LMFDB - Embedded newform 131.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [131,2,Mod(1,131)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(131, 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("131.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	131.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:	$1.04604026648$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 18x^{8} - 2x^{7} + 111x^{6} + 18x^{5} - 270x^{4} - 28x^{3} + 232x^{2} - 16x - 32 $ x^10 - 18x^8 - 2x^7 + 111x^6 + 18x^5 - 270x^4 - 28x^3 + 232x^2 - 16x - 32
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.960983$ of defining polynomial
Character	$\chi$	$=$	131.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.960983 q^{2} -3.31776 q^{3} -1.07651 q^{4} +2.09792 q^{5} +3.18831 q^{6} +0.358420 q^{7} +2.95648 q^{8} +8.00754 q^{9} +O(q^{10})$	\(q-0.960983 q^{2} -3.31776 q^{3} -1.07651 q^{4} +2.09792 q^{5} +3.18831 q^{6} +0.358420 q^{7} +2.95648 q^{8} +8.00754 q^{9} -2.01606 q^{10} -0.806378 q^{11} +3.57161 q^{12} +1.65873 q^{13} -0.344436 q^{14} -6.96040 q^{15} -0.688099 q^{16} -0.884662 q^{17} -7.69511 q^{18} +7.49678 q^{19} -2.25843 q^{20} -1.18915 q^{21} +0.774916 q^{22} -2.46103 q^{23} -9.80888 q^{24} -0.598735 q^{25} -1.59402 q^{26} -16.6138 q^{27} -0.385844 q^{28} +8.68129 q^{29} +6.68882 q^{30} +6.75559 q^{31} -5.25170 q^{32} +2.67537 q^{33} +0.850146 q^{34} +0.751937 q^{35} -8.62021 q^{36} +7.38214 q^{37} -7.20428 q^{38} -5.50329 q^{39} +6.20245 q^{40} -5.16093 q^{41} +1.14276 q^{42} +12.1773 q^{43} +0.868076 q^{44} +16.7992 q^{45} +2.36501 q^{46} -9.66345 q^{47} +2.28295 q^{48} -6.87153 q^{49} +0.575374 q^{50} +2.93510 q^{51} -1.78565 q^{52} -2.36272 q^{53} +15.9656 q^{54} -1.69172 q^{55} +1.05966 q^{56} -24.8725 q^{57} -8.34258 q^{58} +9.59358 q^{59} +7.49295 q^{60} -4.90534 q^{61} -6.49200 q^{62} +2.87007 q^{63} +6.42299 q^{64} +3.47989 q^{65} -2.57099 q^{66} -7.00053 q^{67} +0.952350 q^{68} +8.16511 q^{69} -0.722599 q^{70} +1.15935 q^{71} +23.6741 q^{72} +7.31533 q^{73} -7.09411 q^{74} +1.98646 q^{75} -8.07037 q^{76} -0.289023 q^{77} +5.28856 q^{78} +7.28444 q^{79} -1.44358 q^{80} +31.0981 q^{81} +4.95957 q^{82} -5.93694 q^{83} +1.28014 q^{84} -1.85595 q^{85} -11.7021 q^{86} -28.8025 q^{87} -2.38404 q^{88} -0.889114 q^{89} -16.1437 q^{90} +0.594524 q^{91} +2.64933 q^{92} -22.4134 q^{93} +9.28641 q^{94} +15.7276 q^{95} +17.4239 q^{96} -0.313780 q^{97} +6.60343 q^{98} -6.45711 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} + 16 q^{4} + 4 q^{5} - 4 q^{6} + q^{7} - 6 q^{8} + 15 q^{9}+O(q^{10}) $ 10 * q + q^3 + 16 * q^4 + 4 * q^5 - 4 * q^6 + q^7 - 6 * q^8 + 15 * q^9	\( 10 q + q^{3} + 16 q^{4} + 4 q^{5} - 4 q^{6} + q^{7} - 6 q^{8} + 15 q^{9} + 2 q^{11} - 8 q^{12} + 11 q^{13} - 6 q^{14} - 2 q^{15} + 28 q^{16} - 2 q^{17} - 24 q^{18} - 14 q^{20} + 9 q^{21} - 4 q^{22} - 10 q^{23} - 36 q^{24} + 18 q^{25} - 28 q^{26} - 11 q^{27} - 24 q^{28} + 16 q^{29} - 52 q^{30} + 6 q^{31} - 42 q^{32} - 27 q^{33} - 4 q^{34} - 19 q^{35} + 16 q^{36} + 34 q^{37} - 8 q^{38} + 4 q^{39} + 10 q^{40} - 13 q^{41} + 2 q^{42} + 9 q^{43} + 18 q^{44} + 21 q^{45} + 32 q^{46} - 6 q^{47} + 14 q^{48} + 23 q^{49} + 8 q^{50} - 18 q^{51} + 4 q^{52} + 30 q^{53} + 12 q^{54} - 20 q^{55} - 6 q^{56} - 4 q^{57} - 5 q^{59} + 44 q^{60} + 51 q^{61} + 4 q^{62} - 17 q^{63} + 52 q^{64} - 14 q^{65} + 32 q^{66} - 10 q^{67} + 32 q^{68} + 18 q^{69} - 30 q^{70} - 44 q^{72} - 14 q^{73} + 52 q^{74} - 16 q^{75} - 20 q^{76} - 24 q^{77} + 78 q^{78} + 24 q^{79} + 14 q^{80} + 18 q^{81} - 20 q^{82} - 22 q^{83} + 46 q^{84} + 16 q^{85} - 20 q^{86} - 48 q^{87} + 60 q^{88} + 14 q^{89} + 6 q^{90} - q^{91} - 48 q^{92} + 16 q^{94} - 28 q^{95} - 48 q^{96} + 4 q^{97} + 80 q^{98} - 30 q^{99}+O(q^{100}) \) 10 * q + q^3 + 16 * q^4 + 4 * q^5 - 4 * q^6 + q^7 - 6 * q^8 + 15 * q^9 + 2 * q^11 - 8 * q^12 + 11 * q^13 - 6 * q^14 - 2 * q^15 + 28 * q^16 - 2 * q^17 - 24 * q^18 - 14 * q^20 + 9 * q^21 - 4 * q^22 - 10 * q^23 - 36 * q^24 + 18 * q^25 - 28 * q^26 - 11 * q^27 - 24 * q^28 + 16 * q^29 - 52 * q^30 + 6 * q^31 - 42 * q^32 - 27 * q^33 - 4 * q^34 - 19 * q^35 + 16 * q^36 + 34 * q^37 - 8 * q^38 + 4 * q^39 + 10 * q^40 - 13 * q^41 + 2 * q^42 + 9 * q^43 + 18 * q^44 + 21 * q^45 + 32 * q^46 - 6 * q^47 + 14 * q^48 + 23 * q^49 + 8 * q^50 - 18 * q^51 + 4 * q^52 + 30 * q^53 + 12 * q^54 - 20 * q^55 - 6 * q^56 - 4 * q^57 - 5 * q^59 + 44 * q^60 + 51 * q^61 + 4 * q^62 - 17 * q^63 + 52 * q^64 - 14 * q^65 + 32 * q^66 - 10 * q^67 + 32 * q^68 + 18 * q^69 - 30 * q^70 - 44 * q^72 - 14 * q^73 + 52 * q^74 - 16 * q^75 - 20 * q^76 - 24 * q^77 + 78 * q^78 + 24 * q^79 + 14 * q^80 + 18 * q^81 - 20 * q^82 - 22 * q^83 + 46 * q^84 + 16 * q^85 - 20 * q^86 - 48 * q^87 + 60 * q^88 + 14 * q^89 + 6 * q^90 - q^91 - 48 * q^92 + 16 * q^94 - 28 * q^95 - 48 * q^96 + 4 * q^97 + 80 * q^98 - 30 * 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 $

$2$	−0.960983	−0.679518	−0.339759	−	0.940513i	$-0.610345\pi$
$2$	−0.960983	−0.679518	−0.339759	+	0.940513i	$0.610345\pi$
$3$	−3.31776	−1.91551	−0.957755	−	0.287584i	$-0.907148\pi$
$3$	−3.31776	−1.91551	−0.957755	+	0.287584i	$0.907148\pi$
$4$	−1.07651	−0.538256
$5$	2.09792	0.938218	0.469109	−	0.883140i	$-0.344575\pi$
$5$	2.09792	0.938218	0.469109	+	0.883140i	$0.344575\pi$
$6$	3.18831	1.30162
$7$	0.358420	0.135470	0.0677351	−	0.997703i	$-0.478423\pi$
$7$	0.358420	0.135470	0.0677351	+	0.997703i	$0.478423\pi$
$8$	2.95648	1.04527
$9$	8.00754	2.66918
$10$	−2.01606	−0.637536
$11$	−0.806378	−0.243132	−0.121566	−	0.992583i	$-0.538792\pi$
$11$	−0.806378	−0.243132	−0.121566	+	0.992583i	$0.538792\pi$
$12$	3.57161	1.03103
$13$	1.65873	0.460050	0.230025	−	0.973185i	$-0.426119\pi$
$13$	1.65873	0.460050	0.230025	+	0.973185i	$0.426119\pi$
$14$	−0.344436	−0.0920544
$15$	−6.96040	−1.79717
$16$	−0.688099	−0.172025
$17$	−0.884662	−0.214562	−0.107281	−	0.994229i	$-0.534214\pi$
$17$	−0.884662	−0.214562	−0.107281	+	0.994229i	$0.534214\pi$
$18$	−7.69511	−1.81376
$19$	7.49678	1.71988	0.859940	−	0.510395i	$-0.170501\pi$
$19$	7.49678	1.71988	0.859940	+	0.510395i	$0.170501\pi$
$20$	−2.25843	−0.505001
$21$	−1.18915	−0.259495
$22$	0.774916	0.165213
$23$	−2.46103	−0.513160	−0.256580	−	0.966523i	$-0.582596\pi$
$23$	−2.46103	−0.513160	−0.256580	+	0.966523i	$0.582596\pi$
$24$	−9.80888	−2.00223
$25$	−0.598735	−0.119747
$26$	−1.59402	−0.312612
$27$	−16.6138	−3.19733
$28$	−0.385844	−0.0729176
$29$	8.68129	1.61208	0.806038	−	0.591864i	$-0.201608\pi$
$29$	8.68129	1.61208	0.806038	+	0.591864i	$0.201608\pi$
$30$	6.68882	1.22121
$31$	6.75559	1.21334	0.606669	−	0.794954i	$-0.292505\pi$
$31$	6.75559	1.21334	0.606669	+	0.794954i	$0.292505\pi$
$32$	−5.25170	−0.928378
$33$	2.67537	0.465722
$34$	0.850146	0.145799
$35$	0.751937	0.127101
$36$	−8.62021	−1.43670
$37$	7.38214	1.21362	0.606808	−	0.794849i	$-0.292450\pi$
$37$	7.38214	1.21362	0.606808	+	0.794849i	$0.292450\pi$
$38$	−7.20428	−1.16869
$39$	−5.50329	−0.881231
$40$	6.20245	0.980693
$41$	−5.16093	−0.806002	−0.403001	−	0.915199i	$-0.632033\pi$
$41$	−5.16093	−0.806002	−0.403001	+	0.915199i	$0.632033\pi$
$42$	1.14276	0.176331
$43$	12.1773	1.85701	0.928507	−	0.371314i	$-0.121093\pi$
$43$	12.1773	1.85701	0.928507	+	0.371314i	$0.121093\pi$
$44$	0.868076	0.130867
$45$	16.7992	2.50427
$46$	2.36501	0.348701
$47$	−9.66345	−1.40956	−0.704779	−	0.709427i	$-0.748954\pi$
$47$	−9.66345	−1.40956	−0.704779	+	0.709427i	$0.748954\pi$
$48$	2.28295	0.329515
$49$	−6.87153	−0.981648
$50$	0.575374	0.0813702
$51$	2.93510	0.410996
$52$	−1.78565	−0.247625
$53$	−2.36272	−0.324545	−0.162272	−	0.986746i	$-0.551882\pi$
$53$	−2.36272	−0.324545	−0.162272	+	0.986746i	$0.551882\pi$
$54$	15.9656	2.17264
$55$	−1.69172	−0.228111
$56$	1.05966	0.141603
$57$	−24.8725	−3.29445
$58$	−8.34258	−1.09543
$59$	9.59358	1.24898	0.624489	−	0.781034i	$-0.285307\pi$
$59$	9.59358	1.24898	0.624489	+	0.781034i	$0.285307\pi$
$60$	7.49295	0.967335
$61$	−4.90534	−0.628064	−0.314032	−	0.949412i	$-0.601680\pi$
$61$	−4.90534	−0.628064	−0.314032	+	0.949412i	$0.601680\pi$
$62$	−6.49200	−0.824485
$63$	2.87007	0.361595
$64$	6.42299	0.802874
$65$	3.47989	0.431627
$66$	−2.57099	−0.316467
$67$	−7.00053	−0.855251	−0.427626	−	0.903956i	$-0.640650\pi$
$67$	−7.00053	−0.855251	−0.427626	+	0.903956i	$0.640650\pi$
$68$	0.952350	0.115489
$69$	8.16511	0.982964
$70$	−0.722599	−0.0863671
$71$	1.15935	0.137590	0.0687951	−	0.997631i	$-0.478085\pi$
$71$	1.15935	0.137590	0.0687951	+	0.997631i	$0.478085\pi$
$72$	23.6741	2.79002
$73$	7.31533	0.856195	0.428098	−	0.903733i	$-0.359184\pi$
$73$	7.31533	0.856195	0.428098	+	0.903733i	$0.359184\pi$
$74$	−7.09411	−0.824673
$75$	1.98646	0.229377
$76$	−8.07037	−0.925735
$77$	−0.289023	−0.0329372
$78$	5.28856	0.598812
$79$	7.28444	0.819564	0.409782	−	0.912184i	$-0.365605\pi$
$79$	7.28444	0.819564	0.409782	+	0.912184i	$0.365605\pi$
$80$	−1.44358	−0.161397
$81$	31.0981	3.45535
$82$	4.95957	0.547693
$83$	−5.93694	−0.651664	−0.325832	−	0.945428i	$-0.605644\pi$
$83$	−5.93694	−0.651664	−0.325832	+	0.945428i	$0.605644\pi$
$84$	1.28014	0.139675
$85$	−1.85595	−0.201306
$86$	−11.7021	−1.26187
$87$	−28.8025	−3.08795
$88$	−2.38404	−0.254139
$89$	−0.889114	−0.0942459	−0.0471230	−	0.998889i	$-0.515005\pi$
$89$	−0.889114	−0.0942459	−0.0471230	+	0.998889i	$0.515005\pi$
$90$	−16.1437	−1.70170
$91$	0.594524	0.0623231
$92$	2.64933	0.276212
$93$	−22.4134	−2.32416
$94$	9.28641	0.957820
$95$	15.7276	1.61362
$96$	17.4239	1.77832
$97$	−0.313780	−0.0318596	−0.0159298	−	0.999873i	$-0.505071\pi$
$97$	−0.313780	−0.0318596	−0.0159298	+	0.999873i	$0.505071\pi$
$98$	6.60343	0.667047
$99$	−6.45711	−0.648964
$100$	0.644546	0.0644546
$101$	−14.9584	−1.48842	−0.744211	−	0.667945i	$-0.767174\pi$
$101$	−14.9584	−1.48842	−0.744211	+	0.667945i	$0.767174\pi$
$102$	−2.82058	−0.279279
$103$	−13.0829	−1.28910	−0.644549	−	0.764563i	$-0.722955\pi$
$103$	−13.0829	−1.28910	−0.644549	+	0.764563i	$0.722955\pi$
$104$	4.90401	0.480878
$105$	−2.49475	−0.243463
$106$	2.27053	0.220534
$107$	2.89341	0.279717	0.139858	−	0.990172i	$-0.455335\pi$
$107$	2.89341	0.279717	0.139858	+	0.990172i	$0.455335\pi$
$108$	17.8850	1.72098
$109$	2.92435	0.280102	0.140051	−	0.990144i	$-0.455273\pi$
$109$	2.92435	0.280102	0.140051	+	0.990144i	$0.455273\pi$
$110$	1.62571	0.155005
$111$	−24.4922	−2.32469
$112$	−0.246629	−0.0233042
$113$	11.1098	1.04512	0.522560	−	0.852602i	$-0.324977\pi$
$113$	11.1098	1.04512	0.522560	+	0.852602i	$0.324977\pi$
$114$	23.9021	2.23864
$115$	−5.16304	−0.481456
$116$	−9.34551	−0.867709
$117$	13.2824	1.22796
$118$	−9.21927	−0.848702
$119$	−0.317081	−0.0290668
$120$	−20.5782	−1.87853
$121$	−10.3498	−0.940887
$122$	4.71395	0.426781
$123$	17.1227	1.54391
$124$	−7.27247	−0.653087
$125$	−11.7457	−1.05057
$126$	−2.75809	−0.245710
$127$	−5.00773	−0.444365	−0.222182	−	0.975005i	$-0.571318\pi$
$127$	−5.00773	−0.444365	−0.222182	+	0.975005i	$0.571318\pi$
$128$	4.33101	0.382811
$129$	−40.4012	−3.55713
$130$	−3.34412	−0.293298
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−2.88007	−0.250678
$133$	2.68700	0.232992
$134$	6.72739	0.581158
$135$	−34.8545	−2.99980
$136$	−2.61548	−0.224276
$137$	11.7349	1.00258	0.501291	−	0.865279i	$-0.332859\pi$
$137$	11.7349	1.00258	0.501291	+	0.865279i	$0.332859\pi$
$138$	−7.84653	−0.667941
$139$	1.14801	0.0973726	0.0486863	−	0.998814i	$-0.484497\pi$
$139$	1.14801	0.0973726	0.0486863	+	0.998814i	$0.484497\pi$
$140$	−0.809469	−0.0684126
$141$	32.0610	2.70002
$142$	−1.11412	−0.0934949
$143$	−1.33757	−0.111853
$144$	−5.50998	−0.459165
$145$	18.2127	1.51248
$146$	−7.02991	−0.581800
$147$	22.7981	1.88036
$148$	−7.94696	−0.653236
$149$	−9.68492	−0.793419	−0.396710	−	0.917944i	$-0.629848\pi$
$149$	−9.68492	−0.793419	−0.396710	+	0.917944i	$0.629848\pi$
$150$	−1.90896	−0.155866
$151$	10.7845	0.877633	0.438816	−	0.898577i	$-0.355398\pi$
$151$	10.7845	0.877633	0.438816	+	0.898577i	$0.355398\pi$
$152$	22.1640	1.79774
$153$	−7.08397	−0.572705
$154$	0.277746	0.0223814
$155$	14.1727	1.13838
$156$	5.92435	0.474328
$157$	−4.14806	−0.331051	−0.165526	−	0.986205i	$-0.552932\pi$
$157$	−4.14806	−0.331051	−0.165526	+	0.986205i	$0.552932\pi$
$158$	−7.00022	−0.556908
$159$	7.83894	0.621669
$160$	−11.0176	−0.871021
$161$	−0.882084	−0.0695179
$162$	−29.8848	−2.34797
$163$	14.4453	1.13144	0.565720	−	0.824597i	$-0.308598\pi$
$163$	14.4453	1.13144	0.565720	+	0.824597i	$0.308598\pi$
$164$	5.55580	0.433835
$165$	5.61271	0.436949
$166$	5.70530	0.442817
$167$	7.33746	0.567790	0.283895	−	0.958855i	$-0.408373\pi$
$167$	7.33746	0.567790	0.283895	+	0.958855i	$0.408373\pi$
$168$	−3.51570	−0.271242
$169$	−10.2486	−0.788354
$170$	1.78354	0.136791
$171$	60.0308	4.59067
$172$	−13.1090	−0.999549
$173$	−10.4060	−0.791155	−0.395577	−	0.918433i	$-0.629456\pi$
$173$	−10.4060	−0.791155	−0.395577	+	0.918433i	$0.629456\pi$
$174$	27.6787	2.09832
$175$	−0.214599	−0.0162222
$176$	0.554868	0.0418247
$177$	−31.8292	−2.39243
$178$	0.854424	0.0640418
$179$	−8.95950	−0.669664	−0.334832	−	0.942278i	$-0.608680\pi$
$179$	−8.95950	−0.669664	−0.334832	+	0.942278i	$0.608680\pi$
$180$	−18.0845	−1.34794
$181$	4.61967	0.343377	0.171689	−	0.985151i	$-0.445078\pi$
$181$	4.61967	0.343377	0.171689	+	0.985151i	$0.445078\pi$
$182$	−0.571328	−0.0423496
$183$	16.2747	1.20306
$184$	−7.27598	−0.536392
$185$	15.4871	1.13864
$186$	21.5389	1.57931
$187$	0.713373	0.0521670
$188$	10.4028	0.758703
$189$	−5.95474	−0.433144
$190$	−15.1140	−1.09648
$191$	−15.5312	−1.12380	−0.561899	−	0.827206i	$-0.689929\pi$
$191$	−15.5312	−1.12380	−0.561899	+	0.827206i	$0.689929\pi$
$192$	−21.3100	−1.53791
$193$	18.3986	1.32436	0.662182	−	0.749343i	$-0.269631\pi$
$193$	18.3986	1.32436	0.662182	+	0.749343i	$0.269631\pi$
$194$	0.301537	0.0216491
$195$	−11.5454	−0.826787
$196$	7.39729	0.528378
$197$	15.1407	1.07873	0.539367	−	0.842071i	$-0.318664\pi$
$197$	15.1407	1.07873	0.539367	+	0.842071i	$0.318664\pi$
$198$	6.20517	0.440982
$199$	−4.33171	−0.307066	−0.153533	−	0.988143i	$-0.549065\pi$
$199$	−4.33171	−0.307066	−0.153533	+	0.988143i	$0.549065\pi$
$200$	−1.77015	−0.125168
$201$	23.2261	1.63824
$202$	14.3748	1.01141
$203$	3.11155	0.218388
$204$	−3.15967	−0.221221
$205$	−10.8272	−0.756206
$206$	12.5725	0.875965
$207$	−19.7068	−1.36972
$208$	−1.14137	−0.0791400
$209$	−6.04524	−0.418158
$210$	2.39741	0.165437
$211$	−6.87197	−0.473086	−0.236543	−	0.971621i	$-0.576014\pi$
$211$	−6.87197	−0.473086	−0.236543	+	0.971621i	$0.576014\pi$
$212$	2.54350	0.174688
$213$	−3.84646	−0.263555
$214$	−2.78052	−0.190073
$215$	25.5469	1.74228
$216$	−49.1184	−3.34208
$217$	2.42134	0.164371
$218$	−2.81025	−0.190334
$219$	−24.2705	−1.64005
$220$	1.82115	0.122782
$221$	−1.46742	−0.0987094
$222$	23.5366	1.57967
$223$	2.64775	0.177306	0.0886532	−	0.996063i	$-0.471744\pi$
$223$	2.64775	0.177306	0.0886532	+	0.996063i	$0.471744\pi$
$224$	−1.88232	−0.125768
$225$	−4.79440	−0.319627
$226$	−10.6763	−0.710178
$227$	0.899883	0.0597273	0.0298637	−	0.999554i	$-0.490493\pi$
$227$	0.899883	0.0597273	0.0298637	+	0.999554i	$0.490493\pi$
$228$	26.7756	1.77326
$229$	3.78474	0.250103	0.125051	−	0.992150i	$-0.460090\pi$
$229$	3.78474	0.250103	0.125051	+	0.992150i	$0.460090\pi$
$230$	4.96160	0.327158
$231$	0.958908	0.0630915
$232$	25.6660	1.68506
$233$	8.92940	0.584984	0.292492	−	0.956268i	$-0.405515\pi$
$233$	8.92940	0.584984	0.292492	+	0.956268i	$0.405515\pi$
$234$	−12.7641	−0.834419
$235$	−20.2731	−1.32247
$236$	−10.3276	−0.672270
$237$	−24.1680	−1.56988
$238$	0.304710	0.0197514
$239$	2.93222	0.189669	0.0948347	−	0.995493i	$-0.469768\pi$
$239$	2.93222	0.189669	0.0948347	+	0.995493i	$0.469768\pi$
$240$	4.78944	0.309157
$241$	−10.8034	−0.695909	−0.347954	−	0.937511i	$-0.613124\pi$
$241$	−10.8034	−0.695909	−0.347954	+	0.937511i	$0.613124\pi$
$242$	9.94594	0.639349
$243$	−53.3347	−3.42142
$244$	5.28066	0.338059
$245$	−14.4159	−0.921000
$246$	−16.4547	−1.04911
$247$	12.4352	0.791231
$248$	19.9727	1.26827
$249$	19.6974	1.24827
$250$	11.2874	0.713879
$251$	−0.649904	−0.0410216	−0.0205108	−	0.999790i	$-0.506529\pi$
$251$	−0.649904	−0.0410216	−0.0205108	+	0.999790i	$0.506529\pi$
$252$	−3.08966	−0.194630
$253$	1.98452	0.124766
$254$	4.81235	0.301954
$255$	6.15760	0.385604
$256$	−17.0080	−1.06300
$257$	−20.7743	−1.29587	−0.647933	−	0.761697i	$-0.724366\pi$
$257$	−20.7743	−1.29587	−0.647933	+	0.761697i	$0.724366\pi$
$258$	38.8249	2.41713
$259$	2.64591	0.164409
$260$	−3.74614	−0.232326
$261$	69.5158	4.30292
$262$	−0.960983	−0.0593697
$263$	−23.1590	−1.42804	−0.714022	−	0.700124i	$-0.753128\pi$
$263$	−23.1590	−1.42804	−0.714022	+	0.700124i	$0.753128\pi$
$264$	7.90967	0.486806
$265$	−4.95680	−0.304494
$266$	−2.58216	−0.158322
$267$	2.94987	0.180529
$268$	7.53615	0.460344
$269$	−3.85998	−0.235347	−0.117674	−	0.993052i	$-0.537544\pi$
$269$	−3.85998	−0.235347	−0.117674	+	0.993052i	$0.537544\pi$
$270$	33.4946	2.03841
$271$	7.68895	0.467070	0.233535	−	0.972348i	$-0.424971\pi$
$271$	7.68895	0.467070	0.233535	+	0.972348i	$0.424971\pi$
$272$	0.608735	0.0369100
$273$	−1.97249	−0.119381
$274$	−11.2771	−0.681272
$275$	0.482807	0.0291144
$276$	−8.78984	−0.529086
$277$	11.7035	0.703197	0.351599	−	0.936151i	$-0.385638\pi$
$277$	11.7035	0.703197	0.351599	+	0.936151i	$0.385638\pi$
$278$	−1.10321	−0.0661664
$279$	54.0956	3.23862
$280$	2.22308	0.132855
$281$	−13.4854	−0.804471	−0.402236	−	0.915536i	$-0.631767\pi$
$281$	−13.4854	−0.804471	−0.402236	+	0.915536i	$0.631767\pi$
$282$	−30.8101	−1.83471
$283$	−23.9155	−1.42163	−0.710814	−	0.703380i	$-0.751673\pi$
$283$	−23.9155	−1.42163	−0.710814	+	0.703380i	$0.751673\pi$
$284$	−1.24806	−0.0740587
$285$	−52.1806	−3.09091
$286$	1.28538	0.0760061
$287$	−1.84978	−0.109189
$288$	−42.0532	−2.47801
$289$	−16.2174	−0.953963
$290$	−17.5020	−1.02776
$291$	1.04105	0.0610273
$292$	−7.87504	−0.460852
$293$	5.89760	0.344541	0.172271	−	0.985050i	$-0.444890\pi$
$293$	5.89760	0.344541	0.172271	+	0.985050i	$0.444890\pi$
$294$	−21.9086	−1.27774
$295$	20.1266	1.17181
$296$	21.8251	1.26856
$297$	13.3970	0.777375
$298$	9.30704	0.539142
$299$	−4.08220	−0.236079
$300$	−2.13845	−0.123463
$301$	4.36458	0.251570
$302$	−10.3638	−0.596367
$303$	49.6286	2.85109
$304$	−5.15853	−0.295862
$305$	−10.2910	−0.589261
$306$	6.80758	0.389163
$307$	15.0166	0.857044	0.428522	−	0.903531i	$-0.359034\pi$
$307$	15.0166	0.857044	0.428522	+	0.903531i	$0.359034\pi$
$308$	0.311136	0.0177286
$309$	43.4060	2.46928
$310$	−13.6197	−0.773547
$311$	−25.0701	−1.42160	−0.710798	−	0.703397i	$-0.751666\pi$
$311$	−25.0701	−1.42160	−0.710798	+	0.703397i	$0.751666\pi$
$312$	−16.2703	−0.921126
$313$	−14.3079	−0.808731	−0.404365	−	0.914597i	$-0.632508\pi$
$313$	−14.3079	−0.808731	−0.404365	+	0.914597i	$0.632508\pi$
$314$	3.98621	0.224955
$315$	6.02117	0.339254
$316$	−7.84179	−0.441135
$317$	−27.7493	−1.55856	−0.779278	−	0.626679i	$-0.784414\pi$
$317$	−27.7493	−1.55856	−0.779278	+	0.626679i	$0.784414\pi$
$318$	−7.53309	−0.422435
$319$	−7.00041	−0.391948
$320$	13.4749	0.753271
$321$	−9.59966	−0.535801
$322$	0.847667	0.0472387
$323$	−6.63212	−0.369021
$324$	−33.4775	−1.85986
$325$	−0.993143	−0.0550897
$326$	−13.8816	−0.768833
$327$	−9.70230	−0.536538
$328$	−15.2582	−0.842492
$329$	−3.46358	−0.190953
$330$	−5.39372	−0.296915
$331$	−30.2819	−1.66444	−0.832222	−	0.554442i	$-0.812932\pi$
$331$	−30.2819	−1.66444	−0.832222	+	0.554442i	$0.812932\pi$
$332$	6.39119	0.350762
$333$	59.1128	3.23936
$334$	−7.05118	−0.385823
$335$	−14.6865	−0.802412
$336$	0.818255	0.0446395
$337$	−4.82439	−0.262801	−0.131401	−	0.991329i	$-0.541947\pi$
$337$	−4.82439	−0.262801	−0.131401	+	0.991329i	$0.541947\pi$
$338$	9.84873	0.535700
$339$	−36.8596	−2.00194
$340$	1.99795	0.108354
$341$	−5.44756	−0.295002
$342$	−57.6886	−3.11944
$343$	−4.97184	−0.268454
$344$	36.0018	1.94108
$345$	17.1297	0.922234
$346$	10.0000	0.537604
$347$	−3.83107	−0.205663	−0.102831	−	0.994699i	$-0.532790\pi$
$347$	−3.83107	−0.205663	−0.102831	+	0.994699i	$0.532790\pi$
$348$	31.0062	1.66211
$349$	−28.2450	−1.51192	−0.755959	−	0.654619i	$-0.772829\pi$
$349$	−28.2450	−1.51192	−0.755959	+	0.654619i	$0.772829\pi$
$350$	0.206226	0.0110232
$351$	−27.5579	−1.47093
$352$	4.23486	0.225719
$353$	−2.57212	−0.136900	−0.0684501	−	0.997655i	$-0.521805\pi$
$353$	−2.57212	−0.136900	−0.0684501	+	0.997655i	$0.521805\pi$
$354$	30.5873	1.62570
$355$	2.43223	0.129090
$356$	0.957142	0.0507284
$357$	1.05200	0.0556777
$358$	8.60993	0.455049
$359$	13.4890	0.711924	0.355962	−	0.934500i	$-0.384153\pi$
$359$	13.4890	0.711924	0.355962	+	0.934500i	$0.384153\pi$
$360$	49.6664	2.61765
$361$	37.2017	1.95799
$362$	−4.43943	−0.233331
$363$	34.3380	1.80228
$364$	−0.640013	−0.0335458
$365$	15.3470	0.803298
$366$	−15.6398	−0.817503
$367$	−17.5623	−0.916744	−0.458372	−	0.888760i	$-0.651567\pi$
$367$	−17.5623	−0.916744	−0.458372	+	0.888760i	$0.651567\pi$
$368$	1.69343	0.0882763
$369$	−41.3264	−2.15137
$370$	−14.8829	−0.773723
$371$	−0.846847	−0.0439661
$372$	24.1283	1.25099
$373$	4.60090	0.238225	0.119113	−	0.992881i	$-0.461995\pi$
$373$	4.60090	0.238225	0.119113	+	0.992881i	$0.461995\pi$
$374$	−0.685539	−0.0354484
$375$	38.9694	2.01237
$376$	−28.5697	−1.47337
$377$	14.4000	0.741636
$378$	5.72240	0.294329
$379$	19.2371	0.988146	0.494073	−	0.869421i	$-0.335508\pi$
$379$	19.2371	0.988146	0.494073	+	0.869421i	$0.335508\pi$
$380$	−16.9310	−0.868541
$381$	16.6145	0.851185
$382$	14.9252	0.763641
$383$	19.2110	0.981636	0.490818	−	0.871262i	$-0.336698\pi$
$383$	19.2110	0.981636	0.490818	+	0.871262i	$0.336698\pi$
$384$	−14.3693	−0.733279
$385$	−0.606346	−0.0309022
$386$	−17.6808	−0.899928
$387$	97.5099	4.95671
$388$	0.337788	0.0171486
$389$	33.4052	1.69371	0.846854	−	0.531825i	$-0.178494\pi$
$389$	33.4052	1.69371	0.846854	+	0.531825i	$0.178494\pi$
$390$	11.0950	0.561816
$391$	2.17718	0.110105
$392$	−20.3155	−1.02609
$393$	−3.31776	−0.167359
$394$	−14.5500	−0.733018
$395$	15.2822	0.768929
$396$	6.95115	0.349309
$397$	12.9027	0.647566	0.323783	−	0.946131i	$-0.395045\pi$
$397$	12.9027	0.647566	0.323783	+	0.946131i	$0.395045\pi$
$398$	4.16269	0.208657
$399$	−8.91483	−0.446300
$400$	0.411989	0.0205995
$401$	4.83029	0.241213	0.120607	−	0.992700i	$-0.461516\pi$
$401$	4.83029	0.241213	0.120607	+	0.992700i	$0.461516\pi$
$402$	−22.3199	−1.11321
$403$	11.2057	0.558197
$404$	16.1029	0.801152
$405$	65.2413	3.24187
$406$	−2.99015	−0.148399
$407$	−5.95279	−0.295069
$408$	8.67755	0.429603
$409$	−2.78160	−0.137541	−0.0687706	−	0.997632i	$-0.521908\pi$
$409$	−2.78160	−0.137541	−0.0687706	+	0.997632i	$0.521908\pi$
$410$	10.4048	0.513855
$411$	−38.9337	−1.92046
$412$	14.0839	0.693864
$413$	3.43854	0.169199
$414$	18.9379	0.930747
$415$	−12.4552	−0.611403
$416$	−8.71118	−0.427101
$417$	−3.80881	−0.186518
$418$	5.80937	0.284146
$419$	−7.40533	−0.361774	−0.180887	−	0.983504i	$-0.557897\pi$
$419$	−7.40533	−0.361774	−0.180887	+	0.983504i	$0.557897\pi$
$420$	2.68563	0.131045
$421$	26.7485	1.30364	0.651822	−	0.758372i	$-0.274005\pi$
$421$	26.7485	1.30364	0.651822	+	0.758372i	$0.274005\pi$
$422$	6.60385	0.321470
$423$	−77.3805	−3.76237
$424$	−6.98533	−0.339237
$425$	0.529679	0.0256932
$426$	3.69639	0.179090
$427$	−1.75817	−0.0850840
$428$	−3.11479	−0.150559
$429$	4.43773	0.214256
$430$	−24.5501	−1.18391
$431$	−16.7964	−0.809055	−0.404528	−	0.914526i	$-0.632564\pi$
$431$	−16.7964	−0.809055	−0.404528	+	0.914526i	$0.632564\pi$
$432$	11.4320	0.550021
$433$	−23.9552	−1.15121	−0.575606	−	0.817727i	$-0.695234\pi$
$433$	−23.9552	−1.15121	−0.575606	+	0.817727i	$0.695234\pi$
$434$	−2.32687	−0.111693
$435$	−60.4252	−2.89717
$436$	−3.14810	−0.150767
$437$	−18.4498	−0.882574
$438$	23.3236	1.11444
$439$	−7.85280	−0.374794	−0.187397	−	0.982284i	$-0.560005\pi$
$439$	−7.85280	−0.374794	−0.187397	+	0.982284i	$0.560005\pi$
$440$	−5.00152	−0.238438
$441$	−55.0241	−2.62020
$442$	1.41017	0.0670747
$443$	28.0498	1.33269	0.666344	−	0.745645i	$-0.267858\pi$
$443$	28.0498	1.33269	0.666344	+	0.745645i	$0.267858\pi$
$444$	26.3661	1.25128
$445$	−1.86529	−0.0884232
$446$	−2.54444	−0.120483
$447$	32.1322	1.51980
$448$	2.30213	0.108766
$449$	−6.43490	−0.303682	−0.151841	−	0.988405i	$-0.548520\pi$
$449$	−6.43490	−0.303682	−0.151841	+	0.988405i	$0.548520\pi$
$450$	4.60734	0.217192
$451$	4.16166	0.195965
$452$	−11.9598	−0.562542
$453$	−35.7805	−1.68112
$454$	−0.864772	−0.0405858
$455$	1.24726	0.0584727
$456$	−73.5350	−3.44359
$457$	27.4857	1.28573	0.642863	−	0.765981i	$-0.277746\pi$
$457$	27.4857	1.28573	0.642863	+	0.765981i	$0.277746\pi$
$458$	−3.63707	−0.169949
$459$	14.6976	0.686027
$460$	5.55808	0.259147
$461$	−17.0674	−0.794908	−0.397454	−	0.917622i	$-0.630106\pi$
$461$	−17.0674	−0.794908	−0.397454	+	0.917622i	$0.630106\pi$
$462$	−0.921494	−0.0428718
$463$	−18.4448	−0.857204	−0.428602	−	0.903493i	$-0.640994\pi$
$463$	−18.4448	−0.857204	−0.428602	+	0.903493i	$0.640994\pi$
$464$	−5.97359	−0.277317
$465$	−47.0215	−2.18057
$466$	−8.58100	−0.397507
$467$	32.1553	1.48797	0.743985	−	0.668197i	$-0.232934\pi$
$467$	32.1553	1.48797	0.743985	+	0.668197i	$0.232934\pi$
$468$	−14.2986	−0.660955
$469$	−2.50913	−0.115861
$470$	19.4821	0.898644
$471$	13.7623	0.634132
$472$	28.3632	1.30552
$473$	−9.81948	−0.451500
$474$	23.2251	1.06676
$475$	−4.48859	−0.205951
$476$	0.341342	0.0156454
$477$	−18.9196	−0.866268
$478$	−2.81781	−0.128884
$479$	9.78265	0.446981	0.223490	−	0.974706i	$-0.428255\pi$
$479$	9.78265	0.446981	0.223490	+	0.974706i	$0.428255\pi$
$480$	36.5539	1.66845
$481$	12.2450	0.558324
$482$	10.3819	0.472882
$483$	2.92654	0.133162
$484$	11.1416	0.506438
$485$	−0.658286	−0.0298912
$486$	51.2537	2.32491
$487$	37.5050	1.69951	0.849757	−	0.527175i	$-0.176749\pi$
$487$	37.5050	1.69951	0.849757	+	0.527175i	$0.176749\pi$
$488$	−14.5025	−0.656498
$489$	−47.9259	−2.16729
$490$	13.8535	0.625835
$491$	−42.4814	−1.91716	−0.958578	−	0.284829i	$-0.908063\pi$
$491$	−42.4814	−1.91716	−0.958578	+	0.284829i	$0.908063\pi$
$492$	−18.4328	−0.831016
$493$	−7.68001	−0.345890
$494$	−11.9500	−0.537655
$495$	−13.5465	−0.608870
$496$	−4.64851	−0.208724
$497$	0.415537	0.0186394
$498$	−18.9288	−0.848221
$499$	11.9523	0.535058	0.267529	−	0.963550i	$-0.413793\pi$
$499$	11.9523	0.535058	0.267529	+	0.963550i	$0.413793\pi$
$500$	12.6444	0.565474
$501$	−24.3440	−1.08761
$502$	0.624546	0.0278749
$503$	−6.01717	−0.268293	−0.134146	−	0.990962i	$-0.542829\pi$
$503$	−6.01717	−0.268293	−0.134146	+	0.990962i	$0.542829\pi$
$504$	8.48528	0.377965
$505$	−31.3816	−1.39646
$506$	−1.90709	−0.0847805
$507$	34.0024	1.51010
$508$	5.39088	0.239182
$509$	−0.369305	−0.0163692	−0.00818458	−	0.999967i	$-0.502605\pi$
$509$	−0.369305	−0.0163692	−0.00818458	+	0.999967i	$0.502605\pi$
$510$	−5.91735	−0.262025
$511$	2.62197	0.115989
$512$	7.68238	0.339517
$513$	−124.550	−5.49903
$514$	19.9638	0.880564
$515$	−27.4469	−1.20945
$516$	43.4924	1.91465
$517$	7.79239	0.342709
$518$	−2.54267	−0.111719
$519$	34.5247	1.51547
$520$	10.2882	0.451168
$521$	24.1959	1.06004	0.530022	−	0.847984i	$-0.322184\pi$
$521$	24.1959	1.06004	0.530022	+	0.847984i	$0.322184\pi$
$522$	−66.8035	−2.92391
$523$	−29.5895	−1.29386	−0.646929	−	0.762550i	$-0.723947\pi$
$523$	−29.5895	−1.29386	−0.646929	+	0.762550i	$0.723947\pi$
$524$	−1.07651	−0.0470276
$525$	0.711988	0.0310737
$526$	22.2554	0.970380
$527$	−5.97641	−0.260337
$528$	−1.84092	−0.0801158
$529$	−16.9433	−0.736667
$530$	4.76340	0.206909
$531$	76.8210	3.33375
$532$	−2.89259	−0.125410
$533$	−8.56062	−0.370802
$534$	−2.83477	−0.122673
$535$	6.07015	0.262435
$536$	−20.6969	−0.893970
$537$	29.7255	1.28275
$538$	3.70937	0.159922
$539$	5.54106	0.238670
$540$	37.5213	1.61466
$541$	18.0123	0.774409	0.387205	−	0.921994i	$-0.373441\pi$
$541$	18.0123	0.774409	0.387205	+	0.921994i	$0.373441\pi$
$542$	−7.38895	−0.317383
$543$	−15.3270	−0.657743
$544$	4.64598	0.199195
$545$	6.13505	0.262797
$546$	1.89553	0.0811212
$547$	−20.6897	−0.884630	−0.442315	−	0.896860i	$-0.645843\pi$
$547$	−20.6897	−0.884630	−0.442315	+	0.896860i	$0.645843\pi$
$548$	−12.6328	−0.539646
$549$	−39.2797	−1.67642
$550$	−0.463969	−0.0197837
$551$	65.0818	2.77258
$552$	24.1400	1.02746
$553$	2.61089	0.111026
$554$	−11.2469	−0.477835
$555$	−51.3826	−2.18107
$556$	−1.23584	−0.0524114
$557$	−29.5583	−1.25243	−0.626213	−	0.779652i	$-0.715396\pi$
$557$	−29.5583	−1.25243	−0.626213	+	0.779652i	$0.715396\pi$
$558$	−51.9850	−2.20070
$559$	20.1988	0.854320
$560$	−0.517407	−0.0218644
$561$	−2.36680	−0.0999264
$562$	12.9592	0.546652
$563$	23.3139	0.982565	0.491282	−	0.871000i	$-0.336528\pi$
$563$	23.3139	0.982565	0.491282	+	0.871000i	$0.336528\pi$
$564$	−34.5141	−1.45330
$565$	23.3074	0.980551
$566$	22.9824	0.966022
$567$	11.1462	0.468097
$568$	3.42760	0.143819
$569$	0.799044	0.0334977	0.0167488	−	0.999860i	$-0.494668\pi$
$569$	0.799044	0.0334977	0.0167488	+	0.999860i	$0.494668\pi$
$570$	50.1446	2.10033
$571$	−10.6002	−0.443606	−0.221803	−	0.975092i	$-0.571194\pi$
$571$	−10.6002	−0.443606	−0.221803	+	0.975092i	$0.571194\pi$
$572$	1.43991	0.0602055
$573$	51.5288	2.15265
$574$	1.77761	0.0741960
$575$	1.47351	0.0614494
$576$	51.4324	2.14302
$577$	−12.6869	−0.528161	−0.264081	−	0.964501i	$-0.585069\pi$
$577$	−12.6869	−0.528161	−0.264081	+	0.964501i	$0.585069\pi$
$578$	15.5846	0.648235
$579$	−61.0423	−2.53683
$580$	−19.6061	−0.814100
$581$	−2.12792	−0.0882810
$582$	−1.00043	−0.0414691
$583$	1.90525	0.0789073
$584$	21.6276	0.894957
$585$	27.8654	1.15209
$586$	−5.66749	−0.234122
$587$	22.5700	0.931563	0.465781	−	0.884900i	$-0.345773\pi$
$587$	22.5700	0.931563	0.465781	+	0.884900i	$0.345773\pi$
$588$	−24.5424	−1.01211
$589$	50.6451	2.08680
$590$	−19.3413	−0.796268
$591$	−50.2334	−2.06633
$592$	−5.07964	−0.208772
$593$	−13.5627	−0.556953	−0.278477	−	0.960443i	$-0.589829\pi$
$593$	−13.5627	−0.556953	−0.278477	+	0.960443i	$0.589829\pi$
$594$	−12.8743	−0.528240
$595$	−0.665211	−0.0272710
$596$	10.4259	0.427063
$597$	14.3716	0.588189
$598$	3.92292	0.160420
$599$	42.3126	1.72885	0.864424	−	0.502764i	$-0.167683\pi$
$599$	42.3126	1.72885	0.864424	+	0.502764i	$0.167683\pi$
$600$	5.87292	0.239761
$601$	−2.57297	−0.104954	−0.0524769	−	0.998622i	$-0.516712\pi$
$601$	−2.57297	−0.104954	−0.0524769	+	0.998622i	$0.516712\pi$
$602$	−4.19429	−0.170946
$603$	−56.0571	−2.28282
$604$	−11.6097	−0.472391
$605$	−21.7129	−0.882757
$606$	−47.6922	−1.93736
$607$	5.64796	0.229244	0.114622	−	0.993409i	$-0.463434\pi$
$607$	5.64796	0.229244	0.114622	+	0.993409i	$0.463434\pi$
$608$	−39.3708	−1.59670
$609$	−10.3234	−0.418325
$610$	9.88948	0.400413
$611$	−16.0291	−0.648468
$612$	7.62598	0.308262
$613$	−12.0277	−0.485796	−0.242898	−	0.970052i	$-0.578098\pi$
$613$	−12.0277	−0.485796	−0.242898	+	0.970052i	$0.578098\pi$
$614$	−14.4307	−0.582377
$615$	35.9221	1.44852
$616$	−0.854488	−0.0344283
$617$	−24.9471	−1.00433	−0.502166	−	0.864771i	$-0.667463\pi$
$617$	−24.9471	−1.00433	−0.502166	+	0.864771i	$0.667463\pi$
$618$	−41.7124	−1.67792
$619$	28.9512	1.16365	0.581823	−	0.813315i	$-0.302340\pi$
$619$	28.9512	1.16365	0.581823	+	0.813315i	$0.302340\pi$
$620$	−15.2570	−0.612738
$621$	40.8872	1.64075
$622$	24.0919	0.965999
$623$	−0.318677	−0.0127675
$624$	3.78681	0.151594
$625$	−21.6478	−0.865914
$626$	13.7497	0.549547
$627$	20.0567	0.800986
$628$	4.46544	0.178190
$629$	−6.53070	−0.260396
$630$	−5.78624	−0.230529
$631$	22.5348	0.897096	0.448548	−	0.893759i	$-0.351941\pi$
$631$	22.5348	0.897096	0.448548	+	0.893759i	$0.351941\pi$
$632$	21.5363	0.856667
$633$	22.7996	0.906201
$634$	26.6666	1.05907
$635$	−10.5058	−0.416911
$636$	−8.43872	−0.334617
$637$	−11.3981	−0.451607
$638$	6.72727	0.266335
$639$	9.28358	0.367253
$640$	9.08612	0.359160
$641$	−20.6553	−0.815837	−0.407918	−	0.913018i	$-0.633745\pi$
$641$	−20.6553	−0.815837	−0.407918	+	0.913018i	$0.633745\pi$
$642$	9.22511	0.364086
$643$	2.36382	0.0932199	0.0466100	−	0.998913i	$-0.485158\pi$
$643$	2.36382	0.0932199	0.0466100	+	0.998913i	$0.485158\pi$
$644$	0.949573	0.0374184
$645$	−84.7585	−3.33736
$646$	6.37336	0.250756
$647$	7.40067	0.290950	0.145475	−	0.989362i	$-0.453529\pi$
$647$	7.40067	0.290950	0.145475	+	0.989362i	$0.453529\pi$
$648$	91.9408	3.61178
$649$	−7.73606	−0.303667
$650$	0.954393	0.0374344
$651$	−8.03343	−0.314855
$652$	−15.5505	−0.609004
$653$	35.1775	1.37660	0.688300	−	0.725426i	$-0.258357\pi$
$653$	35.1775	1.37660	0.688300	+	0.725426i	$0.258357\pi$
$654$	9.32375	0.364587
$655$	2.09792	0.0819725
$656$	3.55123	0.138652
$657$	58.5779	2.28534
$658$	3.32844	0.129756
$659$	−0.284882	−0.0110974	−0.00554871	−	0.999985i	$-0.501766\pi$
$659$	−0.284882	−0.0110974	−0.00554871	+	0.999985i	$0.501766\pi$
$660$	−6.04215	−0.235190
$661$	39.2703	1.52744	0.763718	−	0.645550i	$-0.223372\pi$
$661$	39.2703	1.52744	0.763718	+	0.645550i	$0.223372\pi$
$662$	29.1004	1.13102
$663$	4.86855	0.189079
$664$	−17.5524	−0.681166
$665$	5.63711	0.218598
$666$	−56.8064	−2.20120
$667$	−21.3649	−0.827253
$668$	−7.89887	−0.305616
$669$	−8.78460	−0.339632
$670$	14.1135	0.545253
$671$	3.95556	0.152703
$672$	6.24508	0.240909
$673$	18.3962	0.709120	0.354560	−	0.935033i	$-0.384631\pi$
$673$	18.3962	0.709120	0.354560	+	0.935033i	$0.384631\pi$
$674$	4.63615	0.178578
$675$	9.94729	0.382871
$676$	11.0327	0.424336
$677$	−6.67853	−0.256677	−0.128338	−	0.991730i	$-0.540964\pi$
$677$	−6.67853	−0.256677	−0.128338	+	0.991730i	$0.540964\pi$
$678$	35.4215	1.36035
$679$	−0.112465	−0.00431602
$680$	−5.48707	−0.210420
$681$	−2.98560	−0.114408
$682$	5.23501	0.200459
$683$	−37.5101	−1.43528	−0.717642	−	0.696412i	$-0.754779\pi$
$683$	−37.5101	−1.43528	−0.717642	+	0.696412i	$0.754779\pi$
$684$	−64.6239	−2.47096
$685$	24.6189	0.940640
$686$	4.77786	0.182419
$687$	−12.5569	−0.479074
$688$	−8.37916	−0.319452
$689$	−3.91913	−0.149307
$690$	−16.4614	−0.626675
$691$	−23.2683	−0.885167	−0.442584	−	0.896727i	$-0.645938\pi$
$691$	−23.2683	−0.885167	−0.442584	+	0.896727i	$0.645938\pi$
$692$	11.2022	0.425844
$693$	−2.31436	−0.0879153
$694$	3.68159	0.139751
$695$	2.40842	0.0913567
$696$	−85.1538	−3.22775
$697$	4.56568	0.172938
$698$	27.1429	1.02737
$699$	−29.6256	−1.12054
$700$	0.231018	0.00873167
$701$	3.09271	0.116810	0.0584050	−	0.998293i	$-0.481399\pi$
$701$	3.09271	0.116810	0.0584050	+	0.998293i	$0.481399\pi$
$702$	26.4827	0.999526
$703$	55.3423	2.08727
$704$	−5.17936	−0.195205
$705$	67.2614	2.53321
$706$	2.47176	0.0930261
$707$	−5.36141	−0.201637
$708$	34.2645	1.28774
$709$	3.36487	0.126370	0.0631852	−	0.998002i	$-0.479874\pi$
$709$	3.36487	0.126370	0.0631852	+	0.998002i	$0.479874\pi$
$710$	−2.33733	−0.0877186
$711$	58.3305	2.18756
$712$	−2.62864	−0.0985126
$713$	−16.6257	−0.622637
$714$	−1.01095	−0.0378340
$715$	−2.80611	−0.104943
$716$	9.64501	0.360451
$717$	−9.72840	−0.363314
$718$	−12.9627	−0.483765
$719$	36.4265	1.35848	0.679241	−	0.733916i	$-0.262309\pi$
$719$	36.4265	1.35848	0.679241	+	0.733916i	$0.262309\pi$
$720$	−11.5595	−0.430797
$721$	−4.68918	−0.174634
$722$	−35.7502	−1.33049
$723$	35.8431	1.33302
$724$	−4.97313	−0.184825
$725$	−5.19780	−0.193041
$726$	−32.9983	−1.22468
$727$	−43.5712	−1.61596	−0.807982	−	0.589207i	$-0.799440\pi$
$727$	−43.5712	−1.61596	−0.807982	+	0.589207i	$0.799440\pi$
$728$	1.75770	0.0651446
$729$	83.6573	3.09842
$730$	−14.7482	−0.545855
$731$	−10.7728	−0.398445
$732$	−17.5200	−0.647556
$733$	−13.2673	−0.490039	−0.245020	−	0.969518i	$-0.578794\pi$
$733$	−13.2673	−0.490039	−0.245020	+	0.969518i	$0.578794\pi$
$734$	16.8771	0.622944
$735$	47.8286	1.76418
$736$	12.9246	0.476407
$737$	5.64508	0.207939
$738$	39.7140	1.46189
$739$	2.53392	0.0932117	0.0466058	−	0.998913i	$-0.485160\pi$
$739$	2.53392	0.0932117	0.0466058	+	0.998913i	$0.485160\pi$
$740$	−16.6721	−0.612878
$741$	−41.2569	−1.51561
$742$	0.813806	0.0298758
$743$	45.1512	1.65644	0.828218	−	0.560406i	$-0.189355\pi$
$743$	45.1512	1.65644	0.828218	+	0.560406i	$0.189355\pi$
$744$	−66.2647	−2.42938
$745$	−20.3182	−0.744400
$746$	−4.42138	−0.161878
$747$	−47.5403	−1.73941
$748$	−0.767954	−0.0280792
$749$	1.03706	0.0378933
$750$	−37.4489	−1.36744
$751$	−34.0482	−1.24244	−0.621218	−	0.783638i	$-0.713362\pi$
$751$	−34.0482	−1.24244	−0.621218	+	0.783638i	$0.713362\pi$
$752$	6.64941	0.242479
$753$	2.15623	0.0785772
$754$	−13.8381	−0.503955
$755$	22.6251	0.823411
$756$	6.41035	0.233142
$757$	48.0812	1.74754	0.873770	−	0.486339i	$-0.161668\pi$
$757$	48.0812	1.74754	0.873770	+	0.486339i	$0.161668\pi$
$758$	−18.4866	−0.671462
$759$	−6.58417	−0.238990
$760$	46.4984	1.68667
$761$	−19.4800	−0.706148	−0.353074	−	0.935595i	$-0.614864\pi$
$761$	−19.4800	−0.706148	−0.353074	+	0.935595i	$0.614864\pi$
$762$	−15.9662	−0.578395
$763$	1.04815	0.0379455
$764$	16.7195	0.604891
$765$	−14.8616	−0.537322
$766$	−18.4614	−0.667039
$767$	15.9132	0.574592
$768$	56.4285	2.03619
$769$	−28.8652	−1.04090	−0.520452	−	0.853891i	$-0.674237\pi$
$769$	−28.8652	−1.04090	−0.520452	+	0.853891i	$0.674237\pi$
$770$	0.582688	0.0209986
$771$	68.9242	2.48225
$772$	−19.8064	−0.712846
$773$	−9.73384	−0.350102	−0.175051	−	0.984559i	$-0.556009\pi$
$773$	−9.73384	−0.350102	−0.175051	+	0.984559i	$0.556009\pi$
$774$	−93.7054	−3.36817
$775$	−4.04481	−0.145294
$776$	−0.927683	−0.0333019
$777$	−8.77850	−0.314927
$778$	−32.1018	−1.15090
$779$	−38.6904	−1.38623
$780$	12.4288	0.445023
$781$	−0.934879	−0.0334526
$782$	−2.09223	−0.0748181
$783$	−144.230	−5.15435
$784$	4.72830	0.168868
$785$	−8.70229	−0.310598
$786$	3.18831	0.113723
$787$	−54.0244	−1.92576	−0.962880	−	0.269928i	$-0.913000\pi$
$787$	−54.0244	−1.92576	−0.962880	+	0.269928i	$0.913000\pi$
$788$	−16.2992	−0.580635
$789$	76.8359	2.73543
$790$	−14.6859	−0.522501
$791$	3.98198	0.141583
$792$	−19.0903	−0.678344
$793$	−8.13666	−0.288941
$794$	−12.3992	−0.440032
$795$	16.4455	0.583261
$796$	4.66313	0.165280
$797$	44.6486	1.58153	0.790767	−	0.612117i	$-0.209682\pi$
$797$	44.6486	1.58153	0.790767	+	0.612117i	$0.209682\pi$
$798$	8.56700	0.303268
$799$	8.54889	0.302438
$800$	3.14438	0.111171
$801$	−7.11962	−0.251559
$802$	−4.64183	−0.163909
$803$	−5.89893	−0.208169
$804$	−25.0032	−0.881794
$805$	−1.85054	−0.0652230
$806$	−10.7685	−0.379305
$807$	12.8065	0.450810
$808$	−44.2243	−1.55580
$809$	−7.68418	−0.270162	−0.135081	−	0.990835i	$-0.543129\pi$
$809$	−7.68418	−0.270162	−0.135081	+	0.990835i	$0.543129\pi$
$810$	−62.6958	−2.20291
$811$	41.3773	1.45295	0.726477	−	0.687191i	$-0.241156\pi$
$811$	41.3773	1.45295	0.726477	+	0.687191i	$0.241156\pi$
$812$	−3.34962	−0.117549
$813$	−25.5101	−0.894679
$814$	5.72053	0.200505
$815$	30.3050	1.06154
$816$	−2.01964	−0.0707015
$817$	91.2902	3.19384
$818$	2.67307	0.0934617
$819$	4.76068	0.166352
$820$	11.6556	0.407032
$821$	−23.2365	−0.810959	−0.405480	−	0.914104i	$-0.632896\pi$
$821$	−23.2365	−0.810959	−0.405480	+	0.914104i	$0.632896\pi$
$822$	37.4146	1.30498
$823$	−7.61511	−0.265446	−0.132723	−	0.991153i	$-0.542372\pi$
$823$	−7.61511	−0.265446	−0.132723	+	0.991153i	$0.542372\pi$
$824$	−38.6793	−1.34746
$825$	−1.60184	−0.0557689
$826$	−3.30437	−0.114974
$827$	−31.1446	−1.08300	−0.541502	−	0.840699i	$-0.682144\pi$
$827$	−31.1446	−1.08300	−0.541502	+	0.840699i	$0.682144\pi$
$828$	21.2146	0.737259
$829$	−42.6532	−1.48141	−0.740703	−	0.671832i	$-0.765508\pi$
$829$	−42.6532	−1.48141	−0.740703	+	0.671832i	$0.765508\pi$
$830$	11.9693	0.415459
$831$	−38.8295	−1.34698
$832$	10.6540	0.369362
$833$	6.07899	0.210624
$834$	3.66020	0.126742
$835$	15.3934	0.532711
$836$	6.50777	0.225076
$837$	−112.236	−3.87945
$838$	7.11639	0.245832
$839$	−31.0743	−1.07280	−0.536402	−	0.843962i	$-0.680217\pi$
$839$	−31.0743	−1.07280	−0.536402	+	0.843962i	$0.680217\pi$
$840$	−7.37566	−0.254485
$841$	46.3649	1.59879
$842$	−25.7049	−0.885848
$843$	44.7413	1.54097
$844$	7.39776	0.254641
$845$	−21.5007	−0.739648
$846$	74.3613	2.55659
$847$	−3.70956	−0.127462
$848$	1.62579	0.0558297
$849$	79.3459	2.72315
$850$	−0.509012	−0.0174590
$851$	−18.1677	−0.622779
$852$	4.14076	0.141860
$853$	43.7972	1.49959	0.749793	−	0.661672i	$-0.230153\pi$
$853$	43.7972	1.49959	0.749793	+	0.661672i	$0.230153\pi$
$854$	1.68958	0.0578161
$855$	125.940	4.30705
$856$	8.55431	0.292380
$857$	−21.0355	−0.718558	−0.359279	−	0.933230i	$-0.616977\pi$
$857$	−21.0355	−0.718558	−0.359279	+	0.933230i	$0.616977\pi$
$858$	−4.26458	−0.145590
$859$	26.5518	0.905935	0.452968	−	0.891527i	$-0.350365\pi$
$859$	26.5518	0.905935	0.452968	+	0.891527i	$0.350365\pi$
$860$	−27.5015	−0.937795
$861$	6.13714	0.209153
$862$	16.1411	0.549767
$863$	38.7827	1.32018	0.660089	−	0.751187i	$-0.270518\pi$
$863$	38.7827	1.32018	0.660089	+	0.751187i	$0.270518\pi$
$864$	87.2509	2.96834
$865$	−21.8310	−0.742276
$866$	23.0205	0.782269
$867$	53.8054	1.82733
$868$	−2.60660	−0.0884738
$869$	−5.87401	−0.199262
$870$	58.0676	1.96868
$871$	−11.6120	−0.393458
$872$	8.64577	0.292783
$873$	−2.51261	−0.0850389
$874$	17.7299	0.599724
$875$	−4.20990	−0.142321
$876$	26.1275	0.882767
$877$	−26.0776	−0.880579	−0.440289	−	0.897856i	$-0.645124\pi$
$877$	−26.0776	−0.880579	−0.440289	+	0.897856i	$0.645124\pi$
$878$	7.54641	0.254679
$879$	−19.5668	−0.659973
$880$	1.16407	0.0392407
$881$	0.988271	0.0332957	0.0166478	−	0.999861i	$-0.494701\pi$
$881$	0.988271	0.0332957	0.0166478	+	0.999861i	$0.494701\pi$
$882$	52.8772	1.78047
$883$	−50.1414	−1.68739	−0.843696	−	0.536821i	$-0.819625\pi$
$883$	−50.1414	−1.68739	−0.843696	+	0.536821i	$0.819625\pi$
$884$	1.57970	0.0531309
$885$	−66.7751	−2.24462
$886$	−26.9554	−0.905584
$887$	4.54586	0.152635	0.0763175	−	0.997084i	$-0.475684\pi$
$887$	4.54586	0.152635	0.0763175	+	0.997084i	$0.475684\pi$
$888$	−72.4105	−2.42994
$889$	−1.79487	−0.0601982
$890$	1.79251	0.0600851
$891$	−25.0769	−0.840106
$892$	−2.85033	−0.0954362
$893$	−72.4447	−2.42427
$894$	−30.8785	−1.03273
$895$	−18.7963	−0.628291
$896$	1.55232	0.0518595
$897$	13.5438	0.452213
$898$	6.18383	0.206357
$899$	58.6472	1.95599
$900$	5.16123	0.172041
$901$	2.09021	0.0696350
$902$	−3.99929	−0.133162
$903$	−14.4806	−0.481885
$904$	32.8458	1.09244
$905$	9.69170	0.322163
$906$	34.3845	1.14235
$907$	−30.9648	−1.02817	−0.514085	−	0.857739i	$-0.671868\pi$
$907$	−30.9648	−1.02817	−0.514085	+	0.857739i	$0.671868\pi$
$908$	−0.968734	−0.0321486
$909$	−119.780	−3.97287
$910$	−1.19860	−0.0397332
$911$	−0.572234	−0.0189590	−0.00947948	−	0.999955i	$-0.503017\pi$
$911$	−0.572234	−0.0189590	−0.00947948	+	0.999955i	$0.503017\pi$
$912$	17.1148	0.566726
$913$	4.78742	0.158440
$914$	−26.4133	−0.873674
$915$	34.1431	1.12874
$916$	−4.07432	−0.134619
$917$	0.358420	0.0118361
$918$	−14.1242	−0.466167
$919$	−49.5615	−1.63488	−0.817442	−	0.576011i	$-0.804609\pi$
$919$	−49.5615	−1.63488	−0.817442	+	0.576011i	$0.804609\pi$
$920$	−15.2644	−0.503253
$921$	−49.8216	−1.64168
$922$	16.4015	0.540154
$923$	1.92306	0.0632984
$924$	−1.03228	−0.0339594
$925$	−4.41995	−0.145327
$926$	17.7252	0.582485
$927$	−104.762	−3.44084
$928$	−45.5915	−1.49662
$929$	−3.75230	−0.123109	−0.0615545	−	0.998104i	$-0.519606\pi$
$929$	−3.75230	−0.123109	−0.0615545	+	0.998104i	$0.519606\pi$
$930$	45.1869	1.48174
$931$	−51.5144	−1.68832
$932$	−9.61260	−0.314871
$933$	83.1766	2.72308
$934$	−30.9007	−1.01110
$935$	1.49660	0.0489440
$936$	39.2691	1.28355
$937$	−8.19331	−0.267664	−0.133832	−	0.991004i	$-0.542728\pi$
$937$	−8.19331	−0.267664	−0.133832	+	0.991004i	$0.542728\pi$
$938$	2.41124	0.0787296
$939$	47.4702	1.54913
$940$	21.8243	0.711829
$941$	−39.8674	−1.29964	−0.649820	−	0.760088i	$-0.725156\pi$
$941$	−39.8674	−1.29964	−0.649820	+	0.760088i	$0.725156\pi$
$942$	−13.2253	−0.430904
$943$	12.7012	0.413608
$944$	−6.60133	−0.214855
$945$	−12.4926	−0.406383
$946$	9.43635	0.306802
$947$	35.5426	1.15498	0.577489	−	0.816398i	$-0.304032\pi$
$947$	35.5426	1.15498	0.577489	+	0.816398i	$0.304032\pi$
$948$	26.0172	0.844999
$949$	12.1342	0.393893
$950$	4.31346	0.139947
$951$	92.0655	2.98543
$952$	−0.937443	−0.0303827
$953$	7.24123	0.234566	0.117283	−	0.993099i	$-0.462581\pi$
$953$	7.24123	0.234566	0.117283	+	0.993099i	$0.462581\pi$
$954$	18.1814	0.588645
$955$	−32.5832	−1.05437
$956$	−3.15657	−0.102091
$957$	23.2257	0.750780
$958$	−9.40096	−0.303731
$959$	4.20604	0.135820
$960$	−44.7066	−1.44290
$961$	14.6379	0.472191
$962$	−11.7672	−0.379391
$963$	23.1691	0.746615
$964$	11.6300	0.374577
$965$	38.5989	1.24254
$966$	−2.81236	−0.0904861
$967$	−35.6982	−1.14798	−0.573989	−	0.818863i	$-0.694605\pi$
$967$	−35.6982	−1.14798	−0.573989	+	0.818863i	$0.694605\pi$
$968$	−30.5988	−0.983482
$969$	22.0038	0.706864
$970$	0.632601	0.0203116
$971$	−30.4498	−0.977182	−0.488591	−	0.872513i	$-0.662489\pi$
$971$	−30.4498	−0.977182	−0.488591	+	0.872513i	$0.662489\pi$
$972$	57.4154	1.84160
$973$	0.411469	0.0131911
$974$	−36.0417	−1.15485
$975$	3.29501	0.105525
$976$	3.37536	0.108043
$977$	16.8346	0.538587	0.269293	−	0.963058i	$-0.413210\pi$
$977$	16.8346	0.538587	0.269293	+	0.963058i	$0.413210\pi$
$978$	46.0560	1.47271
$979$	0.716962	0.0229142
$980$	15.5189	0.495733
$981$	23.4169	0.747643
$982$	40.8239	1.30274
$983$	−41.4175	−1.32101	−0.660507	−	0.750820i	$-0.729658\pi$
$983$	−41.4175	−1.32101	−0.660507	+	0.750820i	$0.729658\pi$
$984$	50.6230	1.61380
$985$	31.7641	1.01209
$986$	7.38036	0.235039
$987$	11.4913	0.365773
$988$	−13.3866	−0.425885
$989$	−29.9686	−0.952946
$990$	13.0179	0.413738
$991$	0.927072	0.0294494	0.0147247	−	0.999892i	$-0.495313\pi$
$991$	0.927072	0.0294494	0.0147247	+	0.999892i	$0.495313\pi$
$992$	−35.4783	−1.12644
$993$	100.468	3.18826
$994$	−0.399324	−0.0126658
$995$	−9.08757	−0.288095
$996$	−21.2044	−0.671888
$997$	−7.94129	−0.251503	−0.125752	−	0.992062i	$-0.540134\pi$
$997$	−7.94129	−0.251503	−0.125752	+	0.992062i	$0.540134\pi$
$998$	−11.4860	−0.363582
$999$	−122.646	−3.88034

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	131.2.a.b.1.4	✓	10
3.2	odd	2		1179.2.a.g.1.7		10
4.3	odd	2		2096.2.a.r.1.10		10
5.4	even	2		3275.2.a.f.1.7		10
7.6	odd	2		6419.2.a.d.1.4		10
8.3	odd	2		8384.2.a.bu.1.1		10
8.5	even	2		8384.2.a.bt.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
131.2.a.b.1.4	✓	10	1.1	even	1	trivial
1179.2.a.g.1.7		10	3.2	odd	2
2096.2.a.r.1.10		10	4.3	odd	2
3275.2.a.f.1.7		10	5.4	even	2
6419.2.a.d.1.4		10	7.6	odd	2
8384.2.a.bt.1.10		10	8.5	even	2
8384.2.a.bu.1.1		10	8.3	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:	\( N \)	\(=\)	\( 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	131.a (trivial)

\(f(q)\)	\(=\)	\(q-0.960983 q^{2} -3.31776 q^{3} -1.07651 q^{4} +2.09792 q^{5} +3.18831 q^{6} +0.358420 q^{7} +2.95648 q^{8} +8.00754 q^{9} +O(q^{10})\)	\(q-0.960983 q^{2} -3.31776 q^{3} -1.07651 q^{4} +2.09792 q^{5} +3.18831 q^{6} +0.358420 q^{7} +2.95648 q^{8} +8.00754 q^{9} -2.01606 q^{10} -0.806378 q^{11} +3.57161 q^{12} +1.65873 q^{13} -0.344436 q^{14} -6.96040 q^{15} -0.688099 q^{16} -0.884662 q^{17} -7.69511 q^{18} +7.49678 q^{19} -2.25843 q^{20} -1.18915 q^{21} +0.774916 q^{22} -2.46103 q^{23} -9.80888 q^{24} -0.598735 q^{25} -1.59402 q^{26} -16.6138 q^{27} -0.385844 q^{28} +8.68129 q^{29} +6.68882 q^{30} +6.75559 q^{31} -5.25170 q^{32} +2.67537 q^{33} +0.850146 q^{34} +0.751937 q^{35} -8.62021 q^{36} +7.38214 q^{37} -7.20428 q^{38} -5.50329 q^{39} +6.20245 q^{40} -5.16093 q^{41} +1.14276 q^{42} +12.1773 q^{43} +0.868076 q^{44} +16.7992 q^{45} +2.36501 q^{46} -9.66345 q^{47} +2.28295 q^{48} -6.87153 q^{49} +0.575374 q^{50} +2.93510 q^{51} -1.78565 q^{52} -2.36272 q^{53} +15.9656 q^{54} -1.69172 q^{55} +1.05966 q^{56} -24.8725 q^{57} -8.34258 q^{58} +9.59358 q^{59} +7.49295 q^{60} -4.90534 q^{61} -6.49200 q^{62} +2.87007 q^{63} +6.42299 q^{64} +3.47989 q^{65} -2.57099 q^{66} -7.00053 q^{67} +0.952350 q^{68} +8.16511 q^{69} -0.722599 q^{70} +1.15935 q^{71} +23.6741 q^{72} +7.31533 q^{73} -7.09411 q^{74} +1.98646 q^{75} -8.07037 q^{76} -0.289023 q^{77} +5.28856 q^{78} +7.28444 q^{79} -1.44358 q^{80} +31.0981 q^{81} +4.95957 q^{82} -5.93694 q^{83} +1.28014 q^{84} -1.85595 q^{85} -11.7021 q^{86} -28.8025 q^{87} -2.38404 q^{88} -0.889114 q^{89} -16.1437 q^{90} +0.594524 q^{91} +2.64933 q^{92} -22.4134 q^{93} +9.28641 q^{94} +15.7276 q^{95} +17.4239 q^{96} -0.313780 q^{97} +6.60343 q^{98} -6.45711 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} + 16 q^{4} + 4 q^{5} - 4 q^{6} + q^{7} - 6 q^{8} + 15 q^{9}+O(q^{10}) \) 10 * q + q^3 + 16 * q^4 + 4 * q^5 - 4 * q^6 + q^7 - 6 * q^8 + 15 * q^9	\( 10 q + q^{3} + 16 q^{4} + 4 q^{5} - 4 q^{6} + q^{7} - 6 q^{8} + 15 q^{9} + 2 q^{11} - 8 q^{12} + 11 q^{13} - 6 q^{14} - 2 q^{15} + 28 q^{16} - 2 q^{17} - 24 q^{18} - 14 q^{20} + 9 q^{21} - 4 q^{22} - 10 q^{23} - 36 q^{24} + 18 q^{25} - 28 q^{26} - 11 q^{27} - 24 q^{28} + 16 q^{29} - 52 q^{30} + 6 q^{31} - 42 q^{32} - 27 q^{33} - 4 q^{34} - 19 q^{35} + 16 q^{36} + 34 q^{37} - 8 q^{38} + 4 q^{39} + 10 q^{40} - 13 q^{41} + 2 q^{42} + 9 q^{43} + 18 q^{44} + 21 q^{45} + 32 q^{46} - 6 q^{47} + 14 q^{48} + 23 q^{49} + 8 q^{50} - 18 q^{51} + 4 q^{52} + 30 q^{53} + 12 q^{54} - 20 q^{55} - 6 q^{56} - 4 q^{57} - 5 q^{59} + 44 q^{60} + 51 q^{61} + 4 q^{62} - 17 q^{63} + 52 q^{64} - 14 q^{65} + 32 q^{66} - 10 q^{67} + 32 q^{68} + 18 q^{69} - 30 q^{70} - 44 q^{72} - 14 q^{73} + 52 q^{74} - 16 q^{75} - 20 q^{76} - 24 q^{77} + 78 q^{78} + 24 q^{79} + 14 q^{80} + 18 q^{81} - 20 q^{82} - 22 q^{83} + 46 q^{84} + 16 q^{85} - 20 q^{86} - 48 q^{87} + 60 q^{88} + 14 q^{89} + 6 q^{90} - q^{91} - 48 q^{92} + 16 q^{94} - 28 q^{95} - 48 q^{96} + 4 q^{97} + 80 q^{98} - 30 q^{99}+O(q^{100}) \) 10 * q + q^3 + 16 * q^4 + 4 * q^5 - 4 * q^6 + q^7 - 6 * q^8 + 15 * q^9 + 2 * q^11 - 8 * q^12 + 11 * q^13 - 6 * q^14 - 2 * q^15 + 28 * q^16 - 2 * q^17 - 24 * q^18 - 14 * q^20 + 9 * q^21 - 4 * q^22 - 10 * q^23 - 36 * q^24 + 18 * q^25 - 28 * q^26 - 11 * q^27 - 24 * q^28 + 16 * q^29 - 52 * q^30 + 6 * q^31 - 42 * q^32 - 27 * q^33 - 4 * q^34 - 19 * q^35 + 16 * q^36 + 34 * q^37 - 8 * q^38 + 4 * q^39 + 10 * q^40 - 13 * q^41 + 2 * q^42 + 9 * q^43 + 18 * q^44 + 21 * q^45 + 32 * q^46 - 6 * q^47 + 14 * q^48 + 23 * q^49 + 8 * q^50 - 18 * q^51 + 4 * q^52 + 30 * q^53 + 12 * q^54 - 20 * q^55 - 6 * q^56 - 4 * q^57 - 5 * q^59 + 44 * q^60 + 51 * q^61 + 4 * q^62 - 17 * q^63 + 52 * q^64 - 14 * q^65 + 32 * q^66 - 10 * q^67 + 32 * q^68 + 18 * q^69 - 30 * q^70 - 44 * q^72 - 14 * q^73 + 52 * q^74 - 16 * q^75 - 20 * q^76 - 24 * q^77 + 78 * q^78 + 24 * q^79 + 14 * q^80 + 18 * q^81 - 20 * q^82 - 22 * q^83 + 46 * q^84 + 16 * q^85 - 20 * q^86 - 48 * q^87 + 60 * q^88 + 14 * q^89 + 6 * q^90 - q^91 - 48 * q^92 + 16 * q^94 - 28 * q^95 - 48 * q^96 + 4 * q^97 + 80 * q^98 - 30 * q^99

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