LMFDB - Embedded newform 2013.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,2,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2013.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:	$16.0738859269$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 21 x^{12} + 20 x^{11} + 167 x^{10} - 148 x^{9} - 627 x^{8} + 497 x^{7} + 1123 x^{6} + \cdots - 1 $ x^14 - x^13 - 21x^12 + 20x^11 + 167x^10 - 148x^9 - 627x^8 + 497x^7 + 1123x^6 - 745x^5 - 802x^4 + 386x^3 + 74x^2 - 15x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.63401$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.63401 q^{2} -1.00000 q^{3} +4.93799 q^{4} +2.62502 q^{5} +2.63401 q^{6} +5.18852 q^{7} -7.73867 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.63401 q^{2} -1.00000 q^{3} +4.93799 q^{4} +2.62502 q^{5} +2.63401 q^{6} +5.18852 q^{7} -7.73867 q^{8} +1.00000 q^{9} -6.91432 q^{10} -1.00000 q^{11} -4.93799 q^{12} -3.47280 q^{13} -13.6666 q^{14} -2.62502 q^{15} +10.5077 q^{16} +1.94870 q^{17} -2.63401 q^{18} -0.343156 q^{19} +12.9623 q^{20} -5.18852 q^{21} +2.63401 q^{22} -4.48645 q^{23} +7.73867 q^{24} +1.89073 q^{25} +9.14738 q^{26} -1.00000 q^{27} +25.6208 q^{28} -5.47498 q^{29} +6.91432 q^{30} +2.40756 q^{31} -12.2001 q^{32} +1.00000 q^{33} -5.13290 q^{34} +13.6200 q^{35} +4.93799 q^{36} +10.3461 q^{37} +0.903876 q^{38} +3.47280 q^{39} -20.3142 q^{40} -0.436542 q^{41} +13.6666 q^{42} +6.40802 q^{43} -4.93799 q^{44} +2.62502 q^{45} +11.8173 q^{46} +4.42685 q^{47} -10.5077 q^{48} +19.9207 q^{49} -4.98019 q^{50} -1.94870 q^{51} -17.1487 q^{52} +2.47102 q^{53} +2.63401 q^{54} -2.62502 q^{55} -40.1522 q^{56} +0.343156 q^{57} +14.4211 q^{58} +13.7469 q^{59} -12.9623 q^{60} +1.00000 q^{61} -6.34152 q^{62} +5.18852 q^{63} +11.1197 q^{64} -9.11617 q^{65} -2.63401 q^{66} +2.76619 q^{67} +9.62267 q^{68} +4.48645 q^{69} -35.8750 q^{70} -16.0977 q^{71} -7.73867 q^{72} -3.11724 q^{73} -27.2517 q^{74} -1.89073 q^{75} -1.69450 q^{76} -5.18852 q^{77} -9.14738 q^{78} -5.15429 q^{79} +27.5830 q^{80} +1.00000 q^{81} +1.14985 q^{82} +2.12536 q^{83} -25.6208 q^{84} +5.11538 q^{85} -16.8788 q^{86} +5.47498 q^{87} +7.73867 q^{88} +3.14440 q^{89} -6.91432 q^{90} -18.0187 q^{91} -22.1540 q^{92} -2.40756 q^{93} -11.6604 q^{94} -0.900792 q^{95} +12.2001 q^{96} +6.51443 q^{97} -52.4712 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9}+O(q^{10}) $ 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9} + 6 q^{10} - 14 q^{11} - 15 q^{12} + q^{13} - 7 q^{14} - q^{15} + 17 q^{16} - 9 q^{17} - q^{18} + 22 q^{19} + 23 q^{20} - 9 q^{21} + q^{22} + q^{23} + 25 q^{25} + 4 q^{26} - 14 q^{27} + 37 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 4 q^{32} + 14 q^{33} + 8 q^{34} + 18 q^{35} + 15 q^{36} + 18 q^{37} + 8 q^{38} - q^{39} + 16 q^{40} - 25 q^{41} + 7 q^{42} + 25 q^{43} - 15 q^{44} + q^{45} + 20 q^{46} + 36 q^{47} - 17 q^{48} + 25 q^{49} + 2 q^{50} + 9 q^{51} - 13 q^{52} + q^{54} - q^{55} - 40 q^{56} - 22 q^{57} + 33 q^{58} + 17 q^{59} - 23 q^{60} + 14 q^{61} - 13 q^{62} + 9 q^{63} - 6 q^{64} - 61 q^{65} - q^{66} + 22 q^{67} + 66 q^{68} - q^{69} + 44 q^{70} - 13 q^{71} + 20 q^{73} - 12 q^{74} - 25 q^{75} + 49 q^{76} - 9 q^{77} - 4 q^{78} + 31 q^{79} + 88 q^{80} + 14 q^{81} + 2 q^{82} + 32 q^{83} - 37 q^{84} + 2 q^{85} - 14 q^{86} + 6 q^{87} - 21 q^{89} + 6 q^{90} + 45 q^{91} - 14 q^{92} - 9 q^{93} - 31 q^{94} + 23 q^{95} - 4 q^{96} + 37 q^{97} - 38 q^{98} - 14 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9 + 6 * q^10 - 14 * q^11 - 15 * q^12 + q^13 - 7 * q^14 - q^15 + 17 * q^16 - 9 * q^17 - q^18 + 22 * q^19 + 23 * q^20 - 9 * q^21 + q^22 + q^23 + 25 * q^25 + 4 * q^26 - 14 * q^27 + 37 * q^28 - 6 * q^29 - 6 * q^30 + 9 * q^31 + 4 * q^32 + 14 * q^33 + 8 * q^34 + 18 * q^35 + 15 * q^36 + 18 * q^37 + 8 * q^38 - q^39 + 16 * q^40 - 25 * q^41 + 7 * q^42 + 25 * q^43 - 15 * q^44 + q^45 + 20 * q^46 + 36 * q^47 - 17 * q^48 + 25 * q^49 + 2 * q^50 + 9 * q^51 - 13 * q^52 + q^54 - q^55 - 40 * q^56 - 22 * q^57 + 33 * q^58 + 17 * q^59 - 23 * q^60 + 14 * q^61 - 13 * q^62 + 9 * q^63 - 6 * q^64 - 61 * q^65 - q^66 + 22 * q^67 + 66 * q^68 - q^69 + 44 * q^70 - 13 * q^71 + 20 * q^73 - 12 * q^74 - 25 * q^75 + 49 * q^76 - 9 * q^77 - 4 * q^78 + 31 * q^79 + 88 * q^80 + 14 * q^81 + 2 * q^82 + 32 * q^83 - 37 * q^84 + 2 * q^85 - 14 * q^86 + 6 * q^87 - 21 * q^89 + 6 * q^90 + 45 * q^91 - 14 * q^92 - 9 * q^93 - 31 * q^94 + 23 * q^95 - 4 * q^96 + 37 * q^97 - 38 * q^98 - 14 * 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 $

$2$	−2.63401	−1.86252	−0.931262	−	0.364351i	$-0.881291\pi$
$2$	−2.63401	−1.86252	−0.931262	+	0.364351i	$0.881291\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.93799	2.46899
$5$	2.62502	1.17394	0.586972	−	0.809607i	$-0.300320\pi$
$5$	2.62502	1.17394	0.586972	+	0.809607i	$0.300320\pi$
$6$	2.63401	1.07533
$7$	5.18852	1.96107	0.980537	−	0.196333i	$-0.0629034\pi$
$7$	5.18852	1.96107	0.980537	+	0.196333i	$0.0629034\pi$
$8$	−7.73867	−2.73603
$9$	1.00000	0.333333
$10$	−6.91432	−2.18650
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−4.93799	−1.42547
$13$	−3.47280	−0.963182	−0.481591	−	0.876396i	$-0.659941\pi$
$13$	−3.47280	−0.963182	−0.481591	+	0.876396i	$0.659941\pi$
$14$	−13.6666	−3.65255
$15$	−2.62502	−0.677777
$16$	10.5077	2.62694
$17$	1.94870	0.472630	0.236315	−	0.971677i	$-0.424060\pi$
$17$	1.94870	0.472630	0.236315	+	0.971677i	$0.424060\pi$
$18$	−2.63401	−0.620841
$19$	−0.343156	−0.0787255	−0.0393627	−	0.999225i	$-0.512533\pi$
$19$	−0.343156	−0.0787255	−0.0393627	+	0.999225i	$0.512533\pi$
$20$	12.9623	2.89846
$21$	−5.18852	−1.13223
$22$	2.63401	0.561572
$23$	−4.48645	−0.935489	−0.467744	−	0.883864i	$-0.654933\pi$
$23$	−4.48645	−0.935489	−0.467744	+	0.883864i	$0.654933\pi$
$24$	7.73867	1.57965
$25$	1.89073	0.378146
$26$	9.14738	1.79395
$27$	−1.00000	−0.192450
$28$	25.6208	4.84188
$29$	−5.47498	−1.01668	−0.508339	−	0.861157i	$-0.669740\pi$
$29$	−5.47498	−1.01668	−0.508339	+	0.861157i	$0.669740\pi$
$30$	6.91432	1.26238
$31$	2.40756	0.432410	0.216205	−	0.976348i	$-0.430632\pi$
$31$	2.40756	0.432410	0.216205	+	0.976348i	$0.430632\pi$
$32$	−12.2001	−2.15669
$33$	1.00000	0.174078
$34$	−5.13290	−0.880284
$35$	13.6200	2.30219
$36$	4.93799	0.822998
$37$	10.3461	1.70089	0.850444	−	0.526065i	$-0.176333\pi$
$37$	10.3461	1.70089	0.850444	+	0.526065i	$0.176333\pi$
$38$	0.903876	0.146628
$39$	3.47280	0.556093
$40$	−20.3142	−3.21195
$41$	−0.436542	−0.0681764	−0.0340882	−	0.999419i	$-0.510853\pi$
$41$	−0.436542	−0.0681764	−0.0340882	+	0.999419i	$0.510853\pi$
$42$	13.6666	2.10880
$43$	6.40802	0.977214	0.488607	−	0.872504i	$-0.337505\pi$
$43$	6.40802	0.977214	0.488607	+	0.872504i	$0.337505\pi$
$44$	−4.93799	−0.744430
$45$	2.62502	0.391315
$46$	11.8173	1.74237
$47$	4.42685	0.645723	0.322861	−	0.946446i	$-0.395355\pi$
$47$	4.42685	0.645723	0.322861	+	0.946446i	$0.395355\pi$
$48$	−10.5077	−1.51666
$49$	19.9207	2.84581
$50$	−4.98019	−0.704306
$51$	−1.94870	−0.272873
$52$	−17.1487	−2.37809
$53$	2.47102	0.339420	0.169710	−	0.985494i	$-0.445717\pi$
$53$	2.47102	0.339420	0.169710	+	0.985494i	$0.445717\pi$
$54$	2.63401	0.358443
$55$	−2.62502	−0.353958
$56$	−40.1522	−5.36557
$57$	0.343156	0.0454522
$58$	14.4211	1.89359
$59$	13.7469	1.78970	0.894849	−	0.446369i	$-0.147283\pi$
$59$	13.7469	1.78970	0.894849	+	0.446369i	$0.147283\pi$
$60$	−12.9623	−1.67343
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−6.34152	−0.805374
$63$	5.18852	0.653691
$64$	11.1197	1.38996
$65$	−9.11617	−1.13072
$66$	−2.63401	−0.324224
$67$	2.76619	0.337944	0.168972	−	0.985621i	$-0.445955\pi$
$67$	2.76619	0.337944	0.168972	+	0.985621i	$0.445955\pi$
$68$	9.62267	1.16692
$69$	4.48645	0.540105
$70$	−35.8750	−4.28789
$71$	−16.0977	−1.91045	−0.955225	−	0.295881i	$-0.904387\pi$
$71$	−16.0977	−1.91045	−0.955225	+	0.295881i	$0.904387\pi$
$72$	−7.73867	−0.912012
$73$	−3.11724	−0.364845	−0.182422	−	0.983220i	$-0.558394\pi$
$73$	−3.11724	−0.364845	−0.182422	+	0.983220i	$0.558394\pi$
$74$	−27.2517	−3.16794
$75$	−1.89073	−0.218323
$76$	−1.69450	−0.194373
$77$	−5.18852	−0.591286
$78$	−9.14738	−1.03574
$79$	−5.15429	−0.579903	−0.289952	−	0.957041i	$-0.593639\pi$
$79$	−5.15429	−0.579903	−0.289952	+	0.957041i	$0.593639\pi$
$80$	27.5830	3.08388
$81$	1.00000	0.111111
$82$	1.14985	0.126980
$83$	2.12536	0.233289	0.116644	−	0.993174i	$-0.462786\pi$
$83$	2.12536	0.233289	0.116644	+	0.993174i	$0.462786\pi$
$84$	−25.6208	−2.79546
$85$	5.11538	0.554841
$86$	−16.8788	−1.82008
$87$	5.47498	0.586979
$88$	7.73867	0.824946
$89$	3.14440	0.333305	0.166653	−	0.986016i	$-0.446704\pi$
$89$	3.14440	0.333305	0.166653	+	0.986016i	$0.446704\pi$
$90$	−6.91432	−0.728833
$91$	−18.0187	−1.88887
$92$	−22.1540	−2.30972
$93$	−2.40756	−0.249652
$94$	−11.6604	−1.20267
$95$	−0.900792	−0.0924193
$96$	12.2001	1.24517
$97$	6.51443	0.661440	0.330720	−	0.943729i	$-0.392708\pi$
$97$	6.51443	0.661440	0.330720	+	0.943729i	$0.392708\pi$
$98$	−52.4712	−5.30039
$99$	−1.00000	−0.100504
$100$	9.33640	0.933640
$101$	11.1124	1.10572	0.552862	−	0.833273i	$-0.313536\pi$
$101$	11.1124	1.10572	0.552862	+	0.833273i	$0.313536\pi$
$102$	5.13290	0.508232
$103$	−0.504742	−0.0497337	−0.0248668	−	0.999691i	$-0.507916\pi$
$103$	−0.504742	−0.0497337	−0.0248668	+	0.999691i	$0.507916\pi$
$104$	26.8749	2.63530
$105$	−13.6200	−1.32917
$106$	−6.50868	−0.632178
$107$	7.83003	0.756957	0.378479	−	0.925610i	$-0.376447\pi$
$107$	7.83003	0.756957	0.378479	+	0.925610i	$0.376447\pi$
$108$	−4.93799	−0.475158
$109$	−5.69464	−0.545448	−0.272724	−	0.962092i	$-0.587925\pi$
$109$	−5.69464	−0.545448	−0.272724	+	0.962092i	$0.587925\pi$
$110$	6.91432	0.659254
$111$	−10.3461	−0.982008
$112$	54.5196	5.15162
$113$	16.5161	1.55370	0.776850	−	0.629686i	$-0.216816\pi$
$113$	16.5161	1.55370	0.776850	+	0.629686i	$0.216816\pi$
$114$	−0.903876	−0.0846557
$115$	−11.7770	−1.09821
$116$	−27.0354	−2.51017
$117$	−3.47280	−0.321061
$118$	−36.2095	−3.33335
$119$	10.1109	0.926862
$120$	20.3142	1.85442
$121$	1.00000	0.0909091
$122$	−2.63401	−0.238472
$123$	0.436542	0.0393617
$124$	11.8885	1.06762
$125$	−8.16190	−0.730022
$126$	−13.6666	−1.21752
$127$	15.2576	1.35390	0.676948	−	0.736031i	$-0.263302\pi$
$127$	15.2576	1.35390	0.676948	+	0.736031i	$0.263302\pi$
$128$	−4.88904	−0.432134
$129$	−6.40802	−0.564195
$130$	24.0121	2.10600
$131$	−2.57715	−0.225167	−0.112583	−	0.993642i	$-0.535913\pi$
$131$	−2.57715	−0.225167	−0.112583	+	0.993642i	$0.535913\pi$
$132$	4.93799	0.429797
$133$	−1.78047	−0.154387
$134$	−7.28616	−0.629428
$135$	−2.62502	−0.225926
$136$	−15.0804	−1.29313
$137$	14.4185	1.23185	0.615926	−	0.787804i	$-0.288782\pi$
$137$	14.4185	1.23185	0.615926	+	0.787804i	$0.288782\pi$
$138$	−11.8173	−1.00596
$139$	11.3125	0.959516	0.479758	−	0.877401i	$-0.340724\pi$
$139$	11.3125	0.959516	0.479758	+	0.877401i	$0.340724\pi$
$140$	67.2552	5.68410
$141$	−4.42685	−0.372808
$142$	42.4015	3.55826
$143$	3.47280	0.290410
$144$	10.5077	0.875645
$145$	−14.3719	−1.19352
$146$	8.21082	0.679532
$147$	−19.9207	−1.64303
$148$	51.0889	4.19948
$149$	−4.30768	−0.352899	−0.176449	−	0.984310i	$-0.556461\pi$
$149$	−4.30768	−0.352899	−0.176449	+	0.984310i	$0.556461\pi$
$150$	4.98019	0.406631
$151$	−12.6896	−1.03267	−0.516334	−	0.856387i	$-0.672704\pi$
$151$	−12.6896	−1.03267	−0.516334	+	0.856387i	$0.672704\pi$
$152$	2.65558	0.215396
$153$	1.94870	0.157543
$154$	13.6666	1.10128
$155$	6.31989	0.507626
$156$	17.1487	1.37299
$157$	10.8043	0.862274	0.431137	−	0.902286i	$-0.358113\pi$
$157$	10.8043	0.862274	0.431137	+	0.902286i	$0.358113\pi$
$158$	13.5764	1.08008
$159$	−2.47102	−0.195964
$160$	−32.0255	−2.53184
$161$	−23.2780	−1.83456
$162$	−2.63401	−0.206947
$163$	25.0214	1.95983	0.979913	−	0.199427i	$-0.0639080\pi$
$163$	25.0214	1.95983	0.979913	+	0.199427i	$0.0639080\pi$
$164$	−2.15564	−0.168327
$165$	2.62502	0.204358
$166$	−5.59821	−0.434506
$167$	−21.9141	−1.69576	−0.847882	−	0.530185i	$-0.822123\pi$
$167$	−21.9141	−1.69576	−0.847882	+	0.530185i	$0.822123\pi$
$168$	40.1522	3.09781
$169$	−0.939647	−0.0722805
$170$	−13.4740	−1.03340
$171$	−0.343156	−0.0262418
$172$	31.6427	2.41273
$173$	−19.3446	−1.47075	−0.735373	−	0.677663i	$-0.762993\pi$
$173$	−19.3446	−1.47075	−0.735373	+	0.677663i	$0.762993\pi$
$174$	−14.4211	−1.09326
$175$	9.81008	0.741572
$176$	−10.5077	−0.792051
$177$	−13.7469	−1.03328
$178$	−8.28236	−0.620789
$179$	20.9873	1.56866	0.784331	−	0.620343i	$-0.213007\pi$
$179$	20.9873	1.56866	0.784331	+	0.620343i	$0.213007\pi$
$180$	12.9623	0.966154
$181$	−26.3913	−1.96165	−0.980826	−	0.194886i	$-0.937566\pi$
$181$	−26.3913	−1.96165	−0.980826	+	0.194886i	$0.937566\pi$
$182$	47.4613	3.51807
$183$	−1.00000	−0.0739221
$184$	34.7191	2.55953
$185$	27.1587	1.99675
$186$	6.34152	0.464983
$187$	−1.94870	−0.142503
$188$	21.8597	1.59429
$189$	−5.18852	−0.377409
$190$	2.37269	0.172133
$191$	20.2002	1.46164	0.730818	−	0.682572i	$-0.239139\pi$
$191$	20.2002	1.46164	0.730818	+	0.682572i	$0.239139\pi$
$192$	−11.1197	−0.802492
$193$	−16.2353	−1.16864	−0.584321	−	0.811523i	$-0.698639\pi$
$193$	−16.2353	−1.16864	−0.584321	+	0.811523i	$0.698639\pi$
$194$	−17.1591	−1.23195
$195$	9.11617	0.652823
$196$	98.3681	7.02629
$197$	10.8231	0.771112	0.385556	−	0.922685i	$-0.374010\pi$
$197$	10.8231	0.771112	0.385556	+	0.922685i	$0.374010\pi$
$198$	2.63401	0.187191
$199$	17.1207	1.21366	0.606828	−	0.794833i	$-0.292442\pi$
$199$	17.1207	1.21366	0.606828	+	0.794833i	$0.292442\pi$
$200$	−14.6317	−1.03462
$201$	−2.76619	−0.195112
$202$	−29.2701	−2.05944
$203$	−28.4070	−1.99378
$204$	−9.62267	−0.673722
$205$	−1.14593	−0.0800353
$206$	1.32949	0.0926301
$207$	−4.48645	−0.311830
$208$	−36.4913	−2.53022
$209$	0.343156	0.0237366
$210$	35.8750	2.47561
$211$	6.07527	0.418239	0.209119	−	0.977890i	$-0.432940\pi$
$211$	6.07527	0.418239	0.209119	+	0.977890i	$0.432940\pi$
$212$	12.2019	0.838027
$213$	16.0977	1.10300
$214$	−20.6243	−1.40985
$215$	16.8212	1.14719
$216$	7.73867	0.526550
$217$	12.4917	0.847989
$218$	14.9997	1.01591
$219$	3.11724	0.210643
$220$	−12.9623	−0.873919
$221$	−6.76746	−0.455229
$222$	27.2517	1.82901
$223$	−24.7908	−1.66011	−0.830057	−	0.557679i	$-0.811692\pi$
$223$	−24.7908	−1.66011	−0.830057	+	0.557679i	$0.811692\pi$
$224$	−63.3004	−4.22944
$225$	1.89073	0.126049
$226$	−43.5034	−2.89380
$227$	25.6959	1.70549	0.852747	−	0.522324i	$-0.174935\pi$
$227$	25.6959	1.70549	0.852747	+	0.522324i	$0.174935\pi$
$228$	1.69450	0.112221
$229$	−1.69139	−0.111770	−0.0558852	−	0.998437i	$-0.517798\pi$
$229$	−1.69139	−0.111770	−0.0558852	+	0.998437i	$0.517798\pi$
$230$	31.0207	2.04545
$231$	5.18852	0.341379
$232$	42.3691	2.78167
$233$	−8.61616	−0.564463	−0.282232	−	0.959346i	$-0.591075\pi$
$233$	−8.61616	−0.564463	−0.282232	+	0.959346i	$0.591075\pi$
$234$	9.14738	0.597983
$235$	11.6206	0.758043
$236$	67.8822	4.41875
$237$	5.15429	0.334807
$238$	−26.6321	−1.72630
$239$	−13.2629	−0.857905	−0.428953	−	0.903327i	$-0.641117\pi$
$239$	−13.2629	−0.857905	−0.428953	+	0.903327i	$0.641117\pi$
$240$	−27.5830	−1.78048
$241$	2.12784	0.137066	0.0685332	−	0.997649i	$-0.478168\pi$
$241$	2.12784	0.137066	0.0685332	+	0.997649i	$0.478168\pi$
$242$	−2.63401	−0.169320
$243$	−1.00000	−0.0641500
$244$	4.93799	0.316122
$245$	52.2922	3.34083
$246$	−1.14985	−0.0733120
$247$	1.19171	0.0758270
$248$	−18.6313	−1.18309
$249$	−2.12536	−0.134689
$250$	21.4985	1.35968
$251$	1.21883	0.0769321	0.0384661	−	0.999260i	$-0.487753\pi$
$251$	1.21883	0.0769321	0.0384661	+	0.999260i	$0.487753\pi$
$252$	25.6208	1.61396
$253$	4.48645	0.282060
$254$	−40.1887	−2.52166
$255$	−5.11538	−0.320338
$256$	−9.36155	−0.585097
$257$	−10.0350	−0.625964	−0.312982	−	0.949759i	$-0.601328\pi$
$257$	−10.0350	−0.625964	−0.312982	+	0.949759i	$0.601328\pi$
$258$	16.8788	1.05083
$259$	53.6809	3.33557
$260$	−45.0155	−2.79175
$261$	−5.47498	−0.338893
$262$	6.78823	0.419378
$263$	−15.4701	−0.953925	−0.476963	−	0.878924i	$-0.658262\pi$
$263$	−15.4701	−0.953925	−0.476963	+	0.878924i	$0.658262\pi$
$264$	−7.73867	−0.476283
$265$	6.48647	0.398461
$266$	4.68977	0.287549
$267$	−3.14440	−0.192434
$268$	13.6594	0.834381
$269$	−11.4654	−0.699059	−0.349530	−	0.936925i	$-0.613659\pi$
$269$	−11.4654	−0.699059	−0.349530	+	0.936925i	$0.613659\pi$
$270$	6.91432	0.420792
$271$	−10.6925	−0.649521	−0.324760	−	0.945796i	$-0.605284\pi$
$271$	−10.6925	−0.649521	−0.324760	+	0.945796i	$0.605284\pi$
$272$	20.4765	1.24157
$273$	18.0187	1.09054
$274$	−37.9783	−2.29435
$275$	−1.89073	−0.114015
$276$	22.1540	1.33351
$277$	−31.4466	−1.88944	−0.944720	−	0.327877i	$-0.893667\pi$
$277$	−31.4466	−1.88944	−0.944720	+	0.327877i	$0.893667\pi$
$278$	−29.7973	−1.78712
$279$	2.40756	0.144137
$280$	−105.400	−6.29888
$281$	15.8197	0.943723	0.471861	−	0.881673i	$-0.343582\pi$
$281$	15.8197	0.943723	0.471861	+	0.881673i	$0.343582\pi$
$282$	11.6604	0.694364
$283$	−17.7131	−1.05293	−0.526467	−	0.850196i	$-0.676484\pi$
$283$	−17.7131	−1.05293	−0.526467	+	0.850196i	$0.676484\pi$
$284$	−79.4904	−4.71689
$285$	0.900792	0.0533583
$286$	−9.14738	−0.540896
$287$	−2.26500	−0.133699
$288$	−12.2001	−0.718898
$289$	−13.2026	−0.776621
$290$	37.8557	2.22296
$291$	−6.51443	−0.381883
$292$	−15.3929	−0.900799
$293$	−6.92077	−0.404316	−0.202158	−	0.979353i	$-0.564795\pi$
$293$	−6.92077	−0.404316	−0.202158	+	0.979353i	$0.564795\pi$
$294$	52.4712	3.06018
$295$	36.0860	2.10101
$296$	−80.0651	−4.65369
$297$	1.00000	0.0580259
$298$	11.3465	0.657282
$299$	15.5805	0.901046
$300$	−9.33640	−0.539037
$301$	33.2481	1.91639
$302$	33.4246	1.92337
$303$	−11.1124	−0.638390
$304$	−3.60580	−0.206807
$305$	2.62502	0.150308
$306$	−5.13290	−0.293428
$307$	15.9515	0.910401	0.455201	−	0.890389i	$-0.349568\pi$
$307$	15.9515	0.910401	0.455201	+	0.890389i	$0.349568\pi$
$308$	−25.6208	−1.45988
$309$	0.504742	0.0287138
$310$	−16.6466	−0.945465
$311$	−13.8655	−0.786239	−0.393119	−	0.919487i	$-0.628604\pi$
$311$	−13.8655	−0.786239	−0.393119	+	0.919487i	$0.628604\pi$
$312$	−26.8749	−1.52149
$313$	18.1128	1.02380	0.511898	−	0.859046i	$-0.328943\pi$
$313$	18.1128	1.02380	0.511898	+	0.859046i	$0.328943\pi$
$314$	−28.4585	−1.60601
$315$	13.6200	0.767398
$316$	−25.4518	−1.43178
$317$	22.4082	1.25857	0.629286	−	0.777174i	$-0.283348\pi$
$317$	22.4082	1.25857	0.629286	+	0.777174i	$0.283348\pi$
$318$	6.50868	0.364988
$319$	5.47498	0.306540
$320$	29.1893	1.63173
$321$	−7.83003	−0.437029
$322$	61.3144	3.41692
$323$	−0.668710	−0.0372080
$324$	4.93799	0.274333
$325$	−6.56613	−0.364223
$326$	−65.9065	−3.65022
$327$	5.69464	0.314914
$328$	3.37826	0.186533
$329$	22.9688	1.26631
$330$	−6.91432	−0.380621
$331$	−1.51172	−0.0830916	−0.0415458	−	0.999137i	$-0.513228\pi$
$331$	−1.51172	−0.0830916	−0.0415458	+	0.999137i	$0.513228\pi$
$332$	10.4950	0.575988
$333$	10.3461	0.566963
$334$	57.7219	3.15840
$335$	7.26130	0.396727
$336$	−54.5196	−2.97429
$337$	−2.97052	−0.161815	−0.0809074	−	0.996722i	$-0.525782\pi$
$337$	−2.97052	−0.161815	−0.0809074	+	0.996722i	$0.525782\pi$
$338$	2.47503	0.134624
$339$	−16.5161	−0.897029
$340$	25.2597	1.36990
$341$	−2.40756	−0.130377
$342$	0.903876	0.0488760
$343$	67.0392	3.61978
$344$	−49.5896	−2.67369
$345$	11.7770	0.634053
$346$	50.9539	2.73930
$347$	34.9082	1.87397	0.936985	−	0.349369i	$-0.113604\pi$
$347$	34.9082	1.87397	0.936985	+	0.349369i	$0.113604\pi$
$348$	27.0354	1.44925
$349$	−7.36747	−0.394371	−0.197186	−	0.980366i	$-0.563180\pi$
$349$	−7.36747	−0.394371	−0.197186	+	0.980366i	$0.563180\pi$
$350$	−25.8398	−1.38120
$351$	3.47280	0.185364
$352$	12.2001	0.650268
$353$	30.1994	1.60735	0.803675	−	0.595068i	$-0.202875\pi$
$353$	30.1994	1.60735	0.803675	+	0.595068i	$0.202875\pi$
$354$	36.2095	1.92451
$355$	−42.2569	−2.24276
$356$	15.5270	0.822929
$357$	−10.1109	−0.535124
$358$	−55.2806	−2.92167
$359$	−28.2798	−1.49255	−0.746274	−	0.665639i	$-0.768159\pi$
$359$	−28.2798	−1.49255	−0.746274	+	0.665639i	$0.768159\pi$
$360$	−20.3142	−1.07065
$361$	−18.8822	−0.993802
$362$	69.5149	3.65362
$363$	−1.00000	−0.0524864
$364$	−88.9760	−4.66361
$365$	−8.18281	−0.428308
$366$	2.63401	0.137682
$367$	9.06316	0.473093	0.236547	−	0.971620i	$-0.423984\pi$
$367$	9.06316	0.473093	0.236547	+	0.971620i	$0.423984\pi$
$368$	−47.1424	−2.45747
$369$	−0.436542	−0.0227255
$370$	−71.5362	−3.71899
$371$	12.8209	0.665629
$372$	−11.8885	−0.616390
$373$	4.76411	0.246676	0.123338	−	0.992365i	$-0.460640\pi$
$373$	4.76411	0.246676	0.123338	+	0.992365i	$0.460640\pi$
$374$	5.13290	0.265416
$375$	8.16190	0.421479
$376$	−34.2580	−1.76672
$377$	19.0135	0.979245
$378$	13.6666	0.702933
$379$	24.6033	1.26379	0.631893	−	0.775056i	$-0.282278\pi$
$379$	24.6033	1.26379	0.631893	+	0.775056i	$0.282278\pi$
$380$	−4.44810	−0.228183
$381$	−15.2576	−0.781672
$382$	−53.2075	−2.72233
$383$	1.16351	0.0594524	0.0297262	−	0.999558i	$-0.490536\pi$
$383$	1.16351	0.0594524	0.0297262	+	0.999558i	$0.490536\pi$
$384$	4.88904	0.249493
$385$	−13.6200	−0.694137
$386$	42.7638	2.17662
$387$	6.40802	0.325738
$388$	32.1682	1.63309
$389$	4.68535	0.237557	0.118778	−	0.992921i	$-0.462102\pi$
$389$	4.68535	0.237557	0.118778	+	0.992921i	$0.462102\pi$
$390$	−24.0121	−1.21590
$391$	−8.74275	−0.442140
$392$	−154.160	−7.78624
$393$	2.57715	0.130000
$394$	−28.5080	−1.43621
$395$	−13.5301	−0.680774
$396$	−4.93799	−0.248143
$397$	−32.1659	−1.61436	−0.807180	−	0.590306i	$-0.799007\pi$
$397$	−32.1659	−1.61436	−0.807180	+	0.590306i	$0.799007\pi$
$398$	−45.0961	−2.26046
$399$	1.78047	0.0891351
$400$	19.8673	0.993365
$401$	−37.0986	−1.85262	−0.926309	−	0.376765i	$-0.877036\pi$
$401$	−37.0986	−1.85262	−0.926309	+	0.376765i	$0.877036\pi$
$402$	7.28616	0.363401
$403$	−8.36097	−0.416490
$404$	54.8729	2.73003
$405$	2.62502	0.130438
$406$	74.8242	3.71346
$407$	−10.3461	−0.512837
$408$	15.0804	0.746590
$409$	−22.4268	−1.10893	−0.554467	−	0.832206i	$-0.687078\pi$
$409$	−22.4268	−1.10893	−0.554467	+	0.832206i	$0.687078\pi$
$410$	3.01839	0.149068
$411$	−14.4185	−0.711210
$412$	−2.49241	−0.122792
$413$	71.3262	3.50973
$414$	11.8173	0.580790
$415$	5.57912	0.273868
$416$	42.3685	2.07729
$417$	−11.3125	−0.553977
$418$	−0.903876	−0.0442100
$419$	−8.94385	−0.436936	−0.218468	−	0.975844i	$-0.570106\pi$
$419$	−8.94385	−0.436936	−0.218468	+	0.975844i	$0.570106\pi$
$420$	−67.2552	−3.28172
$421$	−40.0168	−1.95030	−0.975151	−	0.221543i	$-0.928891\pi$
$421$	−40.0168	−1.95030	−0.975151	+	0.221543i	$0.928891\pi$
$422$	−16.0023	−0.778980
$423$	4.42685	0.215241
$424$	−19.1224	−0.928666
$425$	3.68447	0.178723
$426$	−42.4015	−2.05436
$427$	5.18852	0.251090
$428$	38.6646	1.86892
$429$	−3.47280	−0.167668
$430$	−44.3071	−2.13668
$431$	−1.04053	−0.0501205	−0.0250603	−	0.999686i	$-0.507978\pi$
$431$	−1.04053	−0.0501205	−0.0250603	+	0.999686i	$0.507978\pi$
$432$	−10.5077	−0.505554
$433$	−15.4980	−0.744785	−0.372393	−	0.928075i	$-0.621463\pi$
$433$	−15.4980	−0.744785	−0.372393	+	0.928075i	$0.621463\pi$
$434$	−32.9031	−1.57940
$435$	14.3719	0.689081
$436$	−28.1201	−1.34671
$437$	1.53955	0.0736468
$438$	−8.21082	−0.392328
$439$	22.0242	1.05116	0.525579	−	0.850745i	$-0.323849\pi$
$439$	22.0242	1.05116	0.525579	+	0.850745i	$0.323849\pi$
$440$	20.3142	0.968440
$441$	19.9207	0.948604
$442$	17.8255	0.847874
$443$	27.4427	1.30384	0.651921	−	0.758287i	$-0.273964\pi$
$443$	27.4427	1.30384	0.651921	+	0.758287i	$0.273964\pi$
$444$	−51.0889	−2.42457
$445$	8.25410	0.391282
$446$	65.2991	3.09200
$447$	4.30768	0.203746
$448$	57.6945	2.72581
$449$	−31.7031	−1.49616	−0.748081	−	0.663607i	$-0.769025\pi$
$449$	−31.7031	−1.49616	−0.748081	+	0.663607i	$0.769025\pi$
$450$	−4.98019	−0.234769
$451$	0.436542	0.0205560
$452$	81.5561	3.83607
$453$	12.6896	0.596211
$454$	−67.6830	−3.17652
$455$	−47.2994	−2.21743
$456$	−2.65558	−0.124359
$457$	−6.80691	−0.318414	−0.159207	−	0.987245i	$-0.550894\pi$
$457$	−6.80691	−0.318414	−0.159207	+	0.987245i	$0.550894\pi$
$458$	4.45514	0.208175
$459$	−1.94870	−0.0909577
$460$	−58.1547	−2.71148
$461$	3.68797	0.171766	0.0858830	−	0.996305i	$-0.472629\pi$
$461$	3.68797	0.171766	0.0858830	+	0.996305i	$0.472629\pi$
$462$	−13.6666	−0.635827
$463$	6.47116	0.300740	0.150370	−	0.988630i	$-0.451953\pi$
$463$	6.47116	0.300740	0.150370	+	0.988630i	$0.451953\pi$
$464$	−57.5296	−2.67075
$465$	−6.31989	−0.293078
$466$	22.6950	1.05133
$467$	−14.4505	−0.668692	−0.334346	−	0.942450i	$-0.608515\pi$
$467$	−14.4505	−0.668692	−0.334346	+	0.942450i	$0.608515\pi$
$468$	−17.1487	−0.792697
$469$	14.3524	0.662733
$470$	−30.6087	−1.41187
$471$	−10.8043	−0.497834
$472$	−106.383	−4.89668
$473$	−6.40802	−0.294641
$474$	−13.5764	−0.623587
$475$	−0.648816	−0.0297697
$476$	49.9274	2.28842
$477$	2.47102	0.113140
$478$	34.9345	1.59787
$479$	−26.3992	−1.20621	−0.603106	−	0.797661i	$-0.706070\pi$
$479$	−26.3992	−1.20621	−0.603106	+	0.797661i	$0.706070\pi$
$480$	32.0255	1.46176
$481$	−35.9300	−1.63827
$482$	−5.60475	−0.255289
$483$	23.2780	1.05919
$484$	4.93799	0.224454
$485$	17.1005	0.776494
$486$	2.63401	0.119481
$487$	1.02748	0.0465596	0.0232798	−	0.999729i	$-0.492589\pi$
$487$	1.02748	0.0465596	0.0232798	+	0.999729i	$0.492589\pi$
$488$	−7.73867	−0.350313
$489$	−25.0214	−1.13151
$490$	−137.738	−6.22237
$491$	26.4321	1.19286	0.596432	−	0.802664i	$-0.296584\pi$
$491$	26.4321	1.19286	0.596432	+	0.802664i	$0.296584\pi$
$492$	2.15564	0.0971837
$493$	−10.6691	−0.480512
$494$	−3.13898	−0.141229
$495$	−2.62502	−0.117986
$496$	25.2980	1.13591
$497$	−83.5234	−3.74653
$498$	5.59821	0.250862
$499$	−21.5904	−0.966520	−0.483260	−	0.875477i	$-0.660547\pi$
$499$	−21.5904	−0.966520	−0.483260	+	0.875477i	$0.660547\pi$
$500$	−40.3033	−1.80242
$501$	21.9141	0.979050
$502$	−3.21042	−0.143288
$503$	−21.8467	−0.974095	−0.487048	−	0.873375i	$-0.661926\pi$
$503$	−21.8467	−0.974095	−0.487048	+	0.873375i	$0.661926\pi$
$504$	−40.1522	−1.78852
$505$	29.1703	1.29806
$506$	−11.8173	−0.525344
$507$	0.939647	0.0417312
$508$	75.3420	3.34276
$509$	39.4287	1.74765	0.873823	−	0.486245i	$-0.161634\pi$
$509$	39.4287	1.74765	0.873823	+	0.486245i	$0.161634\pi$
$510$	13.4740	0.596637
$511$	−16.1738	−0.715488
$512$	34.4365	1.52189
$513$	0.343156	0.0151507
$514$	26.4322	1.16587
$515$	−1.32496	−0.0583846
$516$	−31.6427	−1.39299
$517$	−4.42685	−0.194693
$518$	−141.396	−6.21258
$519$	19.3446	0.849135
$520$	70.5471	3.09370
$521$	4.56305	0.199911	0.0999555	−	0.994992i	$-0.468130\pi$
$521$	4.56305	0.199911	0.0999555	+	0.994992i	$0.468130\pi$
$522$	14.4211	0.631195
$523$	6.29112	0.275092	0.137546	−	0.990495i	$-0.456079\pi$
$523$	6.29112	0.275092	0.137546	+	0.990495i	$0.456079\pi$
$524$	−12.7259	−0.555935
$525$	−9.81008	−0.428147
$526$	40.7482	1.77671
$527$	4.69162	0.204370
$528$	10.5077	0.457291
$529$	−2.87181	−0.124861
$530$	−17.0854	−0.742143
$531$	13.7469	0.596566
$532$	−8.79195	−0.381179
$533$	1.51602	0.0656663
$534$	8.28236	0.358413
$535$	20.5540	0.888626
$536$	−21.4066	−0.924626
$537$	−20.9873	−0.905667
$538$	30.2000	1.30201
$539$	−19.9207	−0.858045
$540$	−12.9623	−0.557809
$541$	14.4263	0.620233	0.310117	−	0.950699i	$-0.399632\pi$
$541$	14.4263	0.620233	0.310117	+	0.950699i	$0.399632\pi$
$542$	28.1640	1.20975
$543$	26.3913	1.13256
$544$	−23.7744	−1.01932
$545$	−14.9486	−0.640326
$546$	−47.4613	−2.03116
$547$	9.30055	0.397663	0.198831	−	0.980034i	$-0.436285\pi$
$547$	9.30055	0.397663	0.198831	+	0.980034i	$0.436285\pi$
$548$	71.1982	3.04144
$549$	1.00000	0.0426790
$550$	4.98019	0.212356
$551$	1.87877	0.0800384
$552$	−34.7191	−1.47774
$553$	−26.7431	−1.13723
$554$	82.8304	3.51913
$555$	−27.1587	−1.15282
$556$	55.8611	2.36904
$557$	−4.86880	−0.206298	−0.103149	−	0.994666i	$-0.532892\pi$
$557$	−4.86880	−0.206298	−0.103149	+	0.994666i	$0.532892\pi$
$558$	−6.34152	−0.268458
$559$	−22.2538	−0.941235
$560$	143.115	6.04771
$561$	1.94870	0.0822743
$562$	−41.6691	−1.75771
$563$	14.5434	0.612929	0.306465	−	0.951882i	$-0.400854\pi$
$563$	14.5434	0.612929	0.306465	+	0.951882i	$0.400854\pi$
$564$	−21.8597	−0.920461
$565$	43.3550	1.82396
$566$	46.6564	1.96111
$567$	5.18852	0.217897
$568$	124.575	5.22706
$569$	25.4145	1.06543	0.532717	−	0.846294i	$-0.321171\pi$
$569$	25.4145	1.06543	0.532717	+	0.846294i	$0.321171\pi$
$570$	−2.37269	−0.0993811
$571$	3.21902	0.134712	0.0673560	−	0.997729i	$-0.478544\pi$
$571$	3.21902	0.134712	0.0673560	+	0.997729i	$0.478544\pi$
$572$	17.1487	0.717021
$573$	−20.2002	−0.843876
$574$	5.96603	0.249017
$575$	−8.48266	−0.353751
$576$	11.1197	0.463319
$577$	16.5724	0.689918	0.344959	−	0.938618i	$-0.387893\pi$
$577$	16.5724	0.689918	0.344959	+	0.938618i	$0.387893\pi$
$578$	34.7756	1.44647
$579$	16.2353	0.674715
$580$	−70.9684	−2.94680
$581$	11.0275	0.457497
$582$	17.1591	0.711266
$583$	−2.47102	−0.102339
$584$	24.1233	0.998228
$585$	−9.11617	−0.376907
$586$	18.2294	0.753048
$587$	7.08569	0.292458	0.146229	−	0.989251i	$-0.453286\pi$
$587$	7.08569	0.292458	0.146229	+	0.989251i	$0.453286\pi$
$588$	−98.3681	−4.05663
$589$	−0.826169	−0.0340417
$590$	−95.0507	−3.91317
$591$	−10.8231	−0.445201
$592$	108.714	4.46812
$593$	−10.7052	−0.439612	−0.219806	−	0.975544i	$-0.570542\pi$
$593$	−10.7052	−0.439612	−0.219806	+	0.975544i	$0.570542\pi$
$594$	−2.63401	−0.108075
$595$	26.5412	1.08809
$596$	−21.2713	−0.871305
$597$	−17.1207	−0.700705
$598$	−41.0392	−1.67822
$599$	−15.1212	−0.617836	−0.308918	−	0.951089i	$-0.599967\pi$
$599$	−15.1212	−0.617836	−0.308918	+	0.951089i	$0.599967\pi$
$600$	14.6317	0.597338
$601$	−0.515149	−0.0210134	−0.0105067	−	0.999945i	$-0.503344\pi$
$601$	−0.515149	−0.0210134	−0.0105067	+	0.999945i	$0.503344\pi$
$602$	−87.5757	−3.56932
$603$	2.76619	0.112648
$604$	−62.6613	−2.54965
$605$	2.62502	0.106722
$606$	29.2701	1.18902
$607$	33.0600	1.34186	0.670932	−	0.741519i	$-0.265894\pi$
$607$	33.0600	1.34186	0.670932	+	0.741519i	$0.265894\pi$
$608$	4.18654	0.169787
$609$	28.4070	1.15111
$610$	−6.91432	−0.279953
$611$	−15.3736	−0.621949
$612$	9.62267	0.388973
$613$	10.2485	0.413933	0.206966	−	0.978348i	$-0.433641\pi$
$613$	10.2485	0.413933	0.206966	+	0.978348i	$0.433641\pi$
$614$	−42.0164	−1.69564
$615$	1.14593	0.0462084
$616$	40.1522	1.61778
$617$	29.1352	1.17294	0.586469	−	0.809971i	$-0.300517\pi$
$617$	29.1352	1.17294	0.586469	+	0.809971i	$0.300517\pi$
$618$	−1.32949	−0.0534800
$619$	−13.3947	−0.538377	−0.269188	−	0.963088i	$-0.586755\pi$
$619$	−13.3947	−0.538377	−0.269188	+	0.963088i	$0.586755\pi$
$620$	31.2075	1.25332
$621$	4.48645	0.180035
$622$	36.5217	1.46439
$623$	16.3147	0.653636
$624$	36.4913	1.46082
$625$	−30.8788	−1.23515
$626$	−47.7092	−1.90684
$627$	−0.343156	−0.0137043
$628$	53.3513	2.12895
$629$	20.1615	0.803891
$630$	−35.8750	−1.42930
$631$	−24.1306	−0.960622	−0.480311	−	0.877098i	$-0.659476\pi$
$631$	−24.1306	−0.960622	−0.480311	+	0.877098i	$0.659476\pi$
$632$	39.8874	1.58664
$633$	−6.07527	−0.241470
$634$	−59.0234	−2.34412
$635$	40.0516	1.58940
$636$	−12.2019	−0.483835
$637$	−69.1806	−2.74104
$638$	−14.4211	−0.570938
$639$	−16.0977	−0.636817
$640$	−12.8338	−0.507302
$641$	31.1854	1.23175	0.615874	−	0.787845i	$-0.288803\pi$
$641$	31.1854	1.23175	0.615874	+	0.787845i	$0.288803\pi$
$642$	20.6243	0.813977
$643$	31.3001	1.23436	0.617178	−	0.786824i	$-0.288276\pi$
$643$	31.3001	1.23436	0.617178	+	0.786824i	$0.288276\pi$
$644$	−114.946	−4.52952
$645$	−16.8212	−0.662333
$646$	1.76139	0.0693008
$647$	−25.8036	−1.01445	−0.507223	−	0.861815i	$-0.669328\pi$
$647$	−25.8036	−1.01445	−0.507223	+	0.861815i	$0.669328\pi$
$648$	−7.73867	−0.304004
$649$	−13.7469	−0.539614
$650$	17.2952	0.678375
$651$	−12.4917	−0.489587
$652$	123.555	4.83880
$653$	−39.3780	−1.54098	−0.770491	−	0.637451i	$-0.779989\pi$
$653$	−39.3780	−1.54098	−0.770491	+	0.637451i	$0.779989\pi$
$654$	−14.9997	−0.586536
$655$	−6.76507	−0.264333
$656$	−4.58707	−0.179095
$657$	−3.11724	−0.121615
$658$	−60.4999	−2.35853
$659$	−17.3863	−0.677275	−0.338637	−	0.940917i	$-0.609966\pi$
$659$	−17.3863	−0.677275	−0.338637	+	0.940917i	$0.609966\pi$
$660$	12.9623	0.504557
$661$	10.6188	0.413025	0.206512	−	0.978444i	$-0.433789\pi$
$661$	10.6188	0.413025	0.206512	+	0.978444i	$0.433789\pi$
$662$	3.98188	0.154760
$663$	6.76746	0.262826
$664$	−16.4475	−0.638286
$665$	−4.67377	−0.181241
$666$	−27.2517	−1.05598
$667$	24.5632	0.951090
$668$	−108.212	−4.18683
$669$	24.7908	0.958467
$670$	−19.1263	−0.738914
$671$	−1.00000	−0.0386046
$672$	63.3004	2.44187
$673$	−25.4524	−0.981117	−0.490559	−	0.871408i	$-0.663207\pi$
$673$	−25.4524	−0.981117	−0.490559	+	0.871408i	$0.663207\pi$
$674$	7.82438	0.301384
$675$	−1.89073	−0.0727742
$676$	−4.63996	−0.178460
$677$	29.4870	1.13328	0.566638	−	0.823967i	$-0.308244\pi$
$677$	29.4870	1.13328	0.566638	+	0.823967i	$0.308244\pi$
$678$	43.5034	1.67074
$679$	33.8002	1.29713
$680$	−39.5863	−1.51807
$681$	−25.6959	−0.984667
$682$	6.34152	0.242829
$683$	10.3877	0.397475	0.198737	−	0.980053i	$-0.436316\pi$
$683$	10.3877	0.397475	0.198737	+	0.980053i	$0.436316\pi$
$684$	−1.69450	−0.0647909
$685$	37.8487	1.44613
$686$	−176.582	−6.74192
$687$	1.69139	0.0645306
$688$	67.3338	2.56708
$689$	−8.58136	−0.326924
$690$	−31.0207	−1.18094
$691$	−8.92858	−0.339659	−0.169830	−	0.985473i	$-0.554322\pi$
$691$	−8.92858	−0.339659	−0.169830	+	0.985473i	$0.554322\pi$
$692$	−95.5236	−3.63126
$693$	−5.18852	−0.197095
$694$	−91.9484	−3.49031
$695$	29.6956	1.12642
$696$	−42.3691	−1.60600
$697$	−0.850690	−0.0322222
$698$	19.4059	0.734526
$699$	8.61616	0.325893
$700$	48.4420	1.83094
$701$	45.5207	1.71929	0.859646	−	0.510891i	$-0.170684\pi$
$701$	45.5207	1.71929	0.859646	+	0.510891i	$0.170684\pi$
$702$	−9.14738	−0.345246
$703$	−3.55033	−0.133903
$704$	−11.1197	−0.419088
$705$	−11.6206	−0.437656
$706$	−79.5453	−2.99373
$707$	57.6568	2.16841
$708$	−67.8822	−2.55117
$709$	16.4201	0.616670	0.308335	−	0.951278i	$-0.400228\pi$
$709$	16.4201	0.616670	0.308335	+	0.951278i	$0.400228\pi$
$710$	111.305	4.17720
$711$	−5.15429	−0.193301
$712$	−24.3335	−0.911935
$713$	−10.8014	−0.404515
$714$	26.6321	0.996681
$715$	9.11617	0.340926
$716$	103.635	3.87301
$717$	13.2629	0.495312
$718$	74.4890	2.77991
$719$	17.6047	0.656545	0.328273	−	0.944583i	$-0.393534\pi$
$719$	17.6047	0.656545	0.328273	+	0.944583i	$0.393534\pi$
$720$	27.5830	1.02796
$721$	−2.61886	−0.0975314
$722$	49.7359	1.85098
$723$	−2.12784	−0.0791353
$724$	−130.320	−4.84331
$725$	−10.3517	−0.384452
$726$	2.63401	0.0977571
$727$	26.0709	0.966914	0.483457	−	0.875368i	$-0.339381\pi$
$727$	26.0709	0.966914	0.483457	+	0.875368i	$0.339381\pi$
$728$	139.441	5.16802
$729$	1.00000	0.0370370
$730$	21.5536	0.797733
$731$	12.4873	0.461860
$732$	−4.93799	−0.182513
$733$	−30.5781	−1.12943	−0.564715	−	0.825286i	$-0.691014\pi$
$733$	−30.5781	−1.12943	−0.564715	+	0.825286i	$0.691014\pi$
$734$	−23.8724	−0.881147
$735$	−52.2922	−1.92883
$736$	54.7351	2.01756
$737$	−2.76619	−0.101894
$738$	1.14985	0.0423267
$739$	−50.2330	−1.84785	−0.923926	−	0.382571i	$-0.875039\pi$
$739$	−50.2330	−1.84785	−0.923926	+	0.382571i	$0.875039\pi$
$740$	134.109	4.92996
$741$	−1.19171	−0.0437787
$742$	−33.7704	−1.23975
$743$	31.2350	1.14590	0.572950	−	0.819590i	$-0.305799\pi$
$743$	31.2350	1.14590	0.572950	+	0.819590i	$0.305799\pi$
$744$	18.6313	0.683057
$745$	−11.3077	−0.414284
$746$	−12.5487	−0.459440
$747$	2.12536	0.0777629
$748$	−9.62267	−0.351840
$749$	40.6262	1.48445
$750$	−21.4985	−0.785014
$751$	−6.93821	−0.253179	−0.126590	−	0.991955i	$-0.540403\pi$
$751$	−6.93821	−0.253179	−0.126590	+	0.991955i	$0.540403\pi$
$752$	46.5162	1.69627
$753$	−1.21883	−0.0444168
$754$	−50.0817	−1.82387
$755$	−33.3105	−1.21229
$756$	−25.6208	−0.931820
$757$	−42.3758	−1.54017	−0.770086	−	0.637939i	$-0.779787\pi$
$757$	−42.3758	−1.54017	−0.770086	+	0.637939i	$0.779787\pi$
$758$	−64.8052	−2.35383
$759$	−4.48645	−0.162848
$760$	6.97094	0.252863
$761$	−38.5976	−1.39916	−0.699582	−	0.714553i	$-0.746630\pi$
$761$	−38.5976	−1.39916	−0.699582	+	0.714553i	$0.746630\pi$
$762$	40.1887	1.45588
$763$	−29.5467	−1.06966
$764$	99.7484	3.60877
$765$	5.11538	0.184947
$766$	−3.06468	−0.110731
$767$	−47.7404	−1.72381
$768$	9.36155	0.337806
$769$	−8.52482	−0.307413	−0.153706	−	0.988117i	$-0.549121\pi$
$769$	−8.52482	−0.307413	−0.153706	+	0.988117i	$0.549121\pi$
$770$	35.8750	1.29285
$771$	10.0350	0.361401
$772$	−80.1696	−2.88537
$773$	−44.8848	−1.61439	−0.807197	−	0.590283i	$-0.799016\pi$
$773$	−44.8848	−1.61439	−0.807197	+	0.590283i	$0.799016\pi$
$774$	−16.8788	−0.606694
$775$	4.55204	0.163514
$776$	−50.4131	−1.80972
$777$	−53.6809	−1.92579
$778$	−12.3412	−0.442455
$779$	0.149802	0.00536722
$780$	45.0155	1.61182
$781$	16.0977	0.576022
$782$	23.0285	0.823496
$783$	5.47498	0.195660
$784$	209.321	7.47577
$785$	28.3614	1.01226
$786$	−6.78823	−0.242128
$787$	−13.9456	−0.497106	−0.248553	−	0.968618i	$-0.579955\pi$
$787$	−13.9456	−0.497106	−0.248553	+	0.968618i	$0.579955\pi$
$788$	53.4442	1.90387
$789$	15.4701	0.550749
$790$	35.6384	1.26796
$791$	85.6938	3.04692
$792$	7.73867	0.274982
$793$	−3.47280	−0.123323
$794$	84.7251	3.00678
$795$	−6.48647	−0.230051
$796$	84.5420	2.99651
$797$	23.5528	0.834282	0.417141	−	0.908842i	$-0.363032\pi$
$797$	23.5528	0.834282	0.417141	+	0.908842i	$0.363032\pi$
$798$	−4.68977	−0.166016
$799$	8.62662	0.305188
$800$	−23.0671	−0.815545
$801$	3.14440	0.111102
$802$	97.7180	3.45054
$803$	3.11724	0.110005
$804$	−13.6594	−0.481730
$805$	−61.1052	−2.15367
$806$	22.0229	0.775722
$807$	11.4654	0.403602
$808$	−85.9952	−3.02530
$809$	−32.6289	−1.14717	−0.573586	−	0.819145i	$-0.694448\pi$
$809$	−32.6289	−1.14717	−0.573586	+	0.819145i	$0.694448\pi$
$810$	−6.91432	−0.242944
$811$	8.24758	0.289612	0.144806	−	0.989460i	$-0.453744\pi$
$811$	8.24758	0.289612	0.144806	+	0.989460i	$0.453744\pi$
$812$	−140.273	−4.92263
$813$	10.6925	0.375001
$814$	27.2517	0.955171
$815$	65.6816	2.30073
$816$	−20.4765	−0.716820
$817$	−2.19895	−0.0769316
$818$	59.0723	2.06542
$819$	−18.0187	−0.629624
$820$	−5.65859	−0.197607
$821$	53.7676	1.87650	0.938251	−	0.345954i	$-0.112445\pi$
$821$	53.7676	1.87650	0.938251	+	0.345954i	$0.112445\pi$
$822$	37.9783	1.32465
$823$	−8.85638	−0.308714	−0.154357	−	0.988015i	$-0.549331\pi$
$823$	−8.85638	−0.308714	−0.154357	+	0.988015i	$0.549331\pi$
$824$	3.90603	0.136073
$825$	1.89073	0.0658268
$826$	−187.874	−6.53696
$827$	−1.91639	−0.0666395	−0.0333198	−	0.999445i	$-0.510608\pi$
$827$	−1.91639	−0.0666395	−0.0333198	+	0.999445i	$0.510608\pi$
$828$	−22.1540	−0.769905
$829$	−35.4299	−1.23053	−0.615266	−	0.788320i	$-0.710951\pi$
$829$	−35.4299	−1.23053	−0.615266	+	0.788320i	$0.710951\pi$
$830$	−14.6954	−0.510086
$831$	31.4466	1.09087
$832$	−38.6164	−1.33878
$833$	38.8195	1.34502
$834$	29.7973	1.03180
$835$	−57.5250	−1.99073
$836$	1.69450	0.0586056
$837$	−2.40756	−0.0832174
$838$	23.5582	0.813803
$839$	−11.2612	−0.388781	−0.194391	−	0.980924i	$-0.562273\pi$
$839$	−11.2612	−0.388781	−0.194391	+	0.980924i	$0.562273\pi$
$840$	105.400	3.63666
$841$	0.975363	0.0336332
$842$	105.405	3.63248
$843$	−15.8197	−0.544859
$844$	29.9996	1.03263
$845$	−2.46659	−0.0848533
$846$	−11.6604	−0.400891
$847$	5.18852	0.178279
$848$	25.9648	0.891635
$849$	17.7131	0.607912
$850$	−9.70492	−0.332876
$851$	−46.4172	−1.59116
$852$	79.4904	2.72330
$853$	5.79874	0.198545	0.0992725	−	0.995060i	$-0.468348\pi$
$853$	5.79874	0.198545	0.0992725	+	0.995060i	$0.468348\pi$
$854$	−13.6666	−0.467661
$855$	−0.900792	−0.0308064
$856$	−60.5940	−2.07106
$857$	40.4860	1.38298	0.691488	−	0.722388i	$-0.256956\pi$
$857$	40.4860	1.38298	0.691488	+	0.722388i	$0.256956\pi$
$858$	9.14738	0.312286
$859$	19.1302	0.652715	0.326357	−	0.945246i	$-0.394179\pi$
$859$	19.1302	0.652715	0.326357	+	0.945246i	$0.394179\pi$
$860$	83.0627	2.83242
$861$	2.26500	0.0771911
$862$	2.74076	0.0933506
$863$	25.2855	0.860727	0.430364	−	0.902656i	$-0.358385\pi$
$863$	25.2855	0.860727	0.430364	+	0.902656i	$0.358385\pi$
$864$	12.2001	0.415056
$865$	−50.7801	−1.72657
$866$	40.8218	1.38718
$867$	13.2026	0.448382
$868$	61.6836	2.09368
$869$	5.15429	0.174847
$870$	−37.8557	−1.28343
$871$	−9.60643	−0.325501
$872$	44.0690	1.49236
$873$	6.51443	0.220480
$874$	−4.05519	−0.137169
$875$	−42.3481	−1.43163
$876$	15.3929	0.520077
$877$	−31.4779	−1.06293	−0.531466	−	0.847080i	$-0.678359\pi$
$877$	−31.4779	−1.06293	−0.531466	+	0.847080i	$0.678359\pi$
$878$	−58.0119	−1.95781
$879$	6.92077	0.233432
$880$	−27.5830	−0.929824
$881$	−7.07691	−0.238427	−0.119214	−	0.992869i	$-0.538037\pi$
$881$	−7.07691	−0.238427	−0.119214	+	0.992869i	$0.538037\pi$
$882$	−52.4712	−1.76680
$883$	39.1958	1.31904	0.659521	−	0.751686i	$-0.270759\pi$
$883$	39.1958	1.31904	0.659521	+	0.751686i	$0.270759\pi$
$884$	−33.4176	−1.12396
$885$	−36.0860	−1.21302
$886$	−72.2842	−2.42843
$887$	−33.0652	−1.11022	−0.555111	−	0.831776i	$-0.687324\pi$
$887$	−33.0652	−1.11022	−0.555111	+	0.831776i	$0.687324\pi$
$888$	80.0651	2.68681
$889$	79.1645	2.65509
$890$	−21.7414	−0.728772
$891$	−1.00000	−0.0335013
$892$	−122.417	−4.09881
$893$	−1.51910	−0.0508348
$894$	−11.3465	−0.379482
$895$	55.0920	1.84152
$896$	−25.3669	−0.847448
$897$	−15.5805	−0.520219
$898$	83.5062	2.78664
$899$	−13.1813	−0.439622
$900$	9.33640	0.311213
$901$	4.81528	0.160420
$902$	−1.14985	−0.0382859
$903$	−33.2481	−1.10643
$904$	−127.812	−4.25098
$905$	−69.2778	−2.30287
$906$	−33.4246	−1.11046
$907$	−49.4081	−1.64057	−0.820285	−	0.571955i	$-0.806185\pi$
$907$	−49.4081	−1.64057	−0.820285	+	0.571955i	$0.806185\pi$
$908$	126.886	4.21085
$909$	11.1124	0.368575
$910$	124.587	4.13002
$911$	11.0990	0.367725	0.183863	−	0.982952i	$-0.441140\pi$
$911$	11.0990	0.367725	0.183863	+	0.982952i	$0.441140\pi$
$912$	3.60580	0.119400
$913$	−2.12536	−0.0703392
$914$	17.9294	0.593053
$915$	−2.62502	−0.0867805
$916$	−8.35207	−0.275960
$917$	−13.3716	−0.441569
$918$	5.13290	0.169411
$919$	9.02754	0.297791	0.148895	−	0.988853i	$-0.452428\pi$
$919$	9.02754	0.297791	0.148895	+	0.988853i	$0.452428\pi$
$920$	91.1384	3.00475
$921$	−15.9515	−0.525620
$922$	−9.71414	−0.319918
$923$	55.9043	1.84011
$924$	25.6208	0.842863
$925$	19.5617	0.643184
$926$	−17.0451	−0.560136
$927$	−0.504742	−0.0165779
$928$	66.7953	2.19266
$929$	−22.1504	−0.726732	−0.363366	−	0.931646i	$-0.618373\pi$
$929$	−22.1504	−0.726732	−0.363366	+	0.931646i	$0.618373\pi$
$930$	16.6466	0.545864
$931$	−6.83591	−0.224038
$932$	−42.5465	−1.39366
$933$	13.8655	0.453935
$934$	38.0628	1.24545
$935$	−5.11538	−0.167291
$936$	26.8749	0.878433
$937$	−32.4015	−1.05851	−0.529255	−	0.848463i	$-0.677529\pi$
$937$	−32.4015	−1.05851	−0.529255	+	0.848463i	$0.677529\pi$
$938$	−37.8044	−1.23436
$939$	−18.1128	−0.591089
$940$	57.3822	1.87160
$941$	−23.0935	−0.752826	−0.376413	−	0.926452i	$-0.622843\pi$
$941$	−23.0935	−0.752826	−0.376413	+	0.926452i	$0.622843\pi$
$942$	28.4585	0.927228
$943$	1.95852	0.0637782
$944$	144.449	4.70142
$945$	−13.6200	−0.443057
$946$	16.8788	0.548776
$947$	−19.1527	−0.622378	−0.311189	−	0.950348i	$-0.600727\pi$
$947$	−19.1527	−0.622378	−0.311189	+	0.950348i	$0.600727\pi$
$948$	25.4518	0.826637
$949$	10.8255	0.351412
$950$	1.70899	0.0554468
$951$	−22.4082	−0.726636
$952$	−78.2448	−2.53593
$953$	−18.1232	−0.587067	−0.293534	−	0.955949i	$-0.594831\pi$
$953$	−18.1232	−0.587067	−0.293534	+	0.955949i	$0.594831\pi$
$954$	−6.50868	−0.210726
$955$	53.0260	1.71588
$956$	−65.4920	−2.11816
$957$	−5.47498	−0.176981
$958$	69.5358	2.24660
$959$	74.8104	2.41575
$960$	−29.1893	−0.942081
$961$	−25.2037	−0.813021
$962$	94.6397	3.05131
$963$	7.83003	0.252319
$964$	10.5073	0.338416
$965$	−42.6180	−1.37192
$966$	−61.3144	−1.97276
$967$	−40.9282	−1.31616	−0.658082	−	0.752947i	$-0.728632\pi$
$967$	−40.9282	−1.31616	−0.658082	+	0.752947i	$0.728632\pi$
$968$	−7.73867	−0.248730
$969$	0.668710	0.0214821
$970$	−45.0429	−1.44624
$971$	13.7378	0.440866	0.220433	−	0.975402i	$-0.429253\pi$
$971$	13.7378	0.440866	0.220433	+	0.975402i	$0.429253\pi$
$972$	−4.93799	−0.158386
$973$	58.6952	1.88168
$974$	−2.70639	−0.0867183
$975$	6.56613	0.210284
$976$	10.5077	0.336345
$977$	−25.1855	−0.805755	−0.402878	−	0.915254i	$-0.631990\pi$
$977$	−25.1855	−0.805755	−0.402878	+	0.915254i	$0.631990\pi$
$978$	65.9065	2.10746
$979$	−3.14440	−0.100495
$980$	258.218	8.24848
$981$	−5.69464	−0.181816
$982$	−69.6223	−2.22174
$983$	0.0437437	0.00139521	0.000697604	−	1.00000i	$-0.499778\pi$
$983$	0.0437437	0.00139521	0.000697604		1.00000i	$0.499778\pi$
$984$	−3.37826	−0.107695
$985$	28.4108	0.905242
$986$	28.1025	0.894965
$987$	−22.9688	−0.731105
$988$	5.88467	0.187216
$989$	−28.7492	−0.914172
$990$	6.91432	0.219751
$991$	12.7220	0.404126	0.202063	−	0.979373i	$-0.435235\pi$
$991$	12.7220	0.404126	0.202063	+	0.979373i	$0.435235\pi$
$992$	−29.3725	−0.932576
$993$	1.51172	0.0479729
$994$	220.001	6.97801
$995$	44.9423	1.42477
$996$	−10.4950	−0.332547
$997$	−56.0727	−1.77584	−0.887920	−	0.459997i	$-0.847850\pi$
$997$	−56.0727	−1.77584	−0.887920	+	0.459997i	$0.847850\pi$
$998$	56.8693	1.80017
$999$	−10.3461	−0.327336

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.h.1.1	✓	14
3.2	odd	2		6039.2.a.j.1.14		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.h.1.1	✓	14	1.1	even	1	trivial
6039.2.a.j.1.14		14	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.63401 q^{2} -1.00000 q^{3} +4.93799 q^{4} +2.62502 q^{5} +2.63401 q^{6} +5.18852 q^{7} -7.73867 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.63401 q^{2} -1.00000 q^{3} +4.93799 q^{4} +2.62502 q^{5} +2.63401 q^{6} +5.18852 q^{7} -7.73867 q^{8} +1.00000 q^{9} -6.91432 q^{10} -1.00000 q^{11} -4.93799 q^{12} -3.47280 q^{13} -13.6666 q^{14} -2.62502 q^{15} +10.5077 q^{16} +1.94870 q^{17} -2.63401 q^{18} -0.343156 q^{19} +12.9623 q^{20} -5.18852 q^{21} +2.63401 q^{22} -4.48645 q^{23} +7.73867 q^{24} +1.89073 q^{25} +9.14738 q^{26} -1.00000 q^{27} +25.6208 q^{28} -5.47498 q^{29} +6.91432 q^{30} +2.40756 q^{31} -12.2001 q^{32} +1.00000 q^{33} -5.13290 q^{34} +13.6200 q^{35} +4.93799 q^{36} +10.3461 q^{37} +0.903876 q^{38} +3.47280 q^{39} -20.3142 q^{40} -0.436542 q^{41} +13.6666 q^{42} +6.40802 q^{43} -4.93799 q^{44} +2.62502 q^{45} +11.8173 q^{46} +4.42685 q^{47} -10.5077 q^{48} +19.9207 q^{49} -4.98019 q^{50} -1.94870 q^{51} -17.1487 q^{52} +2.47102 q^{53} +2.63401 q^{54} -2.62502 q^{55} -40.1522 q^{56} +0.343156 q^{57} +14.4211 q^{58} +13.7469 q^{59} -12.9623 q^{60} +1.00000 q^{61} -6.34152 q^{62} +5.18852 q^{63} +11.1197 q^{64} -9.11617 q^{65} -2.63401 q^{66} +2.76619 q^{67} +9.62267 q^{68} +4.48645 q^{69} -35.8750 q^{70} -16.0977 q^{71} -7.73867 q^{72} -3.11724 q^{73} -27.2517 q^{74} -1.89073 q^{75} -1.69450 q^{76} -5.18852 q^{77} -9.14738 q^{78} -5.15429 q^{79} +27.5830 q^{80} +1.00000 q^{81} +1.14985 q^{82} +2.12536 q^{83} -25.6208 q^{84} +5.11538 q^{85} -16.8788 q^{86} +5.47498 q^{87} +7.73867 q^{88} +3.14440 q^{89} -6.91432 q^{90} -18.0187 q^{91} -22.1540 q^{92} -2.40756 q^{93} -11.6604 q^{94} -0.900792 q^{95} +12.2001 q^{96} +6.51443 q^{97} -52.4712 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9}+O(q^{10}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9} + 6 q^{10} - 14 q^{11} - 15 q^{12} + q^{13} - 7 q^{14} - q^{15} + 17 q^{16} - 9 q^{17} - q^{18} + 22 q^{19} + 23 q^{20} - 9 q^{21} + q^{22} + q^{23} + 25 q^{25} + 4 q^{26} - 14 q^{27} + 37 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 4 q^{32} + 14 q^{33} + 8 q^{34} + 18 q^{35} + 15 q^{36} + 18 q^{37} + 8 q^{38} - q^{39} + 16 q^{40} - 25 q^{41} + 7 q^{42} + 25 q^{43} - 15 q^{44} + q^{45} + 20 q^{46} + 36 q^{47} - 17 q^{48} + 25 q^{49} + 2 q^{50} + 9 q^{51} - 13 q^{52} + q^{54} - q^{55} - 40 q^{56} - 22 q^{57} + 33 q^{58} + 17 q^{59} - 23 q^{60} + 14 q^{61} - 13 q^{62} + 9 q^{63} - 6 q^{64} - 61 q^{65} - q^{66} + 22 q^{67} + 66 q^{68} - q^{69} + 44 q^{70} - 13 q^{71} + 20 q^{73} - 12 q^{74} - 25 q^{75} + 49 q^{76} - 9 q^{77} - 4 q^{78} + 31 q^{79} + 88 q^{80} + 14 q^{81} + 2 q^{82} + 32 q^{83} - 37 q^{84} + 2 q^{85} - 14 q^{86} + 6 q^{87} - 21 q^{89} + 6 q^{90} + 45 q^{91} - 14 q^{92} - 9 q^{93} - 31 q^{94} + 23 q^{95} - 4 q^{96} + 37 q^{97} - 38 q^{98} - 14 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9 + 6 * q^10 - 14 * q^11 - 15 * q^12 + q^13 - 7 * q^14 - q^15 + 17 * q^16 - 9 * q^17 - q^18 + 22 * q^19 + 23 * q^20 - 9 * q^21 + q^22 + q^23 + 25 * q^25 + 4 * q^26 - 14 * q^27 + 37 * q^28 - 6 * q^29 - 6 * q^30 + 9 * q^31 + 4 * q^32 + 14 * q^33 + 8 * q^34 + 18 * q^35 + 15 * q^36 + 18 * q^37 + 8 * q^38 - q^39 + 16 * q^40 - 25 * q^41 + 7 * q^42 + 25 * q^43 - 15 * q^44 + q^45 + 20 * q^46 + 36 * q^47 - 17 * q^48 + 25 * q^49 + 2 * q^50 + 9 * q^51 - 13 * q^52 + q^54 - q^55 - 40 * q^56 - 22 * q^57 + 33 * q^58 + 17 * q^59 - 23 * q^60 + 14 * q^61 - 13 * q^62 + 9 * q^63 - 6 * q^64 - 61 * q^65 - q^66 + 22 * q^67 + 66 * q^68 - q^69 + 44 * q^70 - 13 * q^71 + 20 * q^73 - 12 * q^74 - 25 * q^75 + 49 * q^76 - 9 * q^77 - 4 * q^78 + 31 * q^79 + 88 * q^80 + 14 * q^81 + 2 * q^82 + 32 * q^83 - 37 * q^84 + 2 * q^85 - 14 * q^86 + 6 * q^87 - 21 * q^89 + 6 * q^90 + 45 * q^91 - 14 * q^92 - 9 * q^93 - 31 * q^94 + 23 * q^95 - 4 * q^96 + 37 * q^97 - 38 * q^98 - 14 * q^99

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