LMFDB - Embedded newform 8031.2.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8031,2,Mod(1,8031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8031, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8031 = 3 \cdot 2677 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8031.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:	$64.1278578633$
Analytic rank:	$0$
Dimension:	$132$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59180 q^{2} +1.00000 q^{3} +4.71742 q^{4} +2.79387 q^{5} -2.59180 q^{6} -2.04048 q^{7} -7.04300 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.59180 q^{2} +1.00000 q^{3} +4.71742 q^{4} +2.79387 q^{5} -2.59180 q^{6} -2.04048 q^{7} -7.04300 q^{8} +1.00000 q^{9} -7.24116 q^{10} +5.24663 q^{11} +4.71742 q^{12} -4.28491 q^{13} +5.28852 q^{14} +2.79387 q^{15} +8.81919 q^{16} +6.61045 q^{17} -2.59180 q^{18} +7.02258 q^{19} +13.1799 q^{20} -2.04048 q^{21} -13.5982 q^{22} -4.54890 q^{23} -7.04300 q^{24} +2.80573 q^{25} +11.1056 q^{26} +1.00000 q^{27} -9.62581 q^{28} +2.39061 q^{29} -7.24116 q^{30} +10.9853 q^{31} -8.77157 q^{32} +5.24663 q^{33} -17.1330 q^{34} -5.70085 q^{35} +4.71742 q^{36} -3.75808 q^{37} -18.2011 q^{38} -4.28491 q^{39} -19.6773 q^{40} +10.9256 q^{41} +5.28852 q^{42} +2.09083 q^{43} +24.7505 q^{44} +2.79387 q^{45} +11.7898 q^{46} +10.8730 q^{47} +8.81919 q^{48} -2.83643 q^{49} -7.27190 q^{50} +6.61045 q^{51} -20.2137 q^{52} +2.76743 q^{53} -2.59180 q^{54} +14.6584 q^{55} +14.3711 q^{56} +7.02258 q^{57} -6.19598 q^{58} -3.73743 q^{59} +13.1799 q^{60} +2.80976 q^{61} -28.4718 q^{62} -2.04048 q^{63} +5.09576 q^{64} -11.9715 q^{65} -13.5982 q^{66} +8.51123 q^{67} +31.1843 q^{68} -4.54890 q^{69} +14.7755 q^{70} -10.2338 q^{71} -7.04300 q^{72} +7.89970 q^{73} +9.74019 q^{74} +2.80573 q^{75} +33.1285 q^{76} -10.7057 q^{77} +11.1056 q^{78} -8.82039 q^{79} +24.6397 q^{80} +1.00000 q^{81} -28.3170 q^{82} -5.16944 q^{83} -9.62581 q^{84} +18.4688 q^{85} -5.41900 q^{86} +2.39061 q^{87} -36.9520 q^{88} -9.31451 q^{89} -7.24116 q^{90} +8.74328 q^{91} -21.4591 q^{92} +10.9853 q^{93} -28.1807 q^{94} +19.6202 q^{95} -8.77157 q^{96} +10.5709 q^{97} +7.35145 q^{98} +5.24663 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 4 q^{2} + 132 q^{3} + 156 q^{4} + 20 q^{5} + 4 q^{6} + 44 q^{7} + 9 q^{8} + 132 q^{9}+O(q^{10}) $ 132 * q + 4 * q^2 + 132 * q^3 + 156 * q^4 + 20 * q^5 + 4 * q^6 + 44 * q^7 + 9 * q^8 + 132 * q^9	\( 132 q + 4 q^{2} + 132 q^{3} + 156 q^{4} + 20 q^{5} + 4 q^{6} + 44 q^{7} + 9 q^{8} + 132 q^{9} + 40 q^{10} + 24 q^{11} + 156 q^{12} + 62 q^{13} + 25 q^{14} + 20 q^{15} + 192 q^{16} + 77 q^{17} + 4 q^{18} + 86 q^{19} + 26 q^{20} + 44 q^{21} + 52 q^{22} + 17 q^{23} + 9 q^{24} + 212 q^{25} + 13 q^{26} + 132 q^{27} + 95 q^{28} + 52 q^{29} + 40 q^{30} + 59 q^{31} - 8 q^{32} + 24 q^{33} + 41 q^{34} + 21 q^{35} + 156 q^{36} + 76 q^{37} + 2 q^{38} + 62 q^{39} + 91 q^{40} + 114 q^{41} + 25 q^{42} + 173 q^{43} + 44 q^{44} + 20 q^{45} + 48 q^{46} + 15 q^{47} + 192 q^{48} + 262 q^{49} - 9 q^{50} + 77 q^{51} + 144 q^{52} + 15 q^{53} + 4 q^{54} + 111 q^{55} + 66 q^{56} + 86 q^{57} + 33 q^{58} + 20 q^{59} + 26 q^{60} + 182 q^{61} + 16 q^{62} + 44 q^{63} + 255 q^{64} + 70 q^{65} + 52 q^{66} + 169 q^{67} + 128 q^{68} + 17 q^{69} + 2 q^{70} + 23 q^{71} + 9 q^{72} + 148 q^{73} + 57 q^{74} + 212 q^{75} + 143 q^{76} + 31 q^{77} + 13 q^{78} + 152 q^{79} + 27 q^{80} + 132 q^{81} + 67 q^{82} + 28 q^{83} + 95 q^{84} + 88 q^{85} - 10 q^{86} + 52 q^{87} + 130 q^{88} + 136 q^{89} + 40 q^{90} + 125 q^{91} + 59 q^{93} + 95 q^{94} + 2 q^{95} - 8 q^{96} + 147 q^{97} - 18 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q + 4 * q^2 + 132 * q^3 + 156 * q^4 + 20 * q^5 + 4 * q^6 + 44 * q^7 + 9 * q^8 + 132 * q^9 + 40 * q^10 + 24 * q^11 + 156 * q^12 + 62 * q^13 + 25 * q^14 + 20 * q^15 + 192 * q^16 + 77 * q^17 + 4 * q^18 + 86 * q^19 + 26 * q^20 + 44 * q^21 + 52 * q^22 + 17 * q^23 + 9 * q^24 + 212 * q^25 + 13 * q^26 + 132 * q^27 + 95 * q^28 + 52 * q^29 + 40 * q^30 + 59 * q^31 - 8 * q^32 + 24 * q^33 + 41 * q^34 + 21 * q^35 + 156 * q^36 + 76 * q^37 + 2 * q^38 + 62 * q^39 + 91 * q^40 + 114 * q^41 + 25 * q^42 + 173 * q^43 + 44 * q^44 + 20 * q^45 + 48 * q^46 + 15 * q^47 + 192 * q^48 + 262 * q^49 - 9 * q^50 + 77 * q^51 + 144 * q^52 + 15 * q^53 + 4 * q^54 + 111 * q^55 + 66 * q^56 + 86 * q^57 + 33 * q^58 + 20 * q^59 + 26 * q^60 + 182 * q^61 + 16 * q^62 + 44 * q^63 + 255 * q^64 + 70 * q^65 + 52 * q^66 + 169 * q^67 + 128 * q^68 + 17 * q^69 + 2 * q^70 + 23 * q^71 + 9 * q^72 + 148 * q^73 + 57 * q^74 + 212 * q^75 + 143 * q^76 + 31 * q^77 + 13 * q^78 + 152 * q^79 + 27 * q^80 + 132 * q^81 + 67 * q^82 + 28 * q^83 + 95 * q^84 + 88 * q^85 - 10 * q^86 + 52 * q^87 + 130 * q^88 + 136 * q^89 + 40 * q^90 + 125 * q^91 + 59 * q^93 + 95 * q^94 + 2 * q^95 - 8 * q^96 + 147 * q^97 - 18 * q^98 + 24 * 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 $

$2$	−2.59180	−1.83268	−0.916339	−	0.400403i	$-0.868870\pi$
$2$	−2.59180	−1.83268	−0.916339	+	0.400403i	$0.868870\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.71742	2.35871
$5$	2.79387	1.24946	0.624729	−	0.780841i	$-0.285209\pi$
$5$	2.79387	1.24946	0.624729	+	0.780841i	$0.285209\pi$
$6$	−2.59180	−1.05810
$7$	−2.04048	−0.771230	−0.385615	−	0.922660i	$-0.626011\pi$
$7$	−2.04048	−0.771230	−0.385615	+	0.922660i	$0.626011\pi$
$8$	−7.04300	−2.49008
$9$	1.00000	0.333333
$10$	−7.24116	−2.28986
$11$	5.24663	1.58192	0.790959	−	0.611869i	$-0.209582\pi$
$11$	5.24663	1.58192	0.790959	+	0.611869i	$0.209582\pi$
$12$	4.71742	1.36180
$13$	−4.28491	−1.18842	−0.594210	−	0.804310i	$-0.702535\pi$
$13$	−4.28491	−1.18842	−0.594210	+	0.804310i	$0.702535\pi$
$14$	5.28852	1.41342
$15$	2.79387	0.721375
$16$	8.81919	2.20480
$17$	6.61045	1.60327	0.801635	−	0.597814i	$-0.203964\pi$
$17$	6.61045	1.60327	0.801635	+	0.597814i	$0.203964\pi$
$18$	−2.59180	−0.610893
$19$	7.02258	1.61109	0.805546	−	0.592534i	$-0.201872\pi$
$19$	7.02258	1.61109	0.805546	+	0.592534i	$0.201872\pi$
$20$	13.1799	2.94711
$21$	−2.04048	−0.445270
$22$	−13.5982	−2.89915
$23$	−4.54890	−0.948511	−0.474256	−	0.880387i	$-0.657283\pi$
$23$	−4.54890	−0.948511	−0.474256	+	0.880387i	$0.657283\pi$
$24$	−7.04300	−1.43765
$25$	2.80573	0.561147
$26$	11.1056	2.17799
$27$	1.00000	0.192450
$28$	−9.62581	−1.81911
$29$	2.39061	0.443925	0.221963	−	0.975055i	$-0.428754\pi$
$29$	2.39061	0.443925	0.221963	+	0.975055i	$0.428754\pi$
$30$	−7.24116	−1.32205
$31$	10.9853	1.97302	0.986512	−	0.163689i	$-0.0523392\pi$
$31$	10.9853	1.97302	0.986512	+	0.163689i	$0.0523392\pi$
$32$	−8.77157	−1.55061
$33$	5.24663	0.913321
$34$	−17.1330	−2.93828
$35$	−5.70085	−0.963620
$36$	4.71742	0.786236
$37$	−3.75808	−0.617825	−0.308913	−	0.951090i	$-0.599965\pi$
$37$	−3.75808	−0.617825	−0.308913	+	0.951090i	$0.599965\pi$
$38$	−18.2011	−2.95261
$39$	−4.28491	−0.686134
$40$	−19.6773	−3.11125
$41$	10.9256	1.70630	0.853148	−	0.521668i	$-0.174690\pi$
$41$	10.9256	1.70630	0.853148	+	0.521668i	$0.174690\pi$
$42$	5.28852	0.816036
$43$	2.09083	0.318848	0.159424	−	0.987210i	$-0.449036\pi$
$43$	2.09083	0.318848	0.159424	+	0.987210i	$0.449036\pi$
$44$	24.7505	3.73129
$45$	2.79387	0.416486
$46$	11.7898	1.73832
$47$	10.8730	1.58599	0.792996	−	0.609227i	$-0.208520\pi$
$47$	10.8730	1.58599	0.792996	+	0.609227i	$0.208520\pi$
$48$	8.81919	1.27294
$49$	−2.83643	−0.405204
$50$	−7.27190	−1.02840
$51$	6.61045	0.925649
$52$	−20.2137	−2.80314
$53$	2.76743	0.380136	0.190068	−	0.981771i	$-0.439129\pi$
$53$	2.76743	0.380136	0.190068	+	0.981771i	$0.439129\pi$
$54$	−2.59180	−0.352699
$55$	14.6584	1.97654
$56$	14.3711	1.92042
$57$	7.02258	0.930164
$58$	−6.19598	−0.813572
$59$	−3.73743	−0.486573	−0.243286	−	0.969955i	$-0.578225\pi$
$59$	−3.73743	−0.486573	−0.243286	+	0.969955i	$0.578225\pi$
$60$	13.1799	1.70151
$61$	2.80976	0.359753	0.179877	−	0.983689i	$-0.442430\pi$
$61$	2.80976	0.359753	0.179877	+	0.983689i	$0.442430\pi$
$62$	−28.4718	−3.61592
$63$	−2.04048	−0.257077
$64$	5.09576	0.636970
$65$	−11.9715	−1.48488
$66$	−13.5982	−1.67382
$67$	8.51123	1.03981	0.519906	−	0.854223i	$-0.325967\pi$
$67$	8.51123	1.03981	0.519906	+	0.854223i	$0.325967\pi$
$68$	31.1843	3.78165
$69$	−4.54890	−0.547623
$70$	14.7755	1.76601
$71$	−10.2338	−1.21453	−0.607264	−	0.794500i	$-0.707733\pi$
$71$	−10.2338	−1.21453	−0.607264	+	0.794500i	$0.707733\pi$
$72$	−7.04300	−0.830025
$73$	7.89970	0.924590	0.462295	−	0.886726i	$-0.347026\pi$
$73$	7.89970	0.924590	0.462295	+	0.886726i	$0.347026\pi$
$74$	9.74019	1.13227
$75$	2.80573	0.323978
$76$	33.1285	3.80010
$77$	−10.7057	−1.22002
$78$	11.1056	1.25746
$79$	−8.82039	−0.992371	−0.496186	−	0.868216i	$-0.665266\pi$
$79$	−8.82039	−0.992371	−0.496186	+	0.868216i	$0.665266\pi$
$80$	24.6397	2.75480
$81$	1.00000	0.111111
$82$	−28.3170	−3.12709
$83$	−5.16944	−0.567419	−0.283710	−	0.958910i	$-0.591565\pi$
$83$	−5.16944	−0.567419	−0.283710	+	0.958910i	$0.591565\pi$
$84$	−9.62581	−1.05026
$85$	18.4688	2.00322
$86$	−5.41900	−0.584346
$87$	2.39061	0.256300
$88$	−36.9520	−3.93910
$89$	−9.31451	−0.987336	−0.493668	−	0.869651i	$-0.664344\pi$
$89$	−9.31451	−0.987336	−0.493668	+	0.869651i	$0.664344\pi$
$90$	−7.24116	−0.763285
$91$	8.74328	0.916545
$92$	−21.4591	−2.23726
$93$	10.9853	1.13913
$94$	−28.1807	−2.90661
$95$	19.6202	2.01299
$96$	−8.77157	−0.895245
$97$	10.5709	1.07331	0.536655	−	0.843802i	$-0.319688\pi$
$97$	10.5709	1.07331	0.536655	+	0.843802i	$0.319688\pi$
$98$	7.35145	0.742609
$99$	5.24663	0.527306
$100$	13.2358	1.32358
$101$	−3.81294	−0.379402	−0.189701	−	0.981842i	$-0.560752\pi$
$101$	−3.81294	−0.379402	−0.189701	+	0.981842i	$0.560752\pi$
$102$	−17.1330	−1.69642
$103$	−17.6207	−1.73622	−0.868111	−	0.496370i	$-0.834666\pi$
$103$	−17.6207	−1.73622	−0.868111	+	0.496370i	$0.834666\pi$
$104$	30.1786	2.95926
$105$	−5.70085	−0.556346
$106$	−7.17263	−0.696668
$107$	−8.55484	−0.827028	−0.413514	−	0.910498i	$-0.635699\pi$
$107$	−8.55484	−0.827028	−0.413514	+	0.910498i	$0.635699\pi$
$108$	4.71742	0.453934
$109$	3.20734	0.307207	0.153604	−	0.988133i	$-0.450912\pi$
$109$	3.20734	0.307207	0.153604	+	0.988133i	$0.450912\pi$
$110$	−37.9917	−3.62236
$111$	−3.75808	−0.356701
$112$	−17.9954	−1.70041
$113$	−8.42781	−0.792821	−0.396411	−	0.918073i	$-0.629744\pi$
$113$	−8.42781	−0.792821	−0.396411	+	0.918073i	$0.629744\pi$
$114$	−18.2011	−1.70469
$115$	−12.7091	−1.18513
$116$	11.2775	1.04709
$117$	−4.28491	−0.396140
$118$	9.68668	0.891731
$119$	−13.4885	−1.23649
$120$	−19.6773	−1.79628
$121$	16.5271	1.50247
$122$	−7.28234	−0.659312
$123$	10.9256	0.985131
$124$	51.8224	4.65379
$125$	−6.13050	−0.548329
$126$	5.28852	0.471139
$127$	−14.4272	−1.28021	−0.640104	−	0.768288i	$-0.721109\pi$
$127$	−14.4272	−1.28021	−0.640104	+	0.768288i	$0.721109\pi$
$128$	4.33596	0.383249
$129$	2.09083	0.184087
$130$	31.0277	2.72131
$131$	2.05371	0.179434	0.0897169	−	0.995967i	$-0.471404\pi$
$131$	2.05371	0.179434	0.0897169	+	0.995967i	$0.471404\pi$
$132$	24.7505	2.15426
$133$	−14.3295	−1.24252
$134$	−22.0594	−1.90564
$135$	2.79387	0.240458
$136$	−46.5574	−3.99226
$137$	−14.2476	−1.21725	−0.608626	−	0.793457i	$-0.708279\pi$
$137$	−14.2476	−1.21725	−0.608626	+	0.793457i	$0.708279\pi$
$138$	11.7898	1.00362
$139$	−13.5814	−1.15196	−0.575981	−	0.817463i	$-0.695380\pi$
$139$	−13.5814	−1.15196	−0.575981	+	0.817463i	$0.695380\pi$
$140$	−26.8933	−2.27290
$141$	10.8730	0.915673
$142$	26.5239	2.22584
$143$	−22.4813	−1.87998
$144$	8.81919	0.734933
$145$	6.67906	0.554666
$146$	−20.4744	−1.69448
$147$	−2.83643	−0.233945
$148$	−17.7284	−1.45727
$149$	−7.84941	−0.643049	−0.321524	−	0.946901i	$-0.604195\pi$
$149$	−7.84941	−0.643049	−0.321524	+	0.946901i	$0.604195\pi$
$150$	−7.27190	−0.593748
$151$	19.2166	1.56382	0.781911	−	0.623390i	$-0.214245\pi$
$151$	19.2166	1.56382	0.781911	+	0.623390i	$0.214245\pi$
$152$	−49.4600	−4.01174
$153$	6.61045	0.534423
$154$	27.7469	2.23591
$155$	30.6916	2.46521
$156$	−20.2137	−1.61839
$157$	−10.5695	−0.843535	−0.421768	−	0.906704i	$-0.638590\pi$
$157$	−10.5695	−0.843535	−0.421768	+	0.906704i	$0.638590\pi$
$158$	22.8607	1.81870
$159$	2.76743	0.219472
$160$	−24.5067	−1.93742
$161$	9.28195	0.731521
$162$	−2.59180	−0.203631
$163$	13.7083	1.07372	0.536859	−	0.843672i	$-0.319611\pi$
$163$	13.7083	1.07372	0.536859	+	0.843672i	$0.319611\pi$
$164$	51.5408	4.02466
$165$	14.6584	1.14116
$166$	13.3981	1.03990
$167$	7.75162	0.599838	0.299919	−	0.953965i	$-0.403040\pi$
$167$	7.75162	0.599838	0.299919	+	0.953965i	$0.403040\pi$
$168$	14.3711	1.10876
$169$	5.36044	0.412341
$170$	−47.8673	−3.67126
$171$	7.02258	0.537030
$172$	9.86331	0.752070
$173$	4.35425	0.331047	0.165524	−	0.986206i	$-0.447069\pi$
$173$	4.35425	0.331047	0.165524	+	0.986206i	$0.447069\pi$
$174$	−6.19598	−0.469716
$175$	−5.72505	−0.432773
$176$	46.2710	3.48781
$177$	−3.73743	−0.280923
$178$	24.1413	1.80947
$179$	2.13406	0.159507	0.0797537	−	0.996815i	$-0.474587\pi$
$179$	2.13406	0.159507	0.0797537	+	0.996815i	$0.474587\pi$
$180$	13.1799	0.982370
$181$	−20.1861	−1.50042	−0.750212	−	0.661197i	$-0.770049\pi$
$181$	−20.1861	−1.50042	−0.750212	+	0.661197i	$0.770049\pi$
$182$	−22.6608	−1.67973
$183$	2.80976	0.207704
$184$	32.0379	2.36187
$185$	−10.4996	−0.771947
$186$	−28.4718	−2.08765
$187$	34.6826	2.53624
$188$	51.2925	3.74089
$189$	−2.04048	−0.148423
$190$	−50.8516	−3.68917
$191$	−22.3662	−1.61836	−0.809180	−	0.587560i	$-0.800088\pi$
$191$	−22.3662	−1.61836	−0.809180	+	0.587560i	$0.800088\pi$
$192$	5.09576	0.367755
$193$	5.00882	0.360543	0.180271	−	0.983617i	$-0.442302\pi$
$193$	5.00882	0.360543	0.180271	+	0.983617i	$0.442302\pi$
$194$	−27.3976	−1.96703
$195$	−11.9715	−0.857297
$196$	−13.3806	−0.955759
$197$	6.18275	0.440503	0.220251	−	0.975443i	$-0.429312\pi$
$197$	6.18275	0.440503	0.220251	+	0.975443i	$0.429312\pi$
$198$	−13.5982	−0.966382
$199$	−0.513231	−0.0363820	−0.0181910	−	0.999835i	$-0.505791\pi$
$199$	−0.513231	−0.0363820	−0.0181910	+	0.999835i	$0.505791\pi$
$200$	−19.7608	−1.39730
$201$	8.51123	0.600336
$202$	9.88237	0.695321
$203$	−4.87800	−0.342368
$204$	31.1843	2.18334
$205$	30.5248	2.13195
$206$	45.6694	3.18194
$207$	−4.54890	−0.316170
$208$	−37.7894	−2.62023
$209$	36.8449	2.54862
$210$	14.7755	1.01960
$211$	27.1514	1.86918	0.934589	−	0.355729i	$-0.115768\pi$
$211$	27.1514	1.86918	0.934589	+	0.355729i	$0.115768\pi$
$212$	13.0551	0.896631
$213$	−10.2338	−0.701208
$214$	22.1724	1.51568
$215$	5.84151	0.398388
$216$	−7.04300	−0.479215
$217$	−22.4154	−1.52166
$218$	−8.31277	−0.563012
$219$	7.89970	0.533812
$220$	69.1499	4.66209
$221$	−28.3252	−1.90536
$222$	9.74019	0.653719
$223$	8.55291	0.572745	0.286372	−	0.958118i	$-0.407551\pi$
$223$	8.55291	0.572745	0.286372	+	0.958118i	$0.407551\pi$
$224$	17.8982	1.19588
$225$	2.80573	0.187049
$226$	21.8432	1.45299
$227$	−13.4635	−0.893601	−0.446800	−	0.894634i	$-0.647437\pi$
$227$	−13.4635	−0.893601	−0.446800	+	0.894634i	$0.647437\pi$
$228$	33.1285	2.19399
$229$	22.9109	1.51400	0.756999	−	0.653416i	$-0.226665\pi$
$229$	22.9109	1.51400	0.756999	+	0.653416i	$0.226665\pi$
$230$	32.9393	2.17195
$231$	−10.7057	−0.704381
$232$	−16.8371	−1.10541
$233$	3.24360	0.212495	0.106248	−	0.994340i	$-0.466116\pi$
$233$	3.24360	0.212495	0.106248	+	0.994340i	$0.466116\pi$
$234$	11.1056	0.725997
$235$	30.3778	1.98163
$236$	−17.6310	−1.14768
$237$	−8.82039	−0.572946
$238$	34.9595	2.26609
$239$	20.9594	1.35575	0.677875	−	0.735177i	$-0.262901\pi$
$239$	20.9594	1.35575	0.677875	+	0.735177i	$0.262901\pi$
$240$	24.6397	1.59049
$241$	6.71086	0.432284	0.216142	−	0.976362i	$-0.430653\pi$
$241$	6.71086	0.432284	0.216142	+	0.976362i	$0.430653\pi$
$242$	−42.8350	−2.75354
$243$	1.00000	0.0641500
$244$	13.2548	0.848553
$245$	−7.92463	−0.506286
$246$	−28.3170	−1.80543
$247$	−30.0911	−1.91465
$248$	−77.3697	−4.91298
$249$	−5.16944	−0.327600
$250$	15.8890	1.00491
$251$	−2.59069	−0.163523	−0.0817615	−	0.996652i	$-0.526055\pi$
$251$	−2.59069	−0.163523	−0.0817615	+	0.996652i	$0.526055\pi$
$252$	−9.62581	−0.606369
$253$	−23.8664	−1.50047
$254$	37.3924	2.34621
$255$	18.4688	1.15656
$256$	−21.4295	−1.33934
$257$	−28.4417	−1.77414	−0.887071	−	0.461633i	$-0.847264\pi$
$257$	−28.4417	−1.77414	−0.887071	+	0.461633i	$0.847264\pi$
$258$	−5.41900	−0.337372
$259$	7.66831	0.476485
$260$	−56.4745	−3.50240
$261$	2.39061	0.147975
$262$	−5.32281	−0.328845
$263$	0.597897	0.0368679	0.0184340	−	0.999830i	$-0.494132\pi$
$263$	0.597897	0.0368679	0.0184340	+	0.999830i	$0.494132\pi$
$264$	−36.9520	−2.27424
$265$	7.73187	0.474965
$266$	37.1391	2.27714
$267$	−9.31451	−0.570039
$268$	40.1510	2.45261
$269$	29.6358	1.80692	0.903462	−	0.428668i	$-0.141017\pi$
$269$	29.6358	1.80692	0.903462	+	0.428668i	$0.141017\pi$
$270$	−7.24116	−0.440683
$271$	24.2269	1.47168	0.735840	−	0.677155i	$-0.236788\pi$
$271$	24.2269	1.47168	0.735840	+	0.677155i	$0.236788\pi$
$272$	58.2989	3.53489
$273$	8.74328	0.529168
$274$	36.9268	2.23083
$275$	14.7207	0.887689
$276$	−21.4591	−1.29168
$277$	19.2132	1.15441	0.577205	−	0.816599i	$-0.304143\pi$
$277$	19.2132	1.15441	0.577205	+	0.816599i	$0.304143\pi$
$278$	35.2004	2.11118
$279$	10.9853	0.657675
$280$	40.1511	2.39949
$281$	0.802486	0.0478723	0.0239361	−	0.999713i	$-0.492380\pi$
$281$	0.802486	0.0478723	0.0239361	+	0.999713i	$0.492380\pi$
$282$	−28.1807	−1.67813
$283$	−28.1211	−1.67163	−0.835814	−	0.549013i	$-0.815004\pi$
$283$	−28.1211	−1.67163	−0.835814	+	0.549013i	$0.815004\pi$
$284$	−48.2771	−2.86472
$285$	19.6202	1.16220
$286$	58.2671	3.44540
$287$	−22.2936	−1.31595
$288$	−8.77157	−0.516870
$289$	26.6981	1.57048
$290$	−17.3108	−1.01652
$291$	10.5709	0.619676
$292$	37.2662	2.18084
$293$	−4.33151	−0.253049	−0.126525	−	0.991963i	$-0.540382\pi$
$293$	−4.33151	−0.253049	−0.126525	+	0.991963i	$0.540382\pi$
$294$	7.35145	0.428745
$295$	−10.4419	−0.607952
$296$	26.4682	1.53843
$297$	5.24663	0.304440
$298$	20.3441	1.17850
$299$	19.4916	1.12723
$300$	13.2358	0.764171
$301$	−4.26630	−0.245905
$302$	−49.8055	−2.86598
$303$	−3.81294	−0.219048
$304$	61.9335	3.55213
$305$	7.85012	0.449497
$306$	−17.1330	−0.979426
$307$	−2.72727	−0.155654	−0.0778269	−	0.996967i	$-0.524798\pi$
$307$	−2.72727	−0.155654	−0.0778269	+	0.996967i	$0.524798\pi$
$308$	−50.5031	−2.87768
$309$	−17.6207	−1.00241
$310$	−79.5465	−4.51794
$311$	24.9768	1.41631	0.708153	−	0.706059i	$-0.249529\pi$
$311$	24.9768	1.41631	0.708153	+	0.706059i	$0.249529\pi$
$312$	30.1786	1.70853
$313$	11.1764	0.631730	0.315865	−	0.948804i	$-0.397705\pi$
$313$	11.1764	0.631730	0.315865	+	0.948804i	$0.397705\pi$
$314$	27.3939	1.54593
$315$	−5.70085	−0.321207
$316$	−41.6095	−2.34072
$317$	−16.4681	−0.924943	−0.462471	−	0.886634i	$-0.653037\pi$
$317$	−16.4681	−0.924943	−0.462471	+	0.886634i	$0.653037\pi$
$318$	−7.17263	−0.402221
$319$	12.5426	0.702253
$320$	14.2369	0.795868
$321$	−8.55484	−0.477485
$322$	−24.0570	−1.34064
$323$	46.4225	2.58301
$324$	4.71742	0.262079
$325$	−12.0223	−0.666878
$326$	−35.5291	−1.96778
$327$	3.20734	0.177366
$328$	−76.9492	−4.24881
$329$	−22.1862	−1.22316
$330$	−37.9917	−2.09137
$331$	−9.66997	−0.531509	−0.265755	−	0.964041i	$-0.585621\pi$
$331$	−9.66997	−0.531509	−0.265755	+	0.964041i	$0.585621\pi$
$332$	−24.3864	−1.33838
$333$	−3.75808	−0.205942
$334$	−20.0906	−1.09931
$335$	23.7793	1.29920
$336$	−17.9954	−0.981730
$337$	−13.3899	−0.729397	−0.364698	−	0.931126i	$-0.618828\pi$
$337$	−13.3899	−0.729397	−0.364698	+	0.931126i	$0.618828\pi$
$338$	−13.8932	−0.755689
$339$	−8.42781	−0.457736
$340$	87.1249	4.72501
$341$	57.6360	3.12116
$342$	−18.2011	−0.984204
$343$	20.0711	1.08374
$344$	−14.7257	−0.793956
$345$	−12.7091	−0.684233
$346$	−11.2853	−0.606703
$347$	−16.2726	−0.873559	−0.436779	−	0.899569i	$-0.643881\pi$
$347$	−16.2726	−0.873559	−0.436779	+	0.899569i	$0.643881\pi$
$348$	11.2775	0.604538
$349$	−0.610028	−0.0326540	−0.0163270	−	0.999867i	$-0.505197\pi$
$349$	−0.610028	−0.0326540	−0.0163270	+	0.999867i	$0.505197\pi$
$350$	14.8382	0.793134
$351$	−4.28491	−0.228711
$352$	−46.0212	−2.45294
$353$	−20.2622	−1.07845	−0.539225	−	0.842162i	$-0.681283\pi$
$353$	−20.2622	−1.07845	−0.539225	+	0.842162i	$0.681283\pi$
$354$	9.68668	0.514841
$355$	−28.5919	−1.51750
$356$	−43.9404	−2.32884
$357$	−13.4885	−0.713888
$358$	−5.53106	−0.292326
$359$	−15.6233	−0.824565	−0.412283	−	0.911056i	$-0.635268\pi$
$359$	−15.6233	−0.824565	−0.412283	+	0.911056i	$0.635268\pi$
$360$	−19.6773	−1.03708
$361$	30.3167	1.59562
$362$	52.3184	2.74979
$363$	16.5271	0.867449
$364$	41.2457	2.16186
$365$	22.0708	1.15524
$366$	−7.28234	−0.380654
$367$	−6.78253	−0.354045	−0.177023	−	0.984207i	$-0.556647\pi$
$367$	−6.78253	−0.354045	−0.177023	+	0.984207i	$0.556647\pi$
$368$	−40.1176	−2.09128
$369$	10.9256	0.568766
$370$	27.2129	1.41473
$371$	−5.64690	−0.293173
$372$	51.8224	2.68687
$373$	−6.51368	−0.337266	−0.168633	−	0.985679i	$-0.553935\pi$
$373$	−6.51368	−0.337266	−0.168633	+	0.985679i	$0.553935\pi$
$374$	−89.8903	−4.64812
$375$	−6.13050	−0.316578
$376$	−76.5786	−3.94924
$377$	−10.2435	−0.527569
$378$	5.28852	0.272012
$379$	−28.5948	−1.46882	−0.734408	−	0.678709i	$-0.762540\pi$
$379$	−28.5948	−1.46882	−0.734408	+	0.678709i	$0.762540\pi$
$380$	92.5568	4.74806
$381$	−14.4272	−0.739129
$382$	57.9686	2.96593
$383$	22.7966	1.16485	0.582426	−	0.812884i	$-0.302104\pi$
$383$	22.7966	1.16485	0.582426	+	0.812884i	$0.302104\pi$
$384$	4.33596	0.221269
$385$	−29.9103	−1.52437
$386$	−12.9819	−0.660759
$387$	2.09083	0.106283
$388$	49.8672	2.53162
$389$	−27.8356	−1.41132	−0.705660	−	0.708551i	$-0.749349\pi$
$389$	−27.8356	−1.41132	−0.705660	+	0.708551i	$0.749349\pi$
$390$	31.0277	1.57115
$391$	−30.0703	−1.52072
$392$	19.9770	1.00899
$393$	2.05371	0.103596
$394$	−16.0244	−0.807299
$395$	−24.6431	−1.23993
$396$	24.7505	1.24376
$397$	15.5602	0.780946	0.390473	−	0.920614i	$-0.372311\pi$
$397$	15.5602	0.780946	0.390473	+	0.920614i	$0.372311\pi$
$398$	1.33019	0.0666764
$399$	−14.3295	−0.717370
$400$	24.7443	1.23722
$401$	3.37412	0.168495	0.0842477	−	0.996445i	$-0.473151\pi$
$401$	3.37412	0.168495	0.0842477	+	0.996445i	$0.473151\pi$
$402$	−22.0594	−1.10022
$403$	−47.0711	−2.34478
$404$	−17.9872	−0.894898
$405$	2.79387	0.138829
$406$	12.6428	0.627451
$407$	−19.7173	−0.977349
$408$	−46.5574	−2.30494
$409$	−24.8782	−1.23015	−0.615073	−	0.788470i	$-0.710874\pi$
$409$	−24.8782	−1.23015	−0.615073	+	0.788470i	$0.710874\pi$
$410$	−79.1142	−3.90717
$411$	−14.2476	−0.702781
$412$	−83.1244	−4.09524
$413$	7.62617	0.375259
$414$	11.7898	0.579439
$415$	−14.4428	−0.708967
$416$	37.5854	1.84278
$417$	−13.5814	−0.665086
$418$	−95.4945	−4.67079
$419$	24.5840	1.20101	0.600505	−	0.799621i	$-0.294966\pi$
$419$	24.5840	1.20101	0.600505	+	0.799621i	$0.294966\pi$
$420$	−26.8933	−1.31226
$421$	−24.1536	−1.17717	−0.588586	−	0.808435i	$-0.700315\pi$
$421$	−24.1536	−1.17717	−0.588586	+	0.808435i	$0.700315\pi$
$422$	−70.3709	−3.42560
$423$	10.8730	0.528664
$424$	−19.4910	−0.946568
$425$	18.5472	0.899670
$426$	26.5239	1.28509
$427$	−5.73327	−0.277452
$428$	−40.3568	−1.95072
$429$	−22.4813	−1.08541
$430$	−15.1400	−0.730116
$431$	6.08278	0.292997	0.146499	−	0.989211i	$-0.453200\pi$
$431$	6.08278	0.292997	0.146499	+	0.989211i	$0.453200\pi$
$432$	8.81919	0.424314
$433$	35.5664	1.70921	0.854607	−	0.519275i	$-0.173798\pi$
$433$	35.5664	1.70921	0.854607	+	0.519275i	$0.173798\pi$
$434$	58.0962	2.78870
$435$	6.67906	0.320237
$436$	15.1303	0.724612
$437$	−31.9450	−1.52814
$438$	−20.4744	−0.978306
$439$	4.79773	0.228983	0.114492	−	0.993424i	$-0.463476\pi$
$439$	4.79773	0.228983	0.114492	+	0.993424i	$0.463476\pi$
$440$	−103.239	−4.92174
$441$	−2.83643	−0.135068
$442$	73.4132	3.49191
$443$	−22.0348	−1.04690	−0.523452	−	0.852055i	$-0.675356\pi$
$443$	−22.0348	−1.04690	−0.523452	+	0.852055i	$0.675356\pi$
$444$	−17.7284	−0.841355
$445$	−26.0236	−1.23364
$446$	−22.1674	−1.04966
$447$	−7.84941	−0.371264
$448$	−10.3978	−0.491250
$449$	2.24111	0.105764	0.0528821	−	0.998601i	$-0.483159\pi$
$449$	2.24111	0.105764	0.0528821	+	0.998601i	$0.483159\pi$
$450$	−7.27190	−0.342801
$451$	57.3227	2.69922
$452$	−39.7575	−1.87003
$453$	19.2166	0.902873
$454$	34.8945	1.63768
$455$	24.4276	1.14519
$456$	−49.4600	−2.31618
$457$	25.7081	1.20258	0.601288	−	0.799033i	$-0.294655\pi$
$457$	25.7081	1.20258	0.601288	+	0.799033i	$0.294655\pi$
$458$	−59.3805	−2.77467
$459$	6.61045	0.308550
$460$	−59.9539	−2.79537
$461$	−12.7777	−0.595116	−0.297558	−	0.954704i	$-0.596172\pi$
$461$	−12.7777	−0.595116	−0.297558	+	0.954704i	$0.596172\pi$
$462$	27.7469	1.29090
$463$	22.7122	1.05553	0.527763	−	0.849391i	$-0.323031\pi$
$463$	22.7122	1.05553	0.527763	+	0.849391i	$0.323031\pi$
$464$	21.0833	0.978765
$465$	30.6916	1.42329
$466$	−8.40676	−0.389436
$467$	−2.62497	−0.121469	−0.0607345	−	0.998154i	$-0.519344\pi$
$467$	−2.62497	−0.121469	−0.0607345	+	0.998154i	$0.519344\pi$
$468$	−20.2137	−0.934379
$469$	−17.3670	−0.801934
$470$	−78.7332	−3.63169
$471$	−10.5695	−0.487015
$472$	26.3227	1.21160
$473$	10.9698	0.504392
$474$	22.8607	1.05003
$475$	19.7035	0.904059
$476$	−63.6310	−2.91652
$477$	2.76743	0.126712
$478$	−54.3225	−2.48465
$479$	−30.5181	−1.39441	−0.697203	−	0.716873i	$-0.745573\pi$
$479$	−30.5181	−1.39441	−0.697203	+	0.716873i	$0.745573\pi$
$480$	−24.5067	−1.11857
$481$	16.1030	0.734236
$482$	−17.3932	−0.792238
$483$	9.28195	0.422344
$484$	77.9654	3.54388
$485$	29.5337	1.34106
$486$	−2.59180	−0.117566
$487$	−19.1702	−0.868686	−0.434343	−	0.900748i	$-0.643019\pi$
$487$	−19.1702	−0.868686	−0.434343	+	0.900748i	$0.643019\pi$
$488$	−19.7891	−0.895813
$489$	13.7083	0.619911
$490$	20.5390	0.927859
$491$	39.9698	1.80381	0.901907	−	0.431931i	$-0.142168\pi$
$491$	39.9698	1.80381	0.901907	+	0.431931i	$0.142168\pi$
$492$	51.5408	2.32364
$493$	15.8030	0.711732
$494$	77.9901	3.50894
$495$	14.6584	0.658847
$496$	96.8818	4.35012
$497$	20.8819	0.936681
$498$	13.3981	0.600385
$499$	15.0619	0.674263	0.337132	−	0.941458i	$-0.390543\pi$
$499$	15.0619	0.674263	0.337132	+	0.941458i	$0.390543\pi$
$500$	−28.9201	−1.29335
$501$	7.75162	0.346317
$502$	6.71455	0.299685
$503$	33.8846	1.51084	0.755419	−	0.655242i	$-0.227433\pi$
$503$	33.8846	1.51084	0.755419	+	0.655242i	$0.227433\pi$
$504$	14.3711	0.640140
$505$	−10.6529	−0.474047
$506$	61.8569	2.74987
$507$	5.36044	0.238065
$508$	−68.0592	−3.01964
$509$	−34.9094	−1.54733	−0.773665	−	0.633595i	$-0.781579\pi$
$509$	−34.9094	−1.54733	−0.773665	+	0.633595i	$0.781579\pi$
$510$	−47.8673	−2.11960
$511$	−16.1192	−0.713071
$512$	46.8689	2.07133
$513$	7.02258	0.310055
$514$	73.7150	3.25143
$515$	−49.2301	−2.16934
$516$	9.86331	0.434208
$517$	57.0467	2.50891
$518$	−19.8747	−0.873244
$519$	4.35425	0.191130
$520$	84.3152	3.69747
$521$	27.7590	1.21614	0.608071	−	0.793883i	$-0.291944\pi$
$521$	27.7590	1.21614	0.608071	+	0.793883i	$0.291944\pi$
$522$	−6.19598	−0.271191
$523$	41.0697	1.79585	0.897927	−	0.440144i	$-0.145073\pi$
$523$	41.0697	1.79585	0.897927	+	0.440144i	$0.145073\pi$
$524$	9.68823	0.423232
$525$	−5.72505	−0.249862
$526$	−1.54963	−0.0675670
$527$	72.6180	3.16329
$528$	46.2710	2.01369
$529$	−2.30750	−0.100326
$530$	−20.0394	−0.870457
$531$	−3.73743	−0.162191
$532$	−67.5981	−2.93075
$533$	−46.8153	−2.02780
$534$	24.1413	1.04470
$535$	−23.9012	−1.03334
$536$	−59.9446	−2.58921
$537$	2.13406	0.0920916
$538$	−76.8099	−3.31151
$539$	−14.8817	−0.641000
$540$	13.1799	0.567171
$541$	33.3494	1.43380	0.716902	−	0.697174i	$-0.245560\pi$
$541$	33.3494	1.43380	0.716902	+	0.697174i	$0.245560\pi$
$542$	−62.7913	−2.69712
$543$	−20.1861	−0.866270
$544$	−57.9841	−2.48605
$545$	8.96090	0.383843
$546$	−22.6608	−0.969794
$547$	9.65743	0.412922	0.206461	−	0.978455i	$-0.433805\pi$
$547$	9.65743	0.412922	0.206461	+	0.978455i	$0.433805\pi$
$548$	−67.2118	−2.87114
$549$	2.80976	0.119918
$550$	−38.1530	−1.62685
$551$	16.7883	0.715204
$552$	32.0379	1.36362
$553$	17.9979	0.765347
$554$	−49.7968	−2.11566
$555$	−10.4996	−0.445684
$556$	−64.0693	−2.71714
$557$	−38.8811	−1.64745	−0.823723	−	0.566992i	$-0.808107\pi$
$557$	−38.8811	−1.64745	−0.823723	+	0.566992i	$0.808107\pi$
$558$	−28.4718	−1.20531
$559$	−8.95900	−0.378926
$560$	−50.2769	−2.12459
$561$	34.6826	1.46430
$562$	−2.07988	−0.0877345
$563$	−1.39720	−0.0588851	−0.0294426	−	0.999566i	$-0.509373\pi$
$563$	−1.39720	−0.0588851	−0.0294426	+	0.999566i	$0.509373\pi$
$564$	51.2925	2.15981
$565$	−23.5462	−0.990598
$566$	72.8843	3.06356
$567$	−2.04048	−0.0856922
$568$	72.0766	3.02427
$569$	20.9445	0.878041	0.439021	−	0.898477i	$-0.355326\pi$
$569$	20.9445	0.878041	0.439021	+	0.898477i	$0.355326\pi$
$570$	−50.8516	−2.12994
$571$	−2.84801	−0.119185	−0.0595927	−	0.998223i	$-0.518980\pi$
$571$	−2.84801	−0.119185	−0.0595927	+	0.998223i	$0.518980\pi$
$572$	−106.054	−4.43433
$573$	−22.3662	−0.934361
$574$	57.7804	2.41171
$575$	−12.7630	−0.532254
$576$	5.09576	0.212323
$577$	22.8753	0.952311	0.476155	−	0.879361i	$-0.342030\pi$
$577$	22.8753	0.952311	0.476155	+	0.879361i	$0.342030\pi$
$578$	−69.1961	−2.87818
$579$	5.00882	0.208160
$580$	31.5079	1.30830
$581$	10.5481	0.437611
$582$	−27.3976	−1.13567
$583$	14.5197	0.601345
$584$	−55.6376	−2.30230
$585$	−11.9715	−0.494960
$586$	11.2264	0.463758
$587$	−9.96963	−0.411491	−0.205745	−	0.978606i	$-0.565962\pi$
$587$	−9.96963	−0.411491	−0.205745	+	0.978606i	$0.565962\pi$
$588$	−13.3806	−0.551807
$589$	77.1454	3.17872
$590$	27.0634	1.11418
$591$	6.18275	0.254324
$592$	−33.1433	−1.36218
$593$	−41.6176	−1.70903	−0.854516	−	0.519425i	$-0.826146\pi$
$593$	−41.6176	−1.70903	−0.854516	+	0.519425i	$0.826146\pi$
$594$	−13.5982	−0.557941
$595$	−37.6852	−1.54494
$596$	−37.0289	−1.51676
$597$	−0.513231	−0.0210051
$598$	−50.5184	−2.06585
$599$	−9.05234	−0.369869	−0.184934	−	0.982751i	$-0.559207\pi$
$599$	−9.05234	−0.369869	−0.184934	+	0.982751i	$0.559207\pi$
$600$	−19.7608	−0.806731
$601$	−7.51759	−0.306649	−0.153325	−	0.988176i	$-0.548998\pi$
$601$	−7.51759	−0.306649	−0.153325	+	0.988176i	$0.548998\pi$
$602$	11.0574	0.450665
$603$	8.51123	0.346604
$604$	90.6526	3.68860
$605$	46.1747	1.87727
$606$	9.88237	0.401444
$607$	−28.6009	−1.16087	−0.580437	−	0.814305i	$-0.697118\pi$
$607$	−28.6009	−1.16087	−0.580437	+	0.814305i	$0.697118\pi$
$608$	−61.5991	−2.49817
$609$	−4.87800	−0.197667
$610$	−20.3459	−0.823783
$611$	−46.5899	−1.88482
$612$	31.1843	1.26055
$613$	−25.7888	−1.04160	−0.520800	−	0.853679i	$-0.674366\pi$
$613$	−25.7888	−1.04160	−0.520800	+	0.853679i	$0.674366\pi$
$614$	7.06854	0.285263
$615$	30.5248	1.23088
$616$	75.3999	3.03795
$617$	−2.57447	−0.103644	−0.0518222	−	0.998656i	$-0.516503\pi$
$617$	−2.57447	−0.103644	−0.0518222	+	0.998656i	$0.516503\pi$
$618$	45.6694	1.83709
$619$	−17.3650	−0.697960	−0.348980	−	0.937130i	$-0.613472\pi$
$619$	−17.3650	−0.697960	−0.348980	+	0.937130i	$0.613472\pi$
$620$	144.785	5.81472
$621$	−4.54890	−0.182541
$622$	−64.7349	−2.59563
$623$	19.0061	0.761463
$624$	−37.7894	−1.51279
$625$	−31.1565	−1.24626
$626$	−28.9671	−1.15776
$627$	36.8449	1.47144
$628$	−49.8606	−1.98965
$629$	−24.8426	−0.990541
$630$	14.7755	0.588668
$631$	−16.5674	−0.659539	−0.329769	−	0.944062i	$-0.606971\pi$
$631$	−16.5674	−0.659539	−0.329769	+	0.944062i	$0.606971\pi$
$632$	62.1220	2.47108
$633$	27.1514	1.07917
$634$	42.6821	1.69512
$635$	−40.3078	−1.59957
$636$	13.0551	0.517670
$637$	12.1538	0.481553
$638$	−32.5080	−1.28700
$639$	−10.2338	−0.404843
$640$	12.1141	0.478853
$641$	6.11255	0.241431	0.120716	−	0.992687i	$-0.461481\pi$
$641$	6.11255	0.241431	0.120716	+	0.992687i	$0.461481\pi$
$642$	22.1724	0.875076
$643$	−13.7046	−0.540456	−0.270228	−	0.962796i	$-0.587099\pi$
$643$	−13.7046	−0.540456	−0.270228	+	0.962796i	$0.587099\pi$
$644$	43.7869	1.72544
$645$	5.84151	0.230009
$646$	−120.318	−4.73383
$647$	39.4976	1.55281	0.776406	−	0.630233i	$-0.217040\pi$
$647$	39.4976	1.55281	0.776406	+	0.630233i	$0.217040\pi$
$648$	−7.04300	−0.276675
$649$	−19.6089	−0.769718
$650$	31.1594	1.22217
$651$	−22.4154	−0.878528
$652$	64.6678	2.53259
$653$	29.2251	1.14367	0.571834	−	0.820369i	$-0.306232\pi$
$653$	29.2251	1.14367	0.571834	+	0.820369i	$0.306232\pi$
$654$	−8.31277	−0.325055
$655$	5.73782	0.224195
$656$	96.3552	3.76204
$657$	7.89970	0.308197
$658$	57.5021	2.24167
$659$	−1.56514	−0.0609692	−0.0304846	−	0.999535i	$-0.509705\pi$
$659$	−1.56514	−0.0609692	−0.0304846	+	0.999535i	$0.509705\pi$
$660$	69.1499	2.69166
$661$	−22.9028	−0.890816	−0.445408	−	0.895328i	$-0.646941\pi$
$661$	−22.9028	−0.890816	−0.445408	+	0.895328i	$0.646941\pi$
$662$	25.0626	0.974086
$663$	−28.3252	−1.10006
$664$	36.4083	1.41292
$665$	−40.0347	−1.55248
$666$	9.74019	0.377425
$667$	−10.8746	−0.421068
$668$	36.5676	1.41484
$669$	8.55291	0.330674
$670$	−61.6312	−2.38102
$671$	14.7418	0.569100
$672$	17.8982	0.690440
$673$	−18.8167	−0.725329	−0.362665	−	0.931920i	$-0.618133\pi$
$673$	−18.8167	−0.725329	−0.362665	+	0.931920i	$0.618133\pi$
$674$	34.7040	1.33675
$675$	2.80573	0.107993
$676$	25.2874	0.972594
$677$	−41.5646	−1.59746	−0.798729	−	0.601691i	$-0.794494\pi$
$677$	−41.5646	−1.59746	−0.798729	+	0.601691i	$0.794494\pi$
$678$	21.8432	0.838882
$679$	−21.5697	−0.827769
$680$	−130.076	−4.98817
$681$	−13.4635	−0.515921
$682$	−149.381	−5.72009
$683$	0.717616	0.0274588	0.0137294	−	0.999906i	$-0.495630\pi$
$683$	0.717616	0.0274588	0.0137294	+	0.999906i	$0.495630\pi$
$684$	33.1285	1.26670
$685$	−39.8059	−1.52091
$686$	−52.0202	−1.98614
$687$	22.9109	0.874107
$688$	18.4394	0.702996
$689$	−11.8582	−0.451762
$690$	32.9393	1.25398
$691$	−15.8906	−0.604506	−0.302253	−	0.953228i	$-0.597739\pi$
$691$	−15.8906	−0.604506	−0.302253	+	0.953228i	$0.597739\pi$
$692$	20.5408	0.780844
$693$	−10.7057	−0.406674
$694$	42.1753	1.60095
$695$	−37.9448	−1.43933
$696$	−16.8371	−0.638207
$697$	72.2234	2.73565
$698$	1.58107	0.0598443
$699$	3.24360	0.122684
$700$	−27.0075	−1.02079
$701$	17.8434	0.673936	0.336968	−	0.941516i	$-0.390599\pi$
$701$	17.8434	0.673936	0.336968	+	0.941516i	$0.390599\pi$
$702$	11.1056	0.419155
$703$	−26.3915	−0.995373
$704$	26.7356	1.00763
$705$	30.3778	1.14410
$706$	52.5156	1.97645
$707$	7.78024	0.292606
$708$	−17.6310	−0.662615
$709$	−37.1116	−1.39376	−0.696879	−	0.717189i	$-0.745428\pi$
$709$	−37.1116	−1.39376	−0.696879	+	0.717189i	$0.745428\pi$
$710$	74.1045	2.78109
$711$	−8.82039	−0.330790
$712$	65.6020	2.45854
$713$	−49.9712	−1.87144
$714$	34.9595	1.30833
$715$	−62.8100	−2.34896
$716$	10.0673	0.376231
$717$	20.9594	0.782742
$718$	40.4924	1.51116
$719$	−23.1881	−0.864770	−0.432385	−	0.901689i	$-0.642328\pi$
$719$	−23.1881	−0.864770	−0.432385	+	0.901689i	$0.642328\pi$
$720$	24.6397	0.918268
$721$	35.9548	1.33903
$722$	−78.5747	−2.92425
$723$	6.71086	0.249580
$724$	−95.2265	−3.53906
$725$	6.70742	0.249107
$726$	−42.8350	−1.58976
$727$	31.9785	1.18602	0.593008	−	0.805196i	$-0.297940\pi$
$727$	31.9785	1.18602	0.593008	+	0.805196i	$0.297940\pi$
$728$	−61.5789	−2.28227
$729$	1.00000	0.0370370
$730$	−57.2030	−2.11718
$731$	13.8213	0.511200
$732$	13.2548	0.489912
$733$	42.5473	1.57152	0.785761	−	0.618530i	$-0.212272\pi$
$733$	42.5473	1.57152	0.785761	+	0.618530i	$0.212272\pi$
$734$	17.5789	0.648851
$735$	−7.92463	−0.292304
$736$	39.9010	1.47077
$737$	44.6553	1.64490
$738$	−28.3170	−1.04236
$739$	−44.5961	−1.64049	−0.820246	−	0.572011i	$-0.806164\pi$
$739$	−44.5961	−1.64049	−0.820246	+	0.572011i	$0.806164\pi$
$740$	−49.5311	−1.82080
$741$	−30.0911	−1.10543
$742$	14.6356	0.537291
$743$	34.8309	1.27782	0.638910	−	0.769281i	$-0.279386\pi$
$743$	34.8309	1.27782	0.638910	+	0.769281i	$0.279386\pi$
$744$	−77.3697	−2.83651
$745$	−21.9303	−0.803463
$746$	16.8821	0.618099
$747$	−5.16944	−0.189140
$748$	163.612	5.98226
$749$	17.4560	0.637829
$750$	15.8890	0.580185
$751$	−21.2271	−0.774589	−0.387294	−	0.921956i	$-0.626590\pi$
$751$	−21.2271	−0.774589	−0.387294	+	0.921956i	$0.626590\pi$
$752$	95.8912	3.49679
$753$	−2.59069	−0.0944100
$754$	26.5492	0.966865
$755$	53.6887	1.95393
$756$	−9.62581	−0.350087
$757$	45.7064	1.66123	0.830614	−	0.556848i	$-0.187990\pi$
$757$	45.7064	1.66123	0.830614	+	0.556848i	$0.187990\pi$
$758$	74.1119	2.69187
$759$	−23.8664	−0.866295
$760$	−138.185	−5.01250
$761$	32.4363	1.17581	0.587907	−	0.808929i	$-0.299952\pi$
$761$	32.4363	1.17581	0.587907	+	0.808929i	$0.299952\pi$
$762$	37.3924	1.35459
$763$	−6.54452	−0.236927
$764$	−105.511	−3.81724
$765$	18.4688	0.667740
$766$	−59.0842	−2.13480
$767$	16.0146	0.578252
$768$	−21.4295	−0.773269
$769$	20.7645	0.748787	0.374393	−	0.927270i	$-0.377851\pi$
$769$	20.7645	0.748787	0.374393	+	0.927270i	$0.377851\pi$
$770$	77.5214	2.79368
$771$	−28.4417	−1.02430
$772$	23.6287	0.850416
$773$	−48.2650	−1.73597	−0.867986	−	0.496589i	$-0.834586\pi$
$773$	−48.2650	−1.73597	−0.867986	+	0.496589i	$0.834586\pi$
$774$	−5.41900	−0.194782
$775$	30.8219	1.10716
$776$	−74.4506	−2.67262
$777$	7.66831	0.275099
$778$	72.1442	2.58649
$779$	76.7261	2.74900
$780$	−56.4745	−2.02211
$781$	−53.6929	−1.92128
$782$	77.9361	2.78699
$783$	2.39061	0.0854334
$784$	−25.0150	−0.893393
$785$	−29.5298	−1.05396
$786$	−5.32281	−0.189858
$787$	−25.3490	−0.903595	−0.451797	−	0.892121i	$-0.649217\pi$
$787$	−25.3490	−0.903595	−0.451797	+	0.892121i	$0.649217\pi$
$788$	29.1666	1.03902
$789$	0.597897	0.0212857
$790$	63.8698	2.27239
$791$	17.1968	0.611448
$792$	−36.9520	−1.31303
$793$	−12.0396	−0.427538
$794$	−40.3290	−1.43122
$795$	7.73187	0.274221
$796$	−2.42112	−0.0858144
$797$	24.1054	0.853859	0.426929	−	0.904285i	$-0.359595\pi$
$797$	24.1054	0.853859	0.426929	+	0.904285i	$0.359595\pi$
$798$	37.1391	1.31471
$799$	71.8755	2.54277
$800$	−24.6107	−0.870120
$801$	−9.31451	−0.329112
$802$	−8.74504	−0.308798
$803$	41.4468	1.46263
$804$	40.1510	1.41602
$805$	25.9326	0.914005
$806$	121.999	4.29723
$807$	29.6358	1.04323
$808$	26.8545	0.944739
$809$	20.3353	0.714952	0.357476	−	0.933922i	$-0.383637\pi$
$809$	20.3353	0.714952	0.357476	+	0.933922i	$0.383637\pi$
$810$	−7.24116	−0.254428
$811$	16.4155	0.576425	0.288213	−	0.957566i	$-0.406939\pi$
$811$	16.4155	0.576425	0.288213	+	0.957566i	$0.406939\pi$
$812$	−23.0116	−0.807547
$813$	24.2269	0.849675
$814$	51.1032	1.79117
$815$	38.2993	1.34157
$816$	58.2989	2.04087
$817$	14.6830	0.513694
$818$	64.4792	2.25446
$819$	8.74328	0.305515
$820$	143.998	5.02864
$821$	31.4016	1.09592	0.547962	−	0.836503i	$-0.315404\pi$
$821$	31.4016	1.09592	0.547962	+	0.836503i	$0.315404\pi$
$822$	36.9268	1.28797
$823$	−4.86751	−0.169671	−0.0848353	−	0.996395i	$-0.527036\pi$
$823$	−4.86751	−0.169671	−0.0848353	+	0.996395i	$0.527036\pi$
$824$	124.103	4.32333
$825$	14.7207	0.512507
$826$	−19.7655	−0.687730
$827$	18.5552	0.645226	0.322613	−	0.946531i	$-0.395439\pi$
$827$	18.5552	0.645226	0.322613	+	0.946531i	$0.395439\pi$
$828$	−21.4591	−0.745754
$829$	−31.8866	−1.10747	−0.553734	−	0.832694i	$-0.686797\pi$
$829$	−31.8866	−1.10747	−0.553734	+	0.832694i	$0.686797\pi$
$830$	37.4327	1.29931
$831$	19.2132	0.666499
$832$	−21.8349	−0.756988
$833$	−18.7501	−0.649652
$834$	35.2004	1.21889
$835$	21.6570	0.749473
$836$	173.813	6.01144
$837$	10.9853	0.379709
$838$	−63.7169	−2.20106
$839$	3.67762	0.126966	0.0634828	−	0.997983i	$-0.479779\pi$
$839$	3.67762	0.126966	0.0634828	+	0.997983i	$0.479779\pi$
$840$	40.1511	1.38534
$841$	−23.2850	−0.802930
$842$	62.6011	2.15738
$843$	0.802486	0.0276391
$844$	128.084	4.40885
$845$	14.9764	0.515204
$846$	−28.1807	−0.968871
$847$	−33.7233	−1.15875
$848$	24.4065	0.838124
$849$	−28.1211	−0.965115
$850$	−48.0705	−1.64881
$851$	17.0951	0.586014
$852$	−48.2771	−1.65395
$853$	5.83471	0.199777	0.0998883	−	0.994999i	$-0.468151\pi$
$853$	5.83471	0.199777	0.0998883	+	0.994999i	$0.468151\pi$
$854$	14.8595	0.508481
$855$	19.6202	0.670997
$856$	60.2517	2.05936
$857$	20.7588	0.709106	0.354553	−	0.935036i	$-0.384633\pi$
$857$	20.7588	0.709106	0.354553	+	0.935036i	$0.384633\pi$
$858$	58.2671	1.98920
$859$	−14.1538	−0.482923	−0.241461	−	0.970410i	$-0.577627\pi$
$859$	−14.1538	−0.482923	−0.241461	+	0.970410i	$0.577627\pi$
$860$	27.5568	0.939681
$861$	−22.2936	−0.759763
$862$	−15.7653	−0.536970
$863$	−26.6463	−0.907049	−0.453525	−	0.891244i	$-0.649834\pi$
$863$	−26.6463	−0.907049	−0.453525	+	0.891244i	$0.649834\pi$
$864$	−8.77157	−0.298415
$865$	12.1652	0.413630
$866$	−92.1810	−3.13244
$867$	26.6981	0.906715
$868$	−105.743	−3.58914
$869$	−46.2773	−1.56985
$870$	−17.3108	−0.586891
$871$	−36.4698	−1.23573
$872$	−22.5893	−0.764969
$873$	10.5709	0.357770
$874$	82.7951	2.80059
$875$	12.5092	0.422888
$876$	37.2662	1.25911
$877$	−13.5166	−0.456423	−0.228211	−	0.973612i	$-0.573288\pi$
$877$	−13.5166	−0.456423	−0.228211	+	0.973612i	$0.573288\pi$
$878$	−12.4348	−0.419653
$879$	−4.33151	−0.146098
$880$	129.275	4.35788
$881$	15.2293	0.513088	0.256544	−	0.966533i	$-0.417416\pi$
$881$	15.2293	0.513088	0.256544	+	0.966533i	$0.417416\pi$
$882$	7.35145	0.247536
$883$	−5.33570	−0.179561	−0.0897804	−	0.995962i	$-0.528617\pi$
$883$	−5.33570	−0.179561	−0.0897804	+	0.995962i	$0.528617\pi$
$884$	−133.622	−4.49419
$885$	−10.4419	−0.351001
$886$	57.1097	1.91864
$887$	−25.8185	−0.866902	−0.433451	−	0.901177i	$-0.642704\pi$
$887$	−25.8185	−0.866902	−0.433451	+	0.901177i	$0.642704\pi$
$888$	26.4682	0.888214
$889$	29.4385	0.987336
$890$	67.4478	2.26086
$891$	5.24663	0.175769
$892$	40.3476	1.35094
$893$	76.3566	2.55518
$894$	20.3441	0.680408
$895$	5.96230	0.199298
$896$	−8.84746	−0.295573
$897$	19.4916	0.650806
$898$	−5.80849	−0.193832
$899$	26.2616	0.875875
$900$	13.2358	0.441194
$901$	18.2940	0.609461
$902$	−148.569	−4.94681
$903$	−4.26630	−0.141974
$904$	59.3570	1.97419
$905$	−56.3976	−1.87472
$906$	−49.8055	−1.65468
$907$	28.0518	0.931445	0.465723	−	0.884931i	$-0.345794\pi$
$907$	28.0518	0.931445	0.465723	+	0.884931i	$0.345794\pi$
$908$	−63.5127	−2.10774
$909$	−3.81294	−0.126467
$910$	−63.3115	−2.09876
$911$	−50.7293	−1.68074	−0.840369	−	0.542015i	$-0.817662\pi$
$911$	−50.7293	−1.68074	−0.840369	+	0.542015i	$0.817662\pi$
$912$	61.9335	2.05082
$913$	−27.1221	−0.897611
$914$	−66.6303	−2.20393
$915$	7.85012	0.259517
$916$	108.080	3.57108
$917$	−4.19057	−0.138385
$918$	−17.1330	−0.565472
$919$	31.8503	1.05064	0.525322	−	0.850904i	$-0.323945\pi$
$919$	31.8503	1.05064	0.525322	+	0.850904i	$0.323945\pi$
$920$	89.5099	2.95105
$921$	−2.72727	−0.0898667
$922$	33.1172	1.09066
$923$	43.8509	1.44337
$924$	−50.5031	−1.66143
$925$	−10.5442	−0.346691
$926$	−58.8655	−1.93444
$927$	−17.6207	−0.578741
$928$	−20.9694	−0.688355
$929$	53.0104	1.73921	0.869607	−	0.493744i	$-0.164372\pi$
$929$	53.0104	1.73921	0.869607	+	0.493744i	$0.164372\pi$
$930$	−79.5465	−2.60843
$931$	−19.9191	−0.652821
$932$	15.3014	0.501215
$933$	24.9768	0.817705
$934$	6.80338	0.222613
$935$	96.8988	3.16893
$936$	30.1786	0.986418
$937$	14.1083	0.460897	0.230448	−	0.973085i	$-0.425981\pi$
$937$	14.1083	0.460897	0.230448	+	0.973085i	$0.425981\pi$
$938$	45.0118	1.46969
$939$	11.1764	0.364729
$940$	143.305	4.67409
$941$	−5.39168	−0.175764	−0.0878819	−	0.996131i	$-0.528010\pi$
$941$	−5.39168	−0.175764	−0.0878819	+	0.996131i	$0.528010\pi$
$942$	27.3939	0.892542
$943$	−49.6996	−1.61844
$944$	−32.9612	−1.07279
$945$	−5.70085	−0.185449
$946$	−28.4315	−0.924388
$947$	38.0986	1.23804	0.619019	−	0.785376i	$-0.287531\pi$
$947$	38.0986	1.23804	0.619019	+	0.785376i	$0.287531\pi$
$948$	−41.6095	−1.35141
$949$	−33.8495	−1.09880
$950$	−51.0675	−1.65685
$951$	−16.4681	−0.534016
$952$	94.9996	3.07895
$953$	−4.42538	−0.143352	−0.0716760	−	0.997428i	$-0.522835\pi$
$953$	−4.42538	−0.143352	−0.0716760	+	0.997428i	$0.522835\pi$
$954$	−7.17263	−0.232223
$955$	−62.4883	−2.02207
$956$	98.8741	3.19782
$957$	12.5426	0.405446
$958$	79.0967	2.55550
$959$	29.0719	0.938782
$960$	14.2369	0.459494
$961$	89.6775	2.89282
$962$	−41.7358	−1.34562
$963$	−8.55484	−0.275676
$964$	31.6579	1.01963
$965$	13.9940	0.450483
$966$	−24.0570	−0.774020
$967$	43.9875	1.41454	0.707271	−	0.706943i	$-0.249926\pi$
$967$	43.9875	1.41454	0.707271	+	0.706943i	$0.249926\pi$
$968$	−116.401	−3.74125
$969$	46.4225	1.49130
$970$	−76.5454	−2.45772
$971$	−14.2149	−0.456179	−0.228089	−	0.973640i	$-0.573248\pi$
$971$	−14.2149	−0.456179	−0.228089	+	0.973640i	$0.573248\pi$
$972$	4.71742	0.151311
$973$	27.7127	0.888428
$974$	49.6853	1.59202
$975$	−12.0223	−0.385022
$976$	24.7798	0.793183
$977$	12.7374	0.407505	0.203753	−	0.979022i	$-0.434686\pi$
$977$	12.7374	0.407505	0.203753	+	0.979022i	$0.434686\pi$
$978$	−35.5291	−1.13610
$979$	−48.8698	−1.56188
$980$	−37.3838	−1.19418
$981$	3.20734	0.102402
$982$	−103.594	−3.30581
$983$	−25.6634	−0.818536	−0.409268	−	0.912414i	$-0.634216\pi$
$983$	−25.6634	−0.818536	−0.409268	+	0.912414i	$0.634216\pi$
$984$	−76.9492	−2.45305
$985$	17.2738	0.550390
$986$	−40.9582	−1.30438
$987$	−22.1862	−0.706194
$988$	−141.952	−4.51611
$989$	−9.51097	−0.302431
$990$	−37.9917	−1.20745
$991$	−38.7325	−1.23038	−0.615189	−	0.788380i	$-0.710920\pi$
$991$	−38.7325	−1.23038	−0.615189	+	0.788380i	$0.710920\pi$
$992$	−96.3587	−3.05939
$993$	−9.66997	−0.306867
$994$	−54.1216	−1.71663
$995$	−1.43390	−0.0454577
$996$	−24.3864	−0.772712
$997$	−4.61993	−0.146315	−0.0731573	−	0.997320i	$-0.523308\pi$
$997$	−4.61993	−0.146315	−0.0731573	+	0.997320i	$0.523308\pi$
$998$	−39.0374	−1.23571
$999$	−3.75808	−0.118900

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8031.2.a.d.1.8	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8031.2.a.d.1.8	✓	132	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8031 = 3 \cdot 2677 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59180 q^{2} +1.00000 q^{3} +4.71742 q^{4} +2.79387 q^{5} -2.59180 q^{6} -2.04048 q^{7} -7.04300 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.59180 q^{2} +1.00000 q^{3} +4.71742 q^{4} +2.79387 q^{5} -2.59180 q^{6} -2.04048 q^{7} -7.04300 q^{8} +1.00000 q^{9} -7.24116 q^{10} +5.24663 q^{11} +4.71742 q^{12} -4.28491 q^{13} +5.28852 q^{14} +2.79387 q^{15} +8.81919 q^{16} +6.61045 q^{17} -2.59180 q^{18} +7.02258 q^{19} +13.1799 q^{20} -2.04048 q^{21} -13.5982 q^{22} -4.54890 q^{23} -7.04300 q^{24} +2.80573 q^{25} +11.1056 q^{26} +1.00000 q^{27} -9.62581 q^{28} +2.39061 q^{29} -7.24116 q^{30} +10.9853 q^{31} -8.77157 q^{32} +5.24663 q^{33} -17.1330 q^{34} -5.70085 q^{35} +4.71742 q^{36} -3.75808 q^{37} -18.2011 q^{38} -4.28491 q^{39} -19.6773 q^{40} +10.9256 q^{41} +5.28852 q^{42} +2.09083 q^{43} +24.7505 q^{44} +2.79387 q^{45} +11.7898 q^{46} +10.8730 q^{47} +8.81919 q^{48} -2.83643 q^{49} -7.27190 q^{50} +6.61045 q^{51} -20.2137 q^{52} +2.76743 q^{53} -2.59180 q^{54} +14.6584 q^{55} +14.3711 q^{56} +7.02258 q^{57} -6.19598 q^{58} -3.73743 q^{59} +13.1799 q^{60} +2.80976 q^{61} -28.4718 q^{62} -2.04048 q^{63} +5.09576 q^{64} -11.9715 q^{65} -13.5982 q^{66} +8.51123 q^{67} +31.1843 q^{68} -4.54890 q^{69} +14.7755 q^{70} -10.2338 q^{71} -7.04300 q^{72} +7.89970 q^{73} +9.74019 q^{74} +2.80573 q^{75} +33.1285 q^{76} -10.7057 q^{77} +11.1056 q^{78} -8.82039 q^{79} +24.6397 q^{80} +1.00000 q^{81} -28.3170 q^{82} -5.16944 q^{83} -9.62581 q^{84} +18.4688 q^{85} -5.41900 q^{86} +2.39061 q^{87} -36.9520 q^{88} -9.31451 q^{89} -7.24116 q^{90} +8.74328 q^{91} -21.4591 q^{92} +10.9853 q^{93} -28.1807 q^{94} +19.6202 q^{95} -8.77157 q^{96} +10.5709 q^{97} +7.35145 q^{98} +5.24663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 4 q^{2} + 132 q^{3} + 156 q^{4} + 20 q^{5} + 4 q^{6} + 44 q^{7} + 9 q^{8} + 132 q^{9}+O(q^{10}) \) 132 * q + 4 * q^2 + 132 * q^3 + 156 * q^4 + 20 * q^5 + 4 * q^6 + 44 * q^7 + 9 * q^8 + 132 * q^9	\( 132 q + 4 q^{2} + 132 q^{3} + 156 q^{4} + 20 q^{5} + 4 q^{6} + 44 q^{7} + 9 q^{8} + 132 q^{9} + 40 q^{10} + 24 q^{11} + 156 q^{12} + 62 q^{13} + 25 q^{14} + 20 q^{15} + 192 q^{16} + 77 q^{17} + 4 q^{18} + 86 q^{19} + 26 q^{20} + 44 q^{21} + 52 q^{22} + 17 q^{23} + 9 q^{24} + 212 q^{25} + 13 q^{26} + 132 q^{27} + 95 q^{28} + 52 q^{29} + 40 q^{30} + 59 q^{31} - 8 q^{32} + 24 q^{33} + 41 q^{34} + 21 q^{35} + 156 q^{36} + 76 q^{37} + 2 q^{38} + 62 q^{39} + 91 q^{40} + 114 q^{41} + 25 q^{42} + 173 q^{43} + 44 q^{44} + 20 q^{45} + 48 q^{46} + 15 q^{47} + 192 q^{48} + 262 q^{49} - 9 q^{50} + 77 q^{51} + 144 q^{52} + 15 q^{53} + 4 q^{54} + 111 q^{55} + 66 q^{56} + 86 q^{57} + 33 q^{58} + 20 q^{59} + 26 q^{60} + 182 q^{61} + 16 q^{62} + 44 q^{63} + 255 q^{64} + 70 q^{65} + 52 q^{66} + 169 q^{67} + 128 q^{68} + 17 q^{69} + 2 q^{70} + 23 q^{71} + 9 q^{72} + 148 q^{73} + 57 q^{74} + 212 q^{75} + 143 q^{76} + 31 q^{77} + 13 q^{78} + 152 q^{79} + 27 q^{80} + 132 q^{81} + 67 q^{82} + 28 q^{83} + 95 q^{84} + 88 q^{85} - 10 q^{86} + 52 q^{87} + 130 q^{88} + 136 q^{89} + 40 q^{90} + 125 q^{91} + 59 q^{93} + 95 q^{94} + 2 q^{95} - 8 q^{96} + 147 q^{97} - 18 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q + 4 * q^2 + 132 * q^3 + 156 * q^4 + 20 * q^5 + 4 * q^6 + 44 * q^7 + 9 * q^8 + 132 * q^9 + 40 * q^10 + 24 * q^11 + 156 * q^12 + 62 * q^13 + 25 * q^14 + 20 * q^15 + 192 * q^16 + 77 * q^17 + 4 * q^18 + 86 * q^19 + 26 * q^20 + 44 * q^21 + 52 * q^22 + 17 * q^23 + 9 * q^24 + 212 * q^25 + 13 * q^26 + 132 * q^27 + 95 * q^28 + 52 * q^29 + 40 * q^30 + 59 * q^31 - 8 * q^32 + 24 * q^33 + 41 * q^34 + 21 * q^35 + 156 * q^36 + 76 * q^37 + 2 * q^38 + 62 * q^39 + 91 * q^40 + 114 * q^41 + 25 * q^42 + 173 * q^43 + 44 * q^44 + 20 * q^45 + 48 * q^46 + 15 * q^47 + 192 * q^48 + 262 * q^49 - 9 * q^50 + 77 * q^51 + 144 * q^52 + 15 * q^53 + 4 * q^54 + 111 * q^55 + 66 * q^56 + 86 * q^57 + 33 * q^58 + 20 * q^59 + 26 * q^60 + 182 * q^61 + 16 * q^62 + 44 * q^63 + 255 * q^64 + 70 * q^65 + 52 * q^66 + 169 * q^67 + 128 * q^68 + 17 * q^69 + 2 * q^70 + 23 * q^71 + 9 * q^72 + 148 * q^73 + 57 * q^74 + 212 * q^75 + 143 * q^76 + 31 * q^77 + 13 * q^78 + 152 * q^79 + 27 * q^80 + 132 * q^81 + 67 * q^82 + 28 * q^83 + 95 * q^84 + 88 * q^85 - 10 * q^86 + 52 * q^87 + 130 * q^88 + 136 * q^89 + 40 * q^90 + 125 * q^91 + 59 * q^93 + 95 * q^94 + 2 * q^95 - 8 * q^96 + 147 * q^97 - 18 * q^98 + 24 * q^99

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