0.197294
$750$	−61.2875	−2.23790
$751$	−28.8677	−1.05340	−0.526700	−	0.850052i	$-0.676571\pi$
$751$	−28.8677	−1.05340	−0.526700	+	0.850052i	$0.676571\pi$
$752$	−31.8187	−1.16031
$753$	11.1713	0.407104
$754$	−41.9134	−1.52640
$755$	66.3195	2.41362
$756$	85.1528	3.09698
$757$	22.2621	0.809131	0.404566	−	0.914509i	$-0.367423\pi$
$757$	22.2621	0.809131	0.404566	+	0.914509i	$0.367423\pi$
$758$	6.80323	0.247104
$759$	−12.9435	−0.469821
$760$	57.9143	2.10077
$761$	−1.10166	−0.0399351	−0.0199675	−	0.999801i	$-0.506356\pi$
$761$	−1.10166	−0.0399351	−0.0199675	+	0.999801i	$0.506356\pi$
$762$	34.0941	1.23510
$763$	40.2527	1.45724
$764$	60.0004	2.17074
$765$	0.666581	0.0241003
$766$	−96.3659	−3.48184
$767$	−12.6086	−0.455272
$768$	−51.0373	−1.84165
$769$	−30.6128	−1.10393	−0.551963	−	0.833869i	$-0.686121\pi$
$769$	−30.6128	−1.10393	−0.551963	+	0.833869i	$0.686121\pi$
$770$	172.659	6.22221
$771$	36.2010	1.30375
$772$	−44.9928	−1.61932
$773$	−22.3697	−0.804583	−0.402291	−	0.915512i	$-0.631786\pi$
$773$	−22.3697	−0.804583	−0.402291	+	0.915512i	$0.631786\pi$
$774$	−8.01960	−0.288259
$775$	10.0873	0.362345
$776$	−18.6239	−0.668558
$777$	28.0979	1.00801
$778$	70.6082	2.53143
$779$	27.4262	0.982647
$780$	47.4977	1.70069
$781$	−22.1806	−0.793685
$782$	−1.31205	−0.0469188
$783$	−48.4899	−1.73289
$784$	32.7899	1.17107
$785$	20.6853	0.738289
$786$	−16.2373	−0.579166
$787$	13.7579	0.490416	0.245208	−	0.969471i	$-0.421144\pi$
$787$	13.7579	0.490416	0.245208	+	0.969471i	$0.421144\pi$
$788$	97.2969	3.46606
$789$	45.2424	1.61067
$790$	−154.348	−5.49146
$791$	−57.7745	−2.05422
$792$	14.9039	0.529586
$793$	−19.9533	−0.708563
$794$	35.6530	1.26528
$795$	38.6250	1.36989
$796$	−79.5815	−2.82069
$797$	−13.2106	−0.467942	−0.233971	−	0.972244i	$-0.575172\pi$
$797$	−13.2106	−0.467942	−0.233971	+	0.972244i	$0.575172\pi$
$798$	−40.8433	−1.44584
$799$	2.03009	0.0718193
$800$	−15.7942	−0.558410
$801$	−3.00411	−0.106145
$802$	56.8983	2.00915
$803$	−9.66892	−0.341209
$804$	−1.44319	−0.0508976
$805$	22.8325	0.804739
$806$	−5.27394	−0.185767
$807$	6.50482	0.228981
$808$	−44.1718	−1.55396
$809$	−34.1325	−1.20004	−0.600018	−	0.799986i	$-0.704840\pi$
$809$	−34.1325	−1.20004	−0.600018	+	0.799986i	$0.704840\pi$
$810$	65.8400	2.31338
$811$	37.3883	1.31288	0.656441	−	0.754377i	$-0.272061\pi$
$811$	37.3883	1.31288	0.656441	+	0.754377i	$0.272061\pi$
$812$	−133.688	−4.69152
$813$	−12.1085	−0.424665
$814$	60.8605	2.13316
$815$	−12.7146	−0.445375
$816$	−2.52021	−0.0882250
$817$	16.7229	0.585061
$818$	−25.4892	−0.891209
$819$	3.92750	0.137238
$820$	−150.569	−5.25809
$821$	56.5411	1.97330	0.986649	−	0.162861i	$-0.0520723\pi$
$821$	56.5411	1.97330	0.986649	+	0.162861i	$0.0520723\pi$
$822$	31.6482	1.10386
$823$	20.3282	0.708595	0.354297	−	0.935133i	$-0.384720\pi$
$823$	20.3282	0.708595	0.354297	+	0.935133i	$0.384720\pi$
$824$	23.6223	0.822922
$825$	72.1542	2.51209
$826$	−59.5231	−2.07107
$827$	6.50545	0.226217	0.113108	−	0.993583i	$-0.463919\pi$
$827$	6.50545	0.226217	0.113108	+	0.993583i	$0.463919\pi$
$828$	3.79059	0.131732
$829$	−29.5602	−1.02667	−0.513334	−	0.858189i	$-0.671590\pi$
$829$	−29.5602	−1.02667	−0.513334	+	0.858189i	$0.671590\pi$
$830$	104.482	3.62661
$831$	6.15083	0.213370
$832$	−11.1826	−0.387688
$833$	−2.09205	−0.0724853
$834$	−3.88518	−0.134533
$835$	11.1359	0.385373
$836$	−59.7727	−2.06728
$837$	−6.10146	−0.210897
$838$	82.7054	2.85701
$839$	20.3869	0.703834	0.351917	−	0.936031i	$-0.385530\pi$
$839$	20.3869	0.703834	0.351917	+	0.936031i	$0.385530\pi$
$840$	116.586	4.02258
$841$	47.1280	1.62510
$842$	−6.40158	−0.220613
$843$	−21.1844	−0.729629
$844$	−16.4616	−0.566630
$845$	−34.8706	−1.19959
$846$	−8.68060	−0.298445
$847$	−52.1983	−1.79355
$848$	32.9311	1.13086
$849$	30.0393	1.03094
$850$	7.31406	0.250870
$851$	8.04820	0.275889
$852$	−28.8054	−0.986856
$853$	−20.9930	−0.718788	−0.359394	−	0.933186i	$-0.617017\pi$
$853$	−20.9930	−0.718788	−0.359394	+	0.933186i	$0.617017\pi$
$854$	−94.1959	−3.22332
$855$	5.94357	0.203266
$856$	7.89716	0.269920
$857$	−6.26547	−0.214024	−0.107012	−	0.994258i	$-0.534128\pi$
$857$	−6.26547	−0.214024	−0.107012	+	0.994258i	$0.534128\pi$
$858$	−37.7245	−1.28789
$859$	−28.1468	−0.960355	−0.480177	−	0.877171i	$-0.659428\pi$
$859$	−28.1468	−0.960355	−0.480177	+	0.877171i	$0.659428\pi$
$860$	−91.8081	−3.13063
$861$	55.2109	1.88158
$862$	−84.3166	−2.87184
$863$	28.3593	0.965361	0.482680	−	0.875797i	$-0.339663\pi$
$863$	28.3593	0.965361	0.482680	+	0.875797i	$0.339663\pi$
$864$	9.55342	0.325014
$865$	90.0988	3.06345
$866$	68.3119	2.32133
$867$	−26.4374	−0.897861
$868$	−16.8218	−0.570971
$869$	82.8273	2.80973
$870$	−127.686	−4.32896
$871$	−0.428310	−0.0145127
$872$	58.8722	1.99367
$873$	−1.91131	−0.0646881
$874$	−11.6989	−0.395721
$875$	−58.0155	−1.96128
$876$	−12.5568	−0.424254
$877$	−40.6994	−1.37432	−0.687160	−	0.726506i	$-0.741143\pi$
$877$	−40.6994	−1.37432	−0.687160	+	0.726506i	$0.741143\pi$
$878$	17.1034	0.577211
$879$	−39.9367	−1.34703
$880$	94.9949	3.20228
$881$	−36.7228	−1.23722	−0.618612	−	0.785697i	$-0.712305\pi$
$881$	−36.7228	−1.23722	−0.618612	+	0.785697i	$0.712305\pi$
$882$	8.94556	0.301213
$883$	−6.46902	−0.217700	−0.108850	−	0.994058i	$-0.534717\pi$
$883$	−6.46902	−0.217700	−0.108850	+	0.994058i	$0.534717\pi$
$884$	−2.58370	−0.0868992
$885$	−38.4112	−1.29118
$886$	66.2562	2.22592
$887$	9.69577	0.325552	0.162776	−	0.986663i	$-0.447955\pi$
$887$	9.69577	0.325552	0.162776	+	0.986663i	$0.447955\pi$
$888$	41.0951	1.37906
$889$	32.2738	1.08243
$890$	−50.9007	−1.70619
$891$	−35.3315	−1.18365
$892$	35.5534	1.19042
$893$	18.1013	0.605736
$894$	−1.30730	−0.0437226
$895$	3.69887	0.123640
$896$	−65.4354	−2.18604
$897$	−4.98869	−0.166568
$898$	52.8145	1.76244
$899$	9.57914	0.319482
$900$	−21.1308	−0.704359
$901$	−2.10106	−0.0699964
$902$	119.588	3.98183
$903$	33.6644	1.12028
$904$	−84.4990	−2.81040
$905$	27.9896	0.930405
$906$	−68.4057	−2.27263
$907$	−0.218135	−0.00724306	−0.00362153	−	0.999993i	$-0.501153\pi$
$907$	−0.218135	−0.00724306	−0.00362153	+	0.999993i	$0.501153\pi$
$908$	−28.7062	−0.952647
$909$	−4.53322	−0.150358
$910$	66.5462	2.20599
$911$	16.4478	0.544938	0.272469	−	0.962165i	$-0.412160\pi$
$911$	16.4478	0.544938	0.272469	+	0.962165i	$0.412160\pi$
$912$	−22.4715	−0.744104
$913$	−56.0677	−1.85557
$914$	−38.6890	−1.27972
$915$	−60.7862	−2.00953
$916$	23.4286	0.774104
$917$	−15.3704	−0.507577
$918$	−4.42405	−0.146015
$919$	−37.9728	−1.25261	−0.626304	−	0.779579i	$-0.715433\pi$
$919$	−37.9728	−1.25261	−0.626304	+	0.779579i	$0.715433\pi$
$920$	33.3940	1.10097
$921$	10.6066	0.349498
$922$	18.9214	0.623142
$923$	−8.54884	−0.281389
$924$	−120.327	−3.95846
$925$	−44.8649	−1.47515
$926$	−69.1895	−2.27371
$927$	2.42429	0.0796240
$928$	−14.9986	−0.492354
$929$	10.2888	0.337566	0.168783	−	0.985653i	$-0.446016\pi$
$929$	10.2888	0.337566	0.168783	+	0.985653i	$0.446016\pi$
$930$	−16.0666	−0.526846
$931$	−18.6538	−0.611353
$932$	−5.95832	−0.195171
$933$	−50.1426	−1.64160
$934$	−51.1724	−1.67441
$935$	−6.06083	−0.198210
$936$	5.74424	0.187756
$937$	57.3195	1.87255	0.936274	−	0.351272i	$-0.114251\pi$
$937$	57.3195	1.87255	0.936274	+	0.351272i	$0.114251\pi$
$938$	−2.02198	−0.0660198
$939$	3.69146	0.120466
$940$	−99.3752	−3.24126
$941$	−11.7662	−0.383567	−0.191784	−	0.981437i	$-0.561427\pi$
$941$	−11.7662	−0.383567	−0.191784	+	0.981437i	$0.561427\pi$
$942$	−21.3360	−0.695163
$943$	15.8143	0.514984
$944$	−32.7488	−1.06588
$945$	76.9879	2.50442
$946$	72.9176	2.37075
$947$	14.6619	0.476449	0.238225	−	0.971210i	$-0.423435\pi$
$947$	14.6619	0.476449	0.238225	+	0.971210i	$0.423435\pi$
$948$	107.566	3.49357
$949$	−3.72659	−0.120970
$950$	65.2159	2.11588
$951$	12.6073	0.408820
$952$	−6.34183	−0.205540
$953$	34.3227	1.11182	0.555911	−	0.831242i	$-0.312369\pi$
$953$	34.3227	1.11182	0.555911	+	0.831242i	$0.312369\pi$
$954$	8.98408	0.290870
$955$	54.2473	1.75540
$956$	47.5195	1.53689
$957$	68.5196	2.21493
$958$	−21.6247	−0.698663
$959$	29.9586	0.967413
$960$	−34.0670	−1.09951
$961$	−29.7947	−0.961118
$962$	23.4568	0.756278
$963$	0.810462	0.0261168
$964$	69.0087	2.22262
$965$	−40.6786	−1.30949
$966$	−23.5507	−0.757732
$967$	61.3511	1.97292	0.986459	−	0.164009i	$-0.0524427\pi$
$967$	61.3511	1.97292	0.986459	+	0.164009i	$0.0524427\pi$
$968$	−76.3435	−2.45377
$969$	1.43372	0.0460576
$970$	−32.3846	−1.03981
$971$	13.4895	0.432897	0.216449	−	0.976294i	$-0.430553\pi$
$971$	13.4895	0.432897	0.216449	+	0.976294i	$0.430553\pi$
$972$	23.5763	0.756210
$973$	−3.67776	−0.117903
$974$	1.96887	0.0630868
$975$	27.8096	0.890621
$976$	−51.8254	−1.65889
$977$	−33.5320	−1.07278	−0.536392	−	0.843969i	$-0.680213\pi$
$977$	−33.5320	−1.07278	−0.536392	+	0.843969i	$0.680213\pi$
$978$	13.1146	0.419359
$979$	27.3147	0.872980
$980$	102.408	3.27132
$981$	6.04188	0.192902
$982$	10.3142	0.329139
$983$	49.4173	1.57617	0.788084	−	0.615567i	$-0.211073\pi$
$983$	49.4173	1.57617	0.788084	+	0.615567i	$0.211073\pi$
$984$	80.7497	2.57421
$985$	87.9675	2.80288
$986$	6.94564	0.221194
$987$	36.4391	1.15987
$988$	−23.0376	−0.732923
$989$	9.64263	0.306618
$990$	25.9160	0.823663
$991$	14.6910	0.466675	0.233338	−	0.972396i	$-0.425035\pi$
$991$	14.6910	0.466675	0.233338	+	0.972396i	$0.425035\pi$
$992$	−1.88727	−0.0599208
$993$	−15.1337	−0.480253
$994$	−40.3575	−1.28006
$995$	−71.9508	−2.28100
$996$	−72.8136	−2.30719
$997$	−44.2589	−1.40169	−0.700847	−	0.713312i	$-0.747194\pi$
$997$	−44.2589	−1.40169	−0.700847	+	0.713312i	$0.747194\pi$
$998$	−22.7215	−0.719238
$999$	27.1374	0.858589

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	139.2.a.c.1.1	✓	7
3.2	odd	2		1251.2.a.k.1.7		7
4.3	odd	2		2224.2.a.o.1.2		7
5.4	even	2		3475.2.a.e.1.7		7
7.6	odd	2		6811.2.a.p.1.1		7
8.3	odd	2		8896.2.a.bd.1.6		7
8.5	even	2		8896.2.a.be.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
139.2.a.c.1.1	✓	7	1.1	even	1	trivial
1251.2.a.k.1.7		7	3.2	odd	2
2224.2.a.o.1.2		7	4.3	odd	2
3475.2.a.e.1.7		7	5.4	even	2
6811.2.a.p.1.1		7	7.6	odd	2
8896.2.a.bd.1.6		7	8.3	odd	2
8896.2.a.be.1.2		7	8.5	even	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:	\( N \)	\(=\)	\( 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	139.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48318 q^{2} +1.56460 q^{3} +4.16616 q^{4} +3.76669 q^{5} -3.88518 q^{6} -3.67776 q^{7} -5.37897 q^{8} -0.552027 q^{9} +O(q^{10})\)	\(q-2.48318 q^{2} +1.56460 q^{3} +4.16616 q^{4} +3.76669 q^{5} -3.88518 q^{6} -3.67776 q^{7} -5.37897 q^{8} -0.552027 q^{9} -9.35335 q^{10} +5.01926 q^{11} +6.51838 q^{12} +1.93452 q^{13} +9.13252 q^{14} +5.89336 q^{15} +5.02459 q^{16} -0.320577 q^{17} +1.37078 q^{18} -2.85843 q^{19} +15.6926 q^{20} -5.75422 q^{21} -12.4637 q^{22} -1.64820 q^{23} -8.41593 q^{24} +9.18795 q^{25} -4.80375 q^{26} -5.55750 q^{27} -15.3221 q^{28} +8.72513 q^{29} -14.6343 q^{30} +1.09788 q^{31} -1.71901 q^{32} +7.85313 q^{33} +0.796050 q^{34} -13.8530 q^{35} -2.29983 q^{36} -4.88302 q^{37} +7.09798 q^{38} +3.02675 q^{39} -20.2609 q^{40} -9.59487 q^{41} +14.2887 q^{42} -5.85039 q^{43} +20.9111 q^{44} -2.07931 q^{45} +4.09278 q^{46} -6.33260 q^{47} +7.86147 q^{48} +6.52589 q^{49} -22.8153 q^{50} -0.501575 q^{51} +8.05953 q^{52} +6.55399 q^{53} +13.8003 q^{54} +18.9060 q^{55} +19.7825 q^{56} -4.47230 q^{57} -21.6660 q^{58} -6.51771 q^{59} +24.5527 q^{60} -10.3143 q^{61} -2.72623 q^{62} +2.03022 q^{63} -5.78057 q^{64} +7.28674 q^{65} -19.5007 q^{66} -0.221404 q^{67} -1.33558 q^{68} -2.57878 q^{69} +34.3994 q^{70} -4.41910 q^{71} +2.96933 q^{72} -1.92636 q^{73} +12.1254 q^{74} +14.3755 q^{75} -11.9087 q^{76} -18.4596 q^{77} -7.51595 q^{78} +16.5019 q^{79} +18.9261 q^{80} -7.03919 q^{81} +23.8257 q^{82} -11.1705 q^{83} -23.9730 q^{84} -1.20751 q^{85} +14.5276 q^{86} +13.6513 q^{87} -26.9984 q^{88} +5.44197 q^{89} +5.16330 q^{90} -7.11469 q^{91} -6.86668 q^{92} +1.71774 q^{93} +15.7249 q^{94} -10.7668 q^{95} -2.68957 q^{96} +3.46235 q^{97} -16.2049 q^{98} -2.77077 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + q^{2} - 2 q^{3} + 9 q^{4} + 11 q^{5} - 7 q^{6} - 5 q^{7} + 6 q^{8} + 13 q^{9}+O(q^{10}) \) 7 * q + q^2 - 2 * q^3 + 9 * q^4 + 11 * q^5 - 7 * q^6 - 5 * q^7 + 6 * q^8 + 13 * q^9	\( 7 q + q^{2} - 2 q^{3} + 9 q^{4} + 11 q^{5} - 7 q^{6} - 5 q^{7} + 6 q^{8} + 13 q^{9} - 4 q^{10} + 2 q^{11} - 8 q^{12} + 6 q^{13} + 7 q^{14} - 3 q^{15} + 5 q^{16} + 5 q^{17} - 10 q^{18} - 10 q^{19} + 12 q^{20} - 5 q^{21} - 18 q^{22} - q^{23} - 21 q^{24} + 14 q^{25} - 8 q^{26} - 11 q^{27} - 28 q^{28} + 30 q^{29} - 41 q^{30} - 20 q^{31} - 12 q^{32} - 20 q^{33} - 17 q^{34} - 7 q^{35} + 2 q^{36} + 6 q^{37} + 6 q^{38} + 11 q^{39} - 22 q^{40} + 19 q^{41} + 6 q^{42} - 12 q^{43} + 25 q^{44} + 27 q^{45} + 22 q^{46} - 3 q^{47} + 15 q^{48} - 8 q^{49} + 12 q^{50} + 23 q^{51} - 8 q^{52} + 38 q^{53} - 7 q^{54} + 7 q^{55} + 21 q^{56} - 19 q^{57} - 21 q^{58} - 14 q^{59} - 8 q^{60} + 4 q^{61} - q^{62} - 18 q^{63} - 16 q^{64} + 10 q^{65} + 18 q^{66} + 9 q^{67} - 25 q^{68} + 9 q^{69} + 20 q^{70} + 24 q^{71} + 41 q^{72} - 5 q^{73} + 9 q^{74} - 21 q^{75} + 3 q^{76} - 13 q^{77} + 20 q^{78} + 8 q^{79} + 11 q^{80} + 39 q^{81} + 56 q^{82} - 9 q^{83} - q^{84} - 22 q^{85} + 39 q^{86} - 25 q^{87} - 29 q^{88} + 10 q^{89} + 72 q^{90} + 7 q^{91} + 29 q^{92} - 15 q^{93} - 36 q^{94} - 21 q^{95} - 11 q^{96} - 5 q^{97} - 49 q^{98} - 31 q^{99}+O(q^{100}) \) 7 * q + q^2 - 2 * q^3 + 9 * q^4 + 11 * q^5 - 7 * q^6 - 5 * q^7 + 6 * q^8 + 13 * q^9 - 4 * q^10 + 2 * q^11 - 8 * q^12 + 6 * q^13 + 7 * q^14 - 3 * q^15 + 5 * q^16 + 5 * q^17 - 10 * q^18 - 10 * q^19 + 12 * q^20 - 5 * q^21 - 18 * q^22 - q^23 - 21 * q^24 + 14 * q^25 - 8 * q^26 - 11 * q^27 - 28 * q^28 + 30 * q^29 - 41 * q^30 - 20 * q^31 - 12 * q^32 - 20 * q^33 - 17 * q^34 - 7 * q^35 + 2 * q^36 + 6 * q^37 + 6 * q^38 + 11 * q^39 - 22 * q^40 + 19 * q^41 + 6 * q^42 - 12 * q^43 + 25 * q^44 + 27 * q^45 + 22 * q^46 - 3 * q^47 + 15 * q^48 - 8 * q^49 + 12 * q^50 + 23 * q^51 - 8 * q^52 + 38 * q^53 - 7 * q^54 + 7 * q^55 + 21 * q^56 - 19 * q^57 - 21 * q^58 - 14 * q^59 - 8 * q^60 + 4 * q^61 - q^62 - 18 * q^63 - 16 * q^64 + 10 * q^65 + 18 * q^66 + 9 * q^67 - 25 * q^68 + 9 * q^69 + 20 * q^70 + 24 * q^71 + 41 * q^72 - 5 * q^73 + 9 * q^74 - 21 * q^75 + 3 * q^76 - 13 * q^77 + 20 * q^78 + 8 * q^79 + 11 * q^80 + 39 * q^81 + 56 * q^82 - 9 * q^83 - q^84 - 22 * q^85 + 39 * q^86 - 25 * q^87 - 29 * q^88 + 10 * q^89 + 72 * q^90 + 7 * q^91 + 29 * q^92 - 15 * q^93 - 36 * q^94 - 21 * q^95 - 11 * q^96 - 5 * q^97 - 49 * q^98 - 31 * q^99

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