LMFDB - Embedded newform 1511.2.a.b.1.71

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1511,2,Mod(1,1511)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1511, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1511.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1511 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1511.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:	$12.0653957454$
Analytic rank:	$0$
Dimension:	$87$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.71
Character	$\chi$	$=$	1511.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.15574 q^{2} +2.75955 q^{3} +2.64722 q^{4} -0.234559 q^{5} +5.94888 q^{6} +2.87993 q^{7} +1.39523 q^{8} +4.61514 q^{9} +O(q^{10})$	\(q+2.15574 q^{2} +2.75955 q^{3} +2.64722 q^{4} -0.234559 q^{5} +5.94888 q^{6} +2.87993 q^{7} +1.39523 q^{8} +4.61514 q^{9} -0.505649 q^{10} -4.24089 q^{11} +7.30514 q^{12} +4.71331 q^{13} +6.20839 q^{14} -0.647280 q^{15} -2.28668 q^{16} -5.25937 q^{17} +9.94905 q^{18} -3.09715 q^{19} -0.620930 q^{20} +7.94733 q^{21} -9.14226 q^{22} +7.80043 q^{23} +3.85022 q^{24} -4.94498 q^{25} +10.1607 q^{26} +4.45707 q^{27} +7.62380 q^{28} -6.89503 q^{29} -1.39537 q^{30} +5.75873 q^{31} -7.71994 q^{32} -11.7030 q^{33} -11.3378 q^{34} -0.675515 q^{35} +12.2173 q^{36} -8.80947 q^{37} -6.67664 q^{38} +13.0066 q^{39} -0.327265 q^{40} +2.07953 q^{41} +17.1324 q^{42} +7.16022 q^{43} -11.2266 q^{44} -1.08253 q^{45} +16.8157 q^{46} -0.282179 q^{47} -6.31021 q^{48} +1.29401 q^{49} -10.6601 q^{50} -14.5135 q^{51} +12.4771 q^{52} +12.1004 q^{53} +9.60830 q^{54} +0.994740 q^{55} +4.01817 q^{56} -8.54674 q^{57} -14.8639 q^{58} -1.33904 q^{59} -1.71349 q^{60} -0.140432 q^{61} +12.4143 q^{62} +13.2913 q^{63} -12.0688 q^{64} -1.10555 q^{65} -25.2286 q^{66} -6.33900 q^{67} -13.9227 q^{68} +21.5257 q^{69} -1.45624 q^{70} -6.24925 q^{71} +6.43919 q^{72} -15.2454 q^{73} -18.9909 q^{74} -13.6459 q^{75} -8.19882 q^{76} -12.2135 q^{77} +28.0389 q^{78} +13.4970 q^{79} +0.536362 q^{80} -1.54589 q^{81} +4.48294 q^{82} +9.79512 q^{83} +21.0383 q^{84} +1.23364 q^{85} +15.4356 q^{86} -19.0272 q^{87} -5.91702 q^{88} +14.4022 q^{89} -2.33364 q^{90} +13.5740 q^{91} +20.6494 q^{92} +15.8915 q^{93} -0.608305 q^{94} +0.726465 q^{95} -21.3036 q^{96} -2.48622 q^{97} +2.78954 q^{98} -19.5723 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 87 q + 6 q^{2} + 4 q^{3} + 110 q^{4} + 10 q^{5} + 8 q^{6} + 21 q^{7} + 15 q^{8} + 133 q^{9}+O(q^{10}) $ 87 * q + 6 * q^2 + 4 * q^3 + 110 * q^4 + 10 * q^5 + 8 * q^6 + 21 * q^7 + 15 * q^8 + 133 * q^9	\( 87 q + 6 q^{2} + 4 q^{3} + 110 q^{4} + 10 q^{5} + 8 q^{6} + 21 q^{7} + 15 q^{8} + 133 q^{9} + 25 q^{10} + 17 q^{11} + 34 q^{13} + 12 q^{14} + 16 q^{15} + 152 q^{16} + 32 q^{17} + 14 q^{18} + 56 q^{19} + 3 q^{20} + 38 q^{21} + 32 q^{22} + 8 q^{23} + 8 q^{24} + 179 q^{25} + 11 q^{26} - 2 q^{27} + 45 q^{28} + 40 q^{29} + 24 q^{30} + 31 q^{31} + 26 q^{32} + 31 q^{33} + 31 q^{34} + 22 q^{35} + 180 q^{36} + 35 q^{37} - 15 q^{38} + 59 q^{39} + 42 q^{40} + 45 q^{41} - 30 q^{42} + 82 q^{43} + 25 q^{44} + 20 q^{45} + 69 q^{46} - 7 q^{47} - 39 q^{48} + 222 q^{49} + 17 q^{50} + 53 q^{51} + 54 q^{52} + 16 q^{53} - 7 q^{54} + 49 q^{55} + 12 q^{56} + 52 q^{57} + 17 q^{58} - 7 q^{59} - 6 q^{60} + 131 q^{61} - 8 q^{62} + 19 q^{63} + 213 q^{64} + 57 q^{65} + 17 q^{66} + 38 q^{67} + 13 q^{68} + 45 q^{69} - 5 q^{71} + 4 q^{72} + 91 q^{73} + q^{74} - 44 q^{75} + 150 q^{76} + 5 q^{77} - 87 q^{78} + 120 q^{79} - 41 q^{80} + 247 q^{81} + 20 q^{82} - 33 q^{83} - 16 q^{84} + 110 q^{85} - 22 q^{86} - 13 q^{87} + 78 q^{88} + 53 q^{89} - 33 q^{90} + 32 q^{91} - 31 q^{92} + 13 q^{93} + 79 q^{94} - 25 q^{95} - 51 q^{96} + 92 q^{97} - 36 q^{98} + 35 q^{99}+O(q^{100}) \) 87 * q + 6 * q^2 + 4 * q^3 + 110 * q^4 + 10 * q^5 + 8 * q^6 + 21 * q^7 + 15 * q^8 + 133 * q^9 + 25 * q^10 + 17 * q^11 + 34 * q^13 + 12 * q^14 + 16 * q^15 + 152 * q^16 + 32 * q^17 + 14 * q^18 + 56 * q^19 + 3 * q^20 + 38 * q^21 + 32 * q^22 + 8 * q^23 + 8 * q^24 + 179 * q^25 + 11 * q^26 - 2 * q^27 + 45 * q^28 + 40 * q^29 + 24 * q^30 + 31 * q^31 + 26 * q^32 + 31 * q^33 + 31 * q^34 + 22 * q^35 + 180 * q^36 + 35 * q^37 - 15 * q^38 + 59 * q^39 + 42 * q^40 + 45 * q^41 - 30 * q^42 + 82 * q^43 + 25 * q^44 + 20 * q^45 + 69 * q^46 - 7 * q^47 - 39 * q^48 + 222 * q^49 + 17 * q^50 + 53 * q^51 + 54 * q^52 + 16 * q^53 - 7 * q^54 + 49 * q^55 + 12 * q^56 + 52 * q^57 + 17 * q^58 - 7 * q^59 - 6 * q^60 + 131 * q^61 - 8 * q^62 + 19 * q^63 + 213 * q^64 + 57 * q^65 + 17 * q^66 + 38 * q^67 + 13 * q^68 + 45 * q^69 - 5 * q^71 + 4 * q^72 + 91 * q^73 + q^74 - 44 * q^75 + 150 * q^76 + 5 * q^77 - 87 * q^78 + 120 * q^79 - 41 * q^80 + 247 * q^81 + 20 * q^82 - 33 * q^83 - 16 * q^84 + 110 * q^85 - 22 * q^86 - 13 * q^87 + 78 * q^88 + 53 * q^89 - 33 * q^90 + 32 * q^91 - 31 * q^92 + 13 * q^93 + 79 * q^94 - 25 * q^95 - 51 * q^96 + 92 * q^97 - 36 * q^98 + 35 * 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 $

$2$	2.15574	1.52434	0.762169	−	0.647378i	$-0.224134\pi$
$2$	2.15574	1.52434	0.762169	+	0.647378i	$0.224134\pi$
$3$	2.75955	1.59323	0.796615	−	0.604487i	$-0.206622\pi$
$3$	2.75955	1.59323	0.796615	+	0.604487i	$0.206622\pi$
$4$	2.64722	1.32361
$5$	−0.234559	−0.104898	−0.0524491	−	0.998624i	$-0.516703\pi$
$5$	−0.234559	−0.104898	−0.0524491	+	0.998624i	$0.516703\pi$
$6$	5.94888	2.42862
$7$	2.87993	1.08851	0.544256	−	0.838919i	$-0.316812\pi$
$7$	2.87993	1.08851	0.544256	+	0.838919i	$0.316812\pi$
$8$	1.39523	0.493289
$9$	4.61514	1.53838
$10$	−0.505649	−0.159900
$11$	−4.24089	−1.27868	−0.639338	−	0.768926i	$-0.720792\pi$
$11$	−4.24089	−1.27868	−0.639338	+	0.768926i	$0.720792\pi$
$12$	7.30514	2.10881
$13$	4.71331	1.30724	0.653618	−	0.756825i	$-0.273250\pi$
$13$	4.71331	1.30724	0.653618	+	0.756825i	$0.273250\pi$
$14$	6.20839	1.65926
$15$	−0.647280	−0.167127
$16$	−2.28668	−0.571669
$17$	−5.25937	−1.27559	−0.637793	−	0.770208i	$-0.720152\pi$
$17$	−5.25937	−1.27559	−0.637793	+	0.770208i	$0.720152\pi$
$18$	9.94905	2.34501
$19$	−3.09715	−0.710534	−0.355267	−	0.934765i	$-0.615610\pi$
$19$	−3.09715	−0.710534	−0.355267	+	0.934765i	$0.615610\pi$
$20$	−0.620930	−0.138844
$21$	7.94733	1.73425
$22$	−9.14226	−1.94914
$23$	7.80043	1.62650	0.813251	−	0.581913i	$-0.197696\pi$
$23$	7.80043	1.62650	0.813251	+	0.581913i	$0.197696\pi$
$24$	3.85022	0.785922
$25$	−4.94498	−0.988996
$26$	10.1607	1.99267
$27$	4.45707	0.857764
$28$	7.62380	1.44076
$29$	−6.89503	−1.28037	−0.640187	−	0.768219i	$-0.721143\pi$
$29$	−6.89503	−1.28037	−0.640187	+	0.768219i	$0.721143\pi$
$30$	−1.39537	−0.254758
$31$	5.75873	1.03430	0.517149	−	0.855895i	$-0.326993\pi$
$31$	5.75873	1.03430	0.517149	+	0.855895i	$0.326993\pi$
$32$	−7.71994	−1.36471
$33$	−11.7030	−2.03722
$34$	−11.3378	−1.94442
$35$	−0.675515	−0.114183
$36$	12.2173	2.03621
$37$	−8.80947	−1.44827	−0.724134	−	0.689660i	$-0.757760\pi$
$37$	−8.80947	−1.44827	−0.724134	+	0.689660i	$0.757760\pi$
$38$	−6.67664	−1.08309
$39$	13.0066	2.08273
$40$	−0.327265	−0.0517451
$41$	2.07953	0.324769	0.162384	−	0.986728i	$-0.448082\pi$
$41$	2.07953	0.324769	0.162384	+	0.986728i	$0.448082\pi$
$42$	17.1324	2.64358
$43$	7.16022	1.09192	0.545962	−	0.837810i	$-0.316164\pi$
$43$	7.16022	1.09192	0.545962	+	0.837810i	$0.316164\pi$
$44$	−11.2266	−1.69247
$45$	−1.08253	−0.161373
$46$	16.8157	2.47934
$47$	−0.282179	−0.0411601	−0.0205800	−	0.999788i	$-0.506551\pi$
$47$	−0.282179	−0.0411601	−0.0205800	+	0.999788i	$0.506551\pi$
$48$	−6.31021	−0.910800
$49$	1.29401	0.184858
$50$	−10.6601	−1.50757
$51$	−14.5135	−2.03230
$52$	12.4771	1.73027
$53$	12.1004	1.66211	0.831057	−	0.556187i	$-0.187736\pi$
$53$	12.1004	1.66211	0.831057	+	0.556187i	$0.187736\pi$
$54$	9.60830	1.30752
$55$	0.994740	0.134131
$56$	4.01817	0.536951
$57$	−8.54674	−1.13204
$58$	−14.8639	−1.95172
$59$	−1.33904	−0.174328	−0.0871641	−	0.996194i	$-0.527780\pi$
$59$	−1.33904	−0.174328	−0.0871641	+	0.996194i	$0.527780\pi$
$60$	−1.71349	−0.221211
$61$	−0.140432	−0.0179805	−0.00899025	−	0.999960i	$-0.502862\pi$
$61$	−0.140432	−0.0179805	−0.00899025	+	0.999960i	$0.502862\pi$
$62$	12.4143	1.57662
$63$	13.2913	1.67455
$64$	−12.0688	−1.50861
$65$	−1.10555	−0.137127
$66$	−25.2286	−3.10542
$67$	−6.33900	−0.774432	−0.387216	−	0.921989i	$-0.626563\pi$
$67$	−6.33900	−0.774432	−0.387216	+	0.921989i	$0.626563\pi$
$68$	−13.9227	−1.68838
$69$	21.5257	2.59139
$70$	−1.45624	−0.174053
$71$	−6.24925	−0.741649	−0.370825	−	0.928703i	$-0.620925\pi$
$71$	−6.24925	−0.741649	−0.370825	+	0.928703i	$0.620925\pi$
$72$	6.43919	0.758866
$73$	−15.2454	−1.78434	−0.892168	−	0.451704i	$-0.850816\pi$
$73$	−15.2454	−1.78434	−0.892168	+	0.451704i	$0.850816\pi$
$74$	−18.9909	−2.20765
$75$	−13.6459	−1.57570
$76$	−8.19882	−0.940469
$77$	−12.2135	−1.39185
$78$	28.0389	3.17478
$79$	13.4970	1.51853	0.759266	−	0.650780i	$-0.225558\pi$
$79$	13.4970	1.51853	0.759266	+	0.650780i	$0.225558\pi$
$80$	0.536362	0.0599670
$81$	−1.54589	−0.171765
$82$	4.48294	0.495057
$83$	9.79512	1.07515	0.537577	−	0.843215i	$-0.319340\pi$
$83$	9.79512	1.07515	0.537577	+	0.843215i	$0.319340\pi$
$84$	21.0383	2.29547
$85$	1.23364	0.133807
$86$	15.4356	1.66446
$87$	−19.0272	−2.03993
$88$	−5.91702	−0.630757
$89$	14.4022	1.52663	0.763313	−	0.646029i	$-0.223571\pi$
$89$	14.4022	1.52663	0.763313	+	0.646029i	$0.223571\pi$
$90$	−2.33364	−0.245988
$91$	13.5740	1.42294
$92$	20.6494	2.15285
$93$	15.8915	1.64787
$94$	−0.608305	−0.0627419
$95$	0.726465	0.0745337
$96$	−21.3036	−2.17429
$97$	−2.48622	−0.252437	−0.126219	−	0.992002i	$-0.540284\pi$
$97$	−2.48622	−0.252437	−0.126219	+	0.992002i	$0.540284\pi$
$98$	2.78954	0.281787
$99$	−19.5723	−1.96709
$100$	−13.0904	−1.30904
$101$	9.72920	0.968092	0.484046	−	0.875043i	$-0.339167\pi$
$101$	9.72920	0.968092	0.484046	+	0.875043i	$0.339167\pi$
$102$	−31.2874	−3.09791
$103$	17.7550	1.74945	0.874725	−	0.484620i	$-0.161042\pi$
$103$	17.7550	1.74945	0.874725	+	0.484620i	$0.161042\pi$
$104$	6.57615	0.644845
$105$	−1.86412	−0.181920
$106$	26.0853	2.53362
$107$	−16.4846	−1.59363	−0.796814	−	0.604224i	$-0.793483\pi$
$107$	−16.4846	−1.59363	−0.796814	+	0.604224i	$0.793483\pi$
$108$	11.7988	1.13534
$109$	−0.889025	−0.0851531	−0.0425766	−	0.999093i	$-0.513557\pi$
$109$	−0.889025	−0.0851531	−0.0425766	+	0.999093i	$0.513557\pi$
$110$	2.14440	0.204461
$111$	−24.3102	−2.30742
$112$	−6.58547	−0.622269
$113$	−14.8639	−1.39827	−0.699137	−	0.714987i	$-0.746432\pi$
$113$	−14.8639	−1.39827	−0.699137	+	0.714987i	$0.746432\pi$
$114$	−18.4246	−1.72562
$115$	−1.82966	−0.170617
$116$	−18.2526	−1.69471
$117$	21.7526	2.01103
$118$	−2.88662	−0.265735
$119$	−15.1466	−1.38849
$120$	−0.903105	−0.0824418
$121$	6.98514	0.635012
$122$	−0.302735	−0.0274084
$123$	5.73859	0.517431
$124$	15.2446	1.36901
$125$	2.33269	0.208642
$126$	28.6526	2.55258
$127$	20.2164	1.79391	0.896956	−	0.442120i	$-0.145773\pi$
$127$	20.2164	1.79391	0.896956	+	0.442120i	$0.145773\pi$
$128$	−10.5774	−0.934919
$129$	19.7590	1.73969
$130$	−2.38328	−0.209027
$131$	−8.85552	−0.773711	−0.386855	−	0.922140i	$-0.626439\pi$
$131$	−8.85552	−0.773711	−0.386855	+	0.922140i	$0.626439\pi$
$132$	−30.9803	−2.69649
$133$	−8.91957	−0.773425
$134$	−13.6652	−1.18050
$135$	−1.04545	−0.0899779
$136$	−7.33804	−0.629232
$137$	3.68741	0.315037	0.157519	−	0.987516i	$-0.449651\pi$
$137$	3.68741	0.315037	0.157519	+	0.987516i	$0.449651\pi$
$138$	46.4039	3.95016
$139$	−5.65814	−0.479918	−0.239959	−	0.970783i	$-0.577134\pi$
$139$	−5.65814	−0.479918	−0.239959	+	0.970783i	$0.577134\pi$
$140$	−1.78824	−0.151133
$141$	−0.778689	−0.0655774
$142$	−13.4718	−1.13052
$143$	−19.9886	−1.67153
$144$	−10.5533	−0.879445
$145$	1.61729	0.134309
$146$	−32.8651	−2.71993
$147$	3.57089	0.294522
$148$	−23.3206	−1.91694
$149$	−4.64951	−0.380903	−0.190451	−	0.981697i	$-0.560995\pi$
$149$	−4.64951	−0.380903	−0.190451	+	0.981697i	$0.560995\pi$
$150$	−29.4171	−2.40190
$151$	10.8951	0.886634	0.443317	−	0.896365i	$-0.353802\pi$
$151$	10.8951	0.886634	0.443317	+	0.896365i	$0.353802\pi$
$152$	−4.32124	−0.350499
$153$	−24.2728	−1.96234
$154$	−26.3291	−2.12166
$155$	−1.35076	−0.108496
$156$	34.4314	2.75672
$157$	14.7917	1.18051	0.590254	−	0.807218i	$-0.299028\pi$
$157$	14.7917	1.18051	0.590254	+	0.807218i	$0.299028\pi$
$158$	29.0961	2.31476
$159$	33.3916	2.64813
$160$	1.81079	0.143155
$161$	22.4647	1.77047
$162$	−3.33253	−0.261828
$163$	−3.32135	−0.260149	−0.130074	−	0.991504i	$-0.541522\pi$
$163$	−3.32135	−0.260149	−0.130074	+	0.991504i	$0.541522\pi$
$164$	5.50498	0.429867
$165$	2.74504	0.213701
$166$	21.1157	1.63890
$167$	−14.4762	−1.12021	−0.560103	−	0.828423i	$-0.689238\pi$
$167$	−14.4762	−1.12021	−0.560103	+	0.828423i	$0.689238\pi$
$168$	11.0884	0.855486
$169$	9.21526	0.708866
$170$	2.65940	0.203966
$171$	−14.2938	−1.09307
$172$	18.9547	1.44528
$173$	−3.79073	−0.288204	−0.144102	−	0.989563i	$-0.546029\pi$
$173$	−3.79073	−0.288204	−0.144102	+	0.989563i	$0.546029\pi$
$174$	−41.0177	−3.10955
$175$	−14.2412	−1.07653
$176$	9.69754	0.730980
$177$	−3.69515	−0.277745
$178$	31.0473	2.32710
$179$	−21.8241	−1.63121	−0.815605	−	0.578609i	$-0.803596\pi$
$179$	−21.8241	−1.63121	−0.815605	+	0.578609i	$0.803596\pi$
$180$	−2.86568	−0.213595
$181$	7.69172	0.571721	0.285861	−	0.958271i	$-0.407721\pi$
$181$	7.69172	0.571721	0.285861	+	0.958271i	$0.407721\pi$
$182$	29.2620	2.16905
$183$	−0.387530	−0.0286471
$184$	10.8834	0.802335
$185$	2.06634	0.151921
$186$	34.2580	2.51192
$187$	22.3044	1.63106
$188$	−0.746990	−0.0544798
$189$	12.8361	0.933687
$190$	1.56607	0.113615
$191$	−14.0755	−1.01847	−0.509233	−	0.860629i	$-0.670071\pi$
$191$	−14.0755	−1.01847	−0.509233	+	0.860629i	$0.670071\pi$
$192$	−33.3046	−2.40355
$193$	8.70731	0.626766	0.313383	−	0.949627i	$-0.398538\pi$
$193$	8.70731	0.626766	0.313383	+	0.949627i	$0.398538\pi$
$194$	−5.35964	−0.384800
$195$	−3.05083	−0.218474
$196$	3.42552	0.244680
$197$	−12.1820	−0.867934	−0.433967	−	0.900929i	$-0.642887\pi$
$197$	−12.1820	−0.867934	−0.433967	+	0.900929i	$0.642887\pi$
$198$	−42.1928	−2.99851
$199$	1.59420	0.113010	0.0565049	−	0.998402i	$-0.482004\pi$
$199$	1.59420	0.113010	0.0565049	+	0.998402i	$0.482004\pi$
$200$	−6.89939	−0.487861
$201$	−17.4928	−1.23385
$202$	20.9736	1.47570
$203$	−19.8572	−1.39370
$204$	−38.4204	−2.68997
$205$	−0.487774	−0.0340676
$206$	38.2751	2.66675
$207$	36.0001	2.50218
$208$	−10.7778	−0.747307
$209$	13.1347	0.908543
$210$	−4.01856	−0.277307
$211$	16.7166	1.15082	0.575410	−	0.817865i	$-0.304842\pi$
$211$	16.7166	1.15082	0.575410	+	0.817865i	$0.304842\pi$
$212$	32.0323	2.19999
$213$	−17.2451	−1.18162
$214$	−35.5366	−2.42923
$215$	−1.67950	−0.114541
$216$	6.21865	0.423126
$217$	16.5847	1.12585
$218$	−1.91651	−0.129802
$219$	−42.0704	−2.84286
$220$	2.63329	0.177537
$221$	−24.7890	−1.66749
$222$	−52.4065	−3.51729
$223$	17.8319	1.19411	0.597056	−	0.802199i	$-0.296337\pi$
$223$	17.8319	1.19411	0.597056	+	0.802199i	$0.296337\pi$
$224$	−22.2329	−1.48550
$225$	−22.8218	−1.52145
$226$	−32.0426	−2.13144
$227$	26.6291	1.76744	0.883718	−	0.468021i	$-0.155033\pi$
$227$	26.6291	1.76744	0.883718	+	0.468021i	$0.155033\pi$
$228$	−22.6251	−1.49838
$229$	−13.7027	−0.905501	−0.452750	−	0.891637i	$-0.649557\pi$
$229$	−13.7027	−0.905501	−0.452750	+	0.891637i	$0.649557\pi$
$230$	−3.94428	−0.260078
$231$	−33.7037	−2.21754
$232$	−9.62016	−0.631594
$233$	−12.0605	−0.790111	−0.395055	−	0.918657i	$-0.629275\pi$
$233$	−12.0605	−0.790111	−0.395055	+	0.918657i	$0.629275\pi$
$234$	46.8929	3.06549
$235$	0.0661878	0.00431762
$236$	−3.54473	−0.230742
$237$	37.2458	2.41937
$238$	−32.6522	−2.11653
$239$	−20.9999	−1.35837	−0.679186	−	0.733966i	$-0.737667\pi$
$239$	−20.9999	−1.35837	−0.679186	+	0.733966i	$0.737667\pi$
$240$	1.48012	0.0955413
$241$	−8.69830	−0.560307	−0.280153	−	0.959955i	$-0.590385\pi$
$241$	−8.69830	−0.560307	−0.280153	+	0.959955i	$0.590385\pi$
$242$	15.0581	0.967974
$243$	−17.6372	−1.13143
$244$	−0.371754	−0.0237991
$245$	−0.303522	−0.0193913
$246$	12.3709	0.788740
$247$	−14.5978	−0.928836
$248$	8.03476	0.510208
$249$	27.0302	1.71297
$250$	5.02867	0.318041
$251$	20.1109	1.26939	0.634693	−	0.772764i	$-0.281127\pi$
$251$	20.1109	1.26939	0.634693	+	0.772764i	$0.281127\pi$
$252$	35.1849	2.21644
$253$	−33.0808	−2.07977
$254$	43.5812	2.73453
$255$	3.40428	0.213185
$256$	1.33555	0.0834717
$257$	−13.3480	−0.832624	−0.416312	−	0.909222i	$-0.636678\pi$
$257$	−13.3480	−0.832624	−0.416312	+	0.909222i	$0.636678\pi$
$258$	42.5953	2.65187
$259$	−25.3707	−1.57646
$260$	−2.92663	−0.181502
$261$	−31.8215	−1.96970
$262$	−19.0902	−1.17940
$263$	28.9049	1.78235	0.891176	−	0.453658i	$-0.149881\pi$
$263$	28.9049	1.78235	0.891176	+	0.453658i	$0.149881\pi$
$264$	−16.3283	−1.00494
$265$	−2.83826	−0.174353
$266$	−19.2283	−1.17896
$267$	39.7436	2.43227
$268$	−16.7807	−1.02504
$269$	−18.3489	−1.11875	−0.559375	−	0.828915i	$-0.688959\pi$
$269$	−18.3489	−1.11875	−0.559375	+	0.828915i	$0.688959\pi$
$270$	−2.25372	−0.137157
$271$	2.82699	0.171728	0.0858639	−	0.996307i	$-0.472635\pi$
$271$	2.82699	0.171728	0.0858639	+	0.996307i	$0.472635\pi$
$272$	12.0265	0.729213
$273$	37.4582	2.26707
$274$	7.94911	0.480223
$275$	20.9711	1.26461
$276$	56.9832	3.42999
$277$	24.3168	1.46105	0.730527	−	0.682884i	$-0.239274\pi$
$277$	24.3168	1.46105	0.730527	+	0.682884i	$0.239274\pi$
$278$	−12.1975	−0.731557
$279$	26.5774	1.59114
$280$	−0.942500	−0.0563252
$281$	1.31466	0.0784259	0.0392130	−	0.999231i	$-0.487515\pi$
$281$	1.31466	0.0784259	0.0392130	+	0.999231i	$0.487515\pi$
$282$	−1.67865	−0.0999622
$283$	−19.0164	−1.13041	−0.565204	−	0.824951i	$-0.691202\pi$
$283$	−19.0164	−1.13041	−0.565204	+	0.824951i	$0.691202\pi$
$284$	−16.5431	−0.981653
$285$	2.00472	0.118749
$286$	−43.0902	−2.54798
$287$	5.98892	0.353515
$288$	−35.6286	−2.09944
$289$	10.6610	0.627117
$290$	3.48647	0.204732
$291$	−6.86086	−0.402191
$292$	−40.3578	−2.36176
$293$	25.3364	1.48017	0.740084	−	0.672514i	$-0.234786\pi$
$293$	25.3364	1.48017	0.740084	+	0.672514i	$0.234786\pi$
$294$	7.69790	0.448951
$295$	0.314084	0.0182867
$296$	−12.2912	−0.714414
$297$	−18.9020	−1.09680
$298$	−10.0231	−0.580625
$299$	36.7658	2.12622
$300$	−36.1238	−2.08561
$301$	20.6210	1.18857
$302$	23.4871	1.35153
$303$	26.8483	1.54239
$304$	7.08217	0.406190
$305$	0.0329397	0.00188612
$306$	−52.3257	−2.99126
$307$	−0.174343	−0.00995028	−0.00497514	−	0.999988i	$-0.501584\pi$
$307$	−0.174343	−0.00995028	−0.00497514	+	0.999988i	$0.501584\pi$
$308$	−32.3317	−1.84227
$309$	48.9958	2.78728
$310$	−2.91190	−0.165385
$311$	0.118373	0.00671230	0.00335615	−	0.999994i	$-0.498932\pi$
$311$	0.118373	0.00671230	0.00335615	+	0.999994i	$0.498932\pi$
$312$	18.1473	1.02739
$313$	3.75382	0.212179	0.106089	−	0.994357i	$-0.466167\pi$
$313$	3.75382	0.212179	0.106089	+	0.994357i	$0.466167\pi$
$314$	31.8871	1.79949
$315$	−3.11760	−0.175657
$316$	35.7295	2.00994
$317$	−30.0234	−1.68628	−0.843140	−	0.537694i	$-0.819295\pi$
$317$	−30.0234	−1.68628	−0.843140	+	0.537694i	$0.819295\pi$
$318$	71.9837	4.03665
$319$	29.2410	1.63718
$320$	2.83086	0.158250
$321$	−45.4902	−2.53902
$322$	48.4281	2.69879
$323$	16.2890	0.906347
$324$	−4.09230	−0.227350
$325$	−23.3072	−1.29285
$326$	−7.15998	−0.396554
$327$	−2.45331	−0.135669
$328$	2.90143	0.160205
$329$	−0.812657	−0.0448032
$330$	5.91759	0.325753
$331$	−7.56378	−0.415743	−0.207871	−	0.978156i	$-0.566654\pi$
$331$	−7.56378	−0.415743	−0.207871	+	0.978156i	$0.566654\pi$
$332$	25.9298	1.42308
$333$	−40.6569	−2.22799
$334$	−31.2070	−1.70757
$335$	1.48687	0.0812365
$336$	−18.1730	−0.991417
$337$	29.4742	1.60556	0.802782	−	0.596273i	$-0.203352\pi$
$337$	29.4742	1.60556	0.802782	+	0.596273i	$0.203352\pi$
$338$	19.8657	1.08055
$339$	−41.0177	−2.22777
$340$	3.26570	0.177107
$341$	−24.4221	−1.32253
$342$	−30.8137	−1.66621
$343$	−16.4329	−0.887292
$344$	9.99017	0.538634
$345$	−5.04906	−0.271832
$346$	−8.17182	−0.439320
$347$	24.3932	1.30950	0.654749	−	0.755847i	$-0.272774\pi$
$347$	24.3932	1.30950	0.654749	+	0.755847i	$0.272774\pi$
$348$	−50.3691	−2.70007
$349$	26.3935	1.41281	0.706406	−	0.707807i	$-0.250315\pi$
$349$	26.3935	1.41281	0.706406	+	0.707807i	$0.250315\pi$
$350$	−30.7004	−1.64100
$351$	21.0076	1.12130
$352$	32.7394	1.74502
$353$	−5.64131	−0.300257	−0.150128	−	0.988667i	$-0.547969\pi$
$353$	−5.64131	−0.300257	−0.150128	+	0.988667i	$0.547969\pi$
$354$	−7.96579	−0.423377
$355$	1.46582	0.0777976
$356$	38.1256	2.02066
$357$	−41.7980	−2.21218
$358$	−47.0471	−2.48652
$359$	−29.0655	−1.53402	−0.767010	−	0.641635i	$-0.778256\pi$
$359$	−29.0655	−1.53402	−0.767010	+	0.641635i	$0.778256\pi$
$360$	−1.51037	−0.0796037
$361$	−9.40769	−0.495141
$362$	16.5814	0.871497
$363$	19.2759	1.01172
$364$	35.9333	1.88342
$365$	3.57594	0.187174
$366$	−0.835415	−0.0436678
$367$	18.2593	0.953130	0.476565	−	0.879139i	$-0.341882\pi$
$367$	18.2593	0.953130	0.476565	+	0.879139i	$0.341882\pi$
$368$	−17.8371	−0.929821
$369$	9.59735	0.499618
$370$	4.45450	0.231578
$371$	34.8482	1.80923
$372$	42.0683	2.18114
$373$	18.1110	0.937755	0.468877	−	0.883263i	$-0.344659\pi$
$373$	18.1110	0.937755	0.468877	+	0.883263i	$0.344659\pi$
$374$	48.0825	2.48629
$375$	6.43718	0.332415
$376$	−0.393705	−0.0203038
$377$	−32.4984	−1.67375
$378$	27.6712	1.42325
$379$	26.3522	1.35362	0.676811	−	0.736157i	$-0.263361\pi$
$379$	26.3522	1.35362	0.676811	+	0.736157i	$0.263361\pi$
$380$	1.92311	0.0986535
$381$	55.7881	2.85811
$382$	−30.3431	−1.55249
$383$	15.1818	0.775755	0.387877	−	0.921711i	$-0.373208\pi$
$383$	15.1818	0.775755	0.387877	+	0.921711i	$0.373208\pi$
$384$	−29.1889	−1.48954
$385$	2.86478	0.146003
$386$	18.7707	0.955403
$387$	33.0454	1.67979
$388$	−6.58156	−0.334128
$389$	−37.1663	−1.88441	−0.942203	−	0.335044i	$-0.891249\pi$
$389$	−37.1663	−1.88441	−0.942203	+	0.335044i	$0.891249\pi$
$390$	−6.57679	−0.333029
$391$	−41.0254	−2.07474
$392$	1.80544	0.0911885
$393$	−24.4373	−1.23270
$394$	−26.2613	−1.32303
$395$	−3.16585	−0.159291
$396$	−51.8121	−2.60366
$397$	−7.35323	−0.369048	−0.184524	−	0.982828i	$-0.559074\pi$
$397$	−7.35323	−0.369048	−0.184524	+	0.982828i	$0.559074\pi$
$398$	3.43668	0.172265
$399$	−24.6140	−1.23224
$400$	11.3076	0.565379
$401$	17.6030	0.879050	0.439525	−	0.898230i	$-0.355147\pi$
$401$	17.6030	0.879050	0.439525	+	0.898230i	$0.355147\pi$
$402$	−37.7100	−1.88080
$403$	27.1427	1.35207
$404$	25.7553	1.28137
$405$	0.362602	0.0180179
$406$	−42.8070	−2.12448
$407$	37.3600	1.85186
$408$	−20.2497	−1.00251
$409$	11.3998	0.563684	0.281842	−	0.959461i	$-0.409055\pi$
$409$	11.3998	0.563684	0.281842	+	0.959461i	$0.409055\pi$
$410$	−1.05151	−0.0519306
$411$	10.1756	0.501926
$412$	47.0013	2.31559
$413$	−3.85634	−0.189758
$414$	77.6069	3.81417
$415$	−2.29754	−0.112782
$416$	−36.3865	−1.78399
$417$	−15.6140	−0.764619
$418$	28.3149	1.38493
$419$	1.40129	0.0684577	0.0342289	−	0.999414i	$-0.489102\pi$
$419$	1.40129	0.0684577	0.0342289	+	0.999414i	$0.489102\pi$
$420$	−4.93473	−0.240790
$421$	−8.40259	−0.409517	−0.204759	−	0.978812i	$-0.565641\pi$
$421$	−8.40259	−0.409517	−0.204759	+	0.978812i	$0.565641\pi$
$422$	36.0367	1.75424
$423$	−1.30230	−0.0633199
$424$	16.8828	0.819902
$425$	26.0075	1.26155
$426$	−37.1760	−1.80119
$427$	−0.404435	−0.0195720
$428$	−43.6384	−2.10934
$429$	−55.1597	−2.66313
$430$	−3.62056	−0.174599
$431$	16.9003	0.814058	0.407029	−	0.913415i	$-0.366565\pi$
$431$	16.9003	0.814058	0.407029	+	0.913415i	$0.366565\pi$
$432$	−10.1919	−0.490357
$433$	31.1538	1.49716	0.748579	−	0.663045i	$-0.230736\pi$
$433$	31.1538	1.49716	0.748579	+	0.663045i	$0.230736\pi$
$434$	35.7524	1.71617
$435$	4.46301	0.213985
$436$	−2.35344	−0.112709
$437$	−24.1591	−1.15569
$438$	−90.6929	−4.33348
$439$	0.188002	0.00897284	0.00448642	−	0.999990i	$-0.498572\pi$
$439$	0.188002	0.00897284	0.00448642	+	0.999990i	$0.498572\pi$
$440$	1.38789	0.0661652
$441$	5.97203	0.284382
$442$	−53.4387	−2.54182
$443$	4.01664	0.190836	0.0954182	−	0.995437i	$-0.469581\pi$
$443$	4.01664	0.190836	0.0954182	+	0.995437i	$0.469581\pi$
$444$	−64.3544	−3.05412
$445$	−3.37816	−0.160140
$446$	38.4410	1.82023
$447$	−12.8306	−0.606865
$448$	−34.7574	−1.64213
$449$	11.4341	0.539607	0.269803	−	0.962915i	$-0.413041\pi$
$449$	11.4341	0.539607	0.269803	+	0.962915i	$0.413041\pi$
$450$	−49.1979	−2.31921
$451$	−8.81907	−0.415274
$452$	−39.3479	−1.85077
$453$	30.0657	1.41261
$454$	57.4054	2.69417
$455$	−3.18391	−0.149264
$456$	−11.9247	−0.558425
$457$	−39.4430	−1.84507	−0.922534	−	0.385917i	$-0.873885\pi$
$457$	−39.4430	−1.84507	−0.922534	+	0.385917i	$0.873885\pi$
$458$	−29.5395	−1.38029
$459$	−23.4414	−1.09415
$460$	−4.84352	−0.225830
$461$	−23.1324	−1.07739	−0.538693	−	0.842502i	$-0.681082\pi$
$461$	−23.1324	−1.07739	−0.538693	+	0.842502i	$0.681082\pi$
$462$	−72.6565	−3.38029
$463$	30.6938	1.42646	0.713231	−	0.700929i	$-0.247231\pi$
$463$	30.6938	1.42646	0.713231	+	0.700929i	$0.247231\pi$
$464$	15.7667	0.731951
$465$	−3.72751	−0.172859
$466$	−25.9993	−1.20440
$467$	−21.4232	−0.991348	−0.495674	−	0.868509i	$-0.665079\pi$
$467$	−21.4232	−0.991348	−0.495674	+	0.868509i	$0.665079\pi$
$468$	57.5838	2.66181
$469$	−18.2559	−0.842978
$470$	0.142684	0.00658151
$471$	40.8185	1.88082
$472$	−1.86827	−0.0859941
$473$	−30.3657	−1.39622
$474$	80.2922	3.68794
$475$	15.3153	0.702716
$476$	−40.0964	−1.83782
$477$	55.8449	2.55696
$478$	−45.2704	−2.07062
$479$	35.4080	1.61783	0.808917	−	0.587922i	$-0.200054\pi$
$479$	35.4080	1.61783	0.808917	+	0.587922i	$0.200054\pi$
$480$	4.99696	0.228079
$481$	−41.5217	−1.89323
$482$	−18.7513	−0.854097
$483$	61.9926	2.82076
$484$	18.4912	0.840508
$485$	0.583166	0.0264802
$486$	−38.0212	−1.72468
$487$	−10.3131	−0.467330	−0.233665	−	0.972317i	$-0.575072\pi$
$487$	−10.3131	−0.467330	−0.233665	+	0.972317i	$0.575072\pi$
$488$	−0.195935	−0.00886958
$489$	−9.16546	−0.414476
$490$	−0.654314	−0.0295589
$491$	1.31947	0.0595470	0.0297735	−	0.999557i	$-0.490521\pi$
$491$	1.31947	0.0595470	0.0297735	+	0.999557i	$0.490521\pi$
$492$	15.1913	0.684876
$493$	36.2635	1.63323
$494$	−31.4691	−1.41586
$495$	4.59087	0.206344
$496$	−13.1683	−0.591276
$497$	−17.9974	−0.807294
$498$	58.2700	2.61114
$499$	−21.3196	−0.954394	−0.477197	−	0.878796i	$-0.658347\pi$
$499$	−21.3196	−0.954394	−0.477197	+	0.878796i	$0.658347\pi$
$500$	6.17513	0.276160
$501$	−39.9480	−1.78474
$502$	43.3538	1.93497
$503$	−11.0513	−0.492755	−0.246378	−	0.969174i	$-0.579240\pi$
$503$	−11.0513	−0.492755	−0.246378	+	0.969174i	$0.579240\pi$
$504$	18.5444	0.826035
$505$	−2.28208	−0.101551
$506$	−71.3135	−3.17027
$507$	25.4300	1.12939
$508$	53.5171	2.37444
$509$	9.26332	0.410589	0.205295	−	0.978700i	$-0.434185\pi$
$509$	9.26332	0.410589	0.205295	+	0.978700i	$0.434185\pi$
$510$	7.33875	0.324965
$511$	−43.9056	−1.94227
$512$	24.0339	1.06216
$513$	−13.8042	−0.609471
$514$	−28.7748	−1.26920
$515$	−4.16460	−0.183514
$516$	52.3064	2.30266
$517$	1.19669	0.0526304
$518$	−54.6926	−2.40305
$519$	−10.4607	−0.459174
$520$	−1.54250	−0.0676430
$521$	−7.11929	−0.311902	−0.155951	−	0.987765i	$-0.549844\pi$
$521$	−7.11929	−0.311902	−0.155951	+	0.987765i	$0.549844\pi$
$522$	−68.5990	−3.00250
$523$	−15.2084	−0.665015	−0.332507	−	0.943101i	$-0.607895\pi$
$523$	−15.2084	−0.665015	−0.332507	+	0.943101i	$0.607895\pi$
$524$	−23.4425	−1.02409
$525$	−39.2994	−1.71517
$526$	62.3114	2.71691
$527$	−30.2873	−1.31934
$528$	26.7609	1.16462
$529$	37.8467	1.64551
$530$	−6.11854	−0.265773
$531$	−6.17986	−0.268183
$532$	−23.6120	−1.02371
$533$	9.80148	0.424549
$534$	85.6768	3.70760
$535$	3.86662	0.167169
$536$	−8.84437	−0.382019
$537$	−60.2248	−2.59889
$538$	−39.5554	−1.70535
$539$	−5.48774	−0.236374
$540$	−2.76753	−0.119096
$541$	−37.5286	−1.61348	−0.806740	−	0.590907i	$-0.798770\pi$
$541$	−37.5286	−1.61348	−0.806740	+	0.590907i	$0.798770\pi$
$542$	6.09427	0.261771
$543$	21.2257	0.910883
$544$	40.6021	1.74080
$545$	0.208529	0.00893241
$546$	80.7502	3.45579
$547$	5.03279	0.215187	0.107593	−	0.994195i	$-0.465686\pi$
$547$	5.03279	0.215187	0.107593	+	0.994195i	$0.465686\pi$
$548$	9.76139	0.416986
$549$	−0.648114	−0.0276608
$550$	45.2083	1.92769
$551$	21.3549	0.909750
$552$	30.0334	1.27830
$553$	38.8705	1.65294
$554$	52.4207	2.22714
$555$	5.70219	0.242044
$556$	−14.9783	−0.635223
$557$	17.0702	0.723287	0.361643	−	0.932316i	$-0.382216\pi$
$557$	17.0702	0.723287	0.361643	+	0.932316i	$0.382216\pi$
$558$	57.2939	2.42544
$559$	33.7483	1.42740
$560$	1.54468	0.0652748
$561$	61.5502	2.59865
$562$	2.83406	0.119548
$563$	−13.2580	−0.558757	−0.279379	−	0.960181i	$-0.590128\pi$
$563$	−13.2580	−0.558757	−0.279379	+	0.960181i	$0.590128\pi$
$564$	−2.06136	−0.0867989
$565$	3.48646	0.146676
$566$	−40.9944	−1.72312
$567$	−4.45205	−0.186968
$568$	−8.71915	−0.365847
$569$	15.6832	0.657474	0.328737	−	0.944421i	$-0.393377\pi$
$569$	15.6832	0.657474	0.328737	+	0.944421i	$0.393377\pi$
$570$	4.32165	0.181014
$571$	−3.70493	−0.155047	−0.0775233	−	0.996991i	$-0.524701\pi$
$571$	−3.70493	−0.155047	−0.0775233	+	0.996991i	$0.524701\pi$
$572$	−52.9142	−2.21245
$573$	−38.8421	−1.62265
$574$	12.9106	0.538876
$575$	−38.5730	−1.60860
$576$	−55.6994	−2.32081
$577$	−9.76477	−0.406513	−0.203256	−	0.979126i	$-0.565152\pi$
$577$	−9.76477	−0.406513	−0.203256	+	0.979126i	$0.565152\pi$
$578$	22.9823	0.955939
$579$	24.0283	0.998582
$580$	4.28133	0.177772
$581$	28.2093	1.17032
$582$	−14.7902	−0.613075
$583$	−51.3163	−2.12531
$584$	−21.2708	−0.880193
$585$	−5.10227	−0.210953
$586$	54.6187	2.25628
$587$	−19.2629	−0.795065	−0.397533	−	0.917588i	$-0.630133\pi$
$587$	−19.2629	−0.795065	−0.397533	+	0.917588i	$0.630133\pi$
$588$	9.45291	0.389831
$589$	−17.8356	−0.734904
$590$	0.677085	0.0278751
$591$	−33.6170	−1.38282
$592$	20.1444	0.827930
$593$	−22.7170	−0.932876	−0.466438	−	0.884554i	$-0.654463\pi$
$593$	−22.7170	−0.932876	−0.466438	+	0.884554i	$0.654463\pi$
$594$	−40.7477	−1.67190
$595$	3.55279	0.145650
$596$	−12.3083	−0.504166
$597$	4.39928	0.180051
$598$	79.2576	3.24108
$599$	−26.7036	−1.09108	−0.545540	−	0.838085i	$-0.683676\pi$
$599$	−26.7036	−1.09108	−0.545540	+	0.838085i	$0.683676\pi$
$600$	−19.0393	−0.777274
$601$	−7.25540	−0.295954	−0.147977	−	0.988991i	$-0.547276\pi$
$601$	−7.25540	−0.295954	−0.147977	+	0.988991i	$0.547276\pi$
$602$	44.4534	1.81179
$603$	−29.2554	−1.19137
$604$	28.8418	1.17356
$605$	−1.63843	−0.0666116
$606$	57.8779	2.35113
$607$	−30.2529	−1.22793	−0.613963	−	0.789335i	$-0.710426\pi$
$607$	−30.2529	−1.22793	−0.613963	+	0.789335i	$0.710426\pi$
$608$	23.9098	0.969670
$609$	−54.7971	−2.22049
$610$	0.0710094	0.00287509
$611$	−1.33000	−0.0538059
$612$	−64.2552	−2.59736
$613$	−17.5075	−0.707123	−0.353561	−	0.935411i	$-0.615029\pi$
$613$	−17.5075	−0.707123	−0.353561	+	0.935411i	$0.615029\pi$
$614$	−0.375838	−0.0151676
$615$	−1.34604	−0.0542776
$616$	−17.0406	−0.686586
$617$	10.1510	0.408663	0.204332	−	0.978902i	$-0.434498\pi$
$617$	10.1510	0.408663	0.204332	+	0.978902i	$0.434498\pi$
$618$	105.622	4.24875
$619$	−5.16125	−0.207448	−0.103724	−	0.994606i	$-0.533076\pi$
$619$	−5.16125	−0.207448	−0.103724	+	0.994606i	$0.533076\pi$
$620$	−3.57576	−0.143606
$621$	34.7671	1.39516
$622$	0.255181	0.0102318
$623$	41.4772	1.66175
$624$	−29.7420	−1.19063
$625$	24.1778	0.967110
$626$	8.09226	0.323432
$627$	36.2458	1.44752
$628$	39.1569	1.56253
$629$	46.3323	1.84739
$630$	−6.72073	−0.267760
$631$	22.7364	0.905123	0.452562	−	0.891733i	$-0.350510\pi$
$631$	22.7364	0.905123	0.452562	+	0.891733i	$0.350510\pi$
$632$	18.8315	0.749075
$633$	46.1305	1.83352
$634$	−64.7226	−2.57046
$635$	−4.74194	−0.188178
$636$	88.3949	3.50509
$637$	6.09906	0.241653
$638$	63.0361	2.49562
$639$	−28.8412	−1.14094
$640$	2.48103	0.0980713
$641$	31.9980	1.26384	0.631922	−	0.775032i	$-0.282266\pi$
$641$	31.9980	1.26384	0.631922	+	0.775032i	$0.282266\pi$
$642$	−98.0651	−3.87032
$643$	−30.4027	−1.19897	−0.599484	−	0.800387i	$-0.704627\pi$
$643$	−30.4027	−1.19897	−0.599484	+	0.800387i	$0.704627\pi$
$644$	59.4690	2.34341
$645$	−4.63467	−0.182490
$646$	35.1149	1.38158
$647$	4.55582	0.179108	0.0895538	−	0.995982i	$-0.471456\pi$
$647$	4.55582	0.179108	0.0895538	+	0.995982i	$0.471456\pi$
$648$	−2.15687	−0.0847299
$649$	5.67872	0.222909
$650$	−50.2443	−1.97074
$651$	45.7665	1.79373
$652$	−8.79235	−0.344335
$653$	17.3777	0.680041	0.340021	−	0.940418i	$-0.389566\pi$
$653$	17.3777	0.680041	0.340021	+	0.940418i	$0.389566\pi$
$654$	−5.28871	−0.206805
$655$	2.07715	0.0811608
$656$	−4.75522	−0.185660
$657$	−70.3596	−2.74499
$658$	−1.75188	−0.0682953
$659$	−39.2433	−1.52870	−0.764351	−	0.644800i	$-0.776940\pi$
$659$	−39.2433	−1.52870	−0.764351	+	0.644800i	$0.776940\pi$
$660$	7.26672	0.282857
$661$	−9.45273	−0.367669	−0.183834	−	0.982957i	$-0.558851\pi$
$661$	−9.45273	−0.367669	−0.183834	+	0.982957i	$0.558851\pi$
$662$	−16.3055	−0.633733
$663$	−68.4067	−2.65670
$664$	13.6665	0.530361
$665$	2.09217	0.0811308
$666$	−87.6458	−3.39621
$667$	−53.7842	−2.08253
$668$	−38.3218	−1.48271
$669$	49.2081	1.90250
$670$	3.20531	0.123832
$671$	0.595557	0.0229912
$672$	−61.3529	−2.36674
$673$	26.8728	1.03587	0.517936	−	0.855420i	$-0.326701\pi$
$673$	26.8728	1.03587	0.517936	+	0.855420i	$0.326701\pi$
$674$	63.5388	2.44742
$675$	−22.0402	−0.848326
$676$	24.3948	0.938261
$677$	25.1741	0.967518	0.483759	−	0.875201i	$-0.339271\pi$
$677$	25.1741	0.967518	0.483759	+	0.875201i	$0.339271\pi$
$678$	−88.4234	−3.39588
$679$	−7.16014	−0.274781
$680$	1.72121	0.0660053
$681$	73.4845	2.81593
$682$	−52.6478	−2.01599
$683$	−9.11426	−0.348748	−0.174374	−	0.984680i	$-0.555790\pi$
$683$	−9.11426	−0.348748	−0.174374	+	0.984680i	$0.555790\pi$
$684$	−37.8387	−1.44680
$685$	−0.864918	−0.0330468
$686$	−35.4250	−1.35253
$687$	−37.8134	−1.44267
$688$	−16.3731	−0.624219
$689$	57.0328	2.17278
$690$	−10.8845	−0.414364
$691$	−11.0741	−0.421278	−0.210639	−	0.977564i	$-0.567555\pi$
$691$	−11.0741	−0.421278	−0.210639	+	0.977564i	$0.567555\pi$
$692$	−10.0349	−0.381469
$693$	−56.3669	−2.14120
$694$	52.5855	1.99612
$695$	1.32717	0.0503425
$696$	−26.5474	−1.00628
$697$	−10.9370	−0.414270
$698$	56.8975	2.15360
$699$	−33.2816	−1.25883
$700$	−37.6996	−1.42491
$701$	−14.2140	−0.536854	−0.268427	−	0.963300i	$-0.586504\pi$
$701$	−14.2140	−0.536854	−0.268427	+	0.963300i	$0.586504\pi$
$702$	45.2868	1.70924
$703$	27.2842	1.02904
$704$	51.1826	1.92902
$705$	0.182649	0.00687895
$706$	−12.1612	−0.457693
$707$	28.0194	1.05378
$708$	−9.78187	−0.367625
$709$	−3.99412	−0.150002	−0.0750011	−	0.997183i	$-0.523896\pi$
$709$	−3.99412	−0.150002	−0.0750011	+	0.997183i	$0.523896\pi$
$710$	3.15993	0.118590
$711$	62.2907	2.33608
$712$	20.0943	0.753068
$713$	44.9206	1.68229
$714$	−90.1056	−3.37212
$715$	4.68852	0.175341
$716$	−57.7731	−2.15908
$717$	−57.9505	−2.16420
$718$	−62.6578	−2.33837
$719$	−10.1750	−0.379465	−0.189732	−	0.981836i	$-0.560762\pi$
$719$	−10.1750	−0.379465	−0.189732	+	0.981836i	$0.560762\pi$
$720$	2.47538	0.0922521
$721$	51.1331	1.90430
$722$	−20.2805	−0.754763
$723$	−24.0034	−0.892697
$724$	20.3617	0.756735
$725$	34.0958	1.26629
$726$	41.5538	1.54220
$727$	11.5367	0.427874	0.213937	−	0.976847i	$-0.431371\pi$
$727$	11.5367	0.427874	0.213937	+	0.976847i	$0.431371\pi$
$728$	18.9389	0.701921
$729$	−44.0331	−1.63086
$730$	7.70881	0.285316
$731$	−37.6583	−1.39284
$732$	−1.02588	−0.0379175
$733$	31.1664	1.15116	0.575578	−	0.817747i	$-0.304777\pi$
$733$	31.1664	1.15116	0.575578	+	0.817747i	$0.304777\pi$
$734$	39.3624	1.45289
$735$	−0.837585	−0.0308948
$736$	−60.2189	−2.21970
$737$	26.8830	0.990247
$738$	20.6894	0.761587
$739$	34.6798	1.27572	0.637859	−	0.770153i	$-0.279820\pi$
$739$	34.6798	1.27572	0.637859	+	0.770153i	$0.279820\pi$
$740$	5.47006	0.201083
$741$	−40.2834	−1.47985
$742$	75.1238	2.75788
$743$	41.4385	1.52023	0.760115	−	0.649789i	$-0.225143\pi$
$743$	41.4385	1.52023	0.760115	+	0.649789i	$0.225143\pi$
$744$	22.1724	0.812878
$745$	1.09059	0.0399560
$746$	39.0427	1.42946
$747$	45.2059	1.65400
$748$	59.0446	2.15888
$749$	−47.4746	−1.73468
$750$	13.8769	0.506713
$751$	−18.9125	−0.690126	−0.345063	−	0.938579i	$-0.612142\pi$
$751$	−18.9125	−0.690126	−0.345063	+	0.938579i	$0.612142\pi$
$752$	0.645253	0.0235299
$753$	55.4970	2.02242
$754$	−70.0581	−2.55136
$755$	−2.55556	−0.0930062
$756$	33.9799	1.23584
$757$	46.3867	1.68595	0.842976	−	0.537951i	$-0.180801\pi$
$757$	46.3867	1.68595	0.842976	+	0.537951i	$0.180801\pi$
$758$	56.8085	2.06338
$759$	−91.2882	−3.31355
$760$	1.01359	0.0367666
$761$	−1.78487	−0.0647015	−0.0323507	−	0.999477i	$-0.510299\pi$
$761$	−1.78487	−0.0647015	−0.0323507	+	0.999477i	$0.510299\pi$
$762$	120.265	4.35673
$763$	−2.56033	−0.0926902
$764$	−37.2609	−1.34805
$765$	5.69340	0.205845
$766$	32.7281	1.18251
$767$	−6.31131	−0.227888
$768$	3.68552	0.132990
$769$	−28.6772	−1.03413	−0.517064	−	0.855947i	$-0.672975\pi$
$769$	−28.6772	−1.03413	−0.517064	+	0.855947i	$0.672975\pi$
$770$	6.17573	0.222558
$771$	−36.8345	−1.32656
$772$	23.0501	0.829592
$773$	−41.5587	−1.49476	−0.747381	−	0.664396i	$-0.768689\pi$
$773$	−41.5587	−1.49476	−0.747381	+	0.664396i	$0.768689\pi$
$774$	71.2374	2.56058
$775$	−28.4768	−1.02292
$776$	−3.46885	−0.124524
$777$	−70.0117	−2.51166
$778$	−80.1208	−2.87247
$779$	−6.44062	−0.230759
$780$	−8.07620	−0.289174
$781$	26.5024	0.948329
$782$	−88.4400	−3.16261
$783$	−30.7317	−1.09826
$784$	−2.95898	−0.105678
$785$	−3.46954	−0.123833
$786$	−52.6805	−1.87905
$787$	24.0974	0.858979	0.429490	−	0.903072i	$-0.358694\pi$
$787$	24.0974	0.858979	0.429490	+	0.903072i	$0.358694\pi$
$788$	−32.2485	−1.14880
$789$	79.7646	2.83970
$790$	−6.82476	−0.242814
$791$	−42.8069	−1.52204
$792$	−27.3079	−0.970344
$793$	−0.661900	−0.0235048
$794$	−15.8516	−0.562554
$795$	−7.83232	−0.277784
$796$	4.22019	0.149581
$797$	16.8982	0.598566	0.299283	−	0.954164i	$-0.403253\pi$
$797$	16.8982	0.598566	0.299283	+	0.954164i	$0.403253\pi$
$798$	−53.0615	−1.87836
$799$	1.48409	0.0525032
$800$	38.1750	1.34969
$801$	66.4680	2.34853
$802$	37.9474	1.33997
$803$	64.6539	2.28159
$804$	−46.3073	−1.63313
$805$	−5.26931	−0.185719
$806$	58.5125	2.06102
$807$	−50.6347	−1.78242
$808$	13.5745	0.477549
$809$	5.94920	0.209163	0.104581	−	0.994516i	$-0.466650\pi$
$809$	5.94920	0.209163	0.104581	+	0.994516i	$0.466650\pi$
$810$	0.781676	0.0274653
$811$	12.9082	0.453267	0.226633	−	0.973980i	$-0.427228\pi$
$811$	12.9082	0.453267	0.226633	+	0.973980i	$0.427228\pi$
$812$	−52.5663	−1.84472
$813$	7.80125	0.273602
$814$	80.5384	2.82287
$815$	0.779055	0.0272891
$816$	33.1877	1.16180
$817$	−22.1763	−0.775849
$818$	24.5750	0.859245
$819$	62.6460	2.18903
$820$	−1.29124	−0.0450922
$821$	−19.1554	−0.668527	−0.334263	−	0.942480i	$-0.608487\pi$
$821$	−19.1554	−0.668527	−0.334263	+	0.942480i	$0.608487\pi$
$822$	21.9360	0.765106
$823$	−22.7013	−0.791318	−0.395659	−	0.918397i	$-0.629484\pi$
$823$	−22.7013	−0.791318	−0.395659	+	0.918397i	$0.629484\pi$
$824$	24.7723	0.862984
$825$	57.8709	2.01481
$826$	−8.31328	−0.289256
$827$	−4.65868	−0.161998	−0.0809991	−	0.996714i	$-0.525811\pi$
$827$	−4.65868	−0.161998	−0.0809991	+	0.996714i	$0.525811\pi$
$828$	95.3001	3.31191
$829$	42.5528	1.47792	0.738960	−	0.673749i	$-0.235317\pi$
$829$	42.5528	1.47792	0.738960	+	0.673749i	$0.235317\pi$
$830$	−4.95289	−0.171917
$831$	67.1035	2.32780
$832$	−56.8842	−1.97210
$833$	−6.80567	−0.235802
$834$	−33.6596	−1.16554
$835$	3.39554	0.117507
$836$	34.7703	1.20255
$837$	25.6671	0.887184
$838$	3.02083	0.104353
$839$	39.1198	1.35057	0.675283	−	0.737559i	$-0.264022\pi$
$839$	39.1198	1.35057	0.675283	+	0.737559i	$0.264022\pi$
$840$	−2.60088	−0.0897389
$841$	18.5414	0.639359
$842$	−18.1138	−0.624243
$843$	3.62787	0.124951
$844$	44.2526	1.52324
$845$	−2.16153	−0.0743587
$846$	−2.80742	−0.0965209
$847$	20.1167	0.691219
$848$	−27.6696	−0.950179
$849$	−52.4768	−1.80100
$850$	56.0654	1.92303
$851$	−68.7176	−2.35561
$852$	−45.6516	−1.56400
$853$	33.3367	1.14143	0.570714	−	0.821149i	$-0.306667\pi$
$853$	33.3367	1.14143	0.570714	+	0.821149i	$0.306667\pi$
$854$	−0.871857	−0.0298343
$855$	3.35274	0.114661
$856$	−22.9999	−0.786119
$857$	18.8138	0.642667	0.321334	−	0.946966i	$-0.395869\pi$
$857$	18.8138	0.642667	0.321334	+	0.946966i	$0.395869\pi$
$858$	−118.910	−4.05952
$859$	−46.6368	−1.59123	−0.795614	−	0.605804i	$-0.792852\pi$
$859$	−46.6368	−1.59123	−0.795614	+	0.605804i	$0.792852\pi$
$860$	−4.44599	−0.151607
$861$	16.5267	0.563230
$862$	36.4326	1.24090
$863$	20.3097	0.691352	0.345676	−	0.938354i	$-0.387650\pi$
$863$	20.3097	0.691352	0.345676	+	0.938354i	$0.387650\pi$
$864$	−34.4084	−1.17060
$865$	0.889150	0.0302320
$866$	67.1596	2.28218
$867$	29.4196	0.999142
$868$	43.9034	1.49018
$869$	−57.2393	−1.94171
$870$	9.62109	0.326186
$871$	−29.8776	−1.01236
$872$	−1.24040	−0.0420051
$873$	−11.4743	−0.388345
$874$	−52.0807	−1.76166
$875$	6.71799	0.227109
$876$	−111.370	−3.76283
$877$	−11.6557	−0.393585	−0.196793	−	0.980445i	$-0.563053\pi$
$877$	−11.6557	−0.393585	−0.196793	+	0.980445i	$0.563053\pi$
$878$	0.405283	0.0136776
$879$	69.9172	2.35825
$880$	−2.27465	−0.0766784
$881$	−11.4380	−0.385356	−0.192678	−	0.981262i	$-0.561717\pi$
$881$	−11.4380	−0.385356	−0.192678	+	0.981262i	$0.561717\pi$
$882$	12.8741	0.433495
$883$	33.5205	1.12805	0.564027	−	0.825756i	$-0.309251\pi$
$883$	33.5205	1.12805	0.564027	+	0.825756i	$0.309251\pi$
$884$	−65.6219	−2.20710
$885$	0.866733	0.0291349
$886$	8.65884	0.290899
$887$	54.6176	1.83388	0.916940	−	0.399026i	$-0.130652\pi$
$887$	54.6176	1.83388	0.916940	+	0.399026i	$0.130652\pi$
$888$	−33.9184	−1.13823
$889$	58.2217	1.95269
$890$	−7.28244	−0.244108
$891$	6.55593	0.219632
$892$	47.2049	1.58054
$893$	0.873950	0.0292456
$894$	−27.6594	−0.925068
$895$	5.11905	0.171111
$896$	−30.4622	−1.01767
$897$	101.457	3.38756
$898$	24.6489	0.822544
$899$	−39.7066	−1.32429
$900$	−60.4142	−2.01381
$901$	−63.6404	−2.12017
$902$	−19.0116	−0.633018
$903$	56.9047	1.89367
$904$	−20.7385	−0.689753
$905$	−1.80417	−0.0599725
$906$	64.8139	2.15330
$907$	9.31536	0.309311	0.154656	−	0.987968i	$-0.450573\pi$
$907$	9.31536	0.309311	0.154656	+	0.987968i	$0.450573\pi$
$908$	70.4930	2.33939
$909$	44.9017	1.48929
$910$	−6.86368	−0.227529
$911$	−33.2587	−1.10191	−0.550954	−	0.834535i	$-0.685736\pi$
$911$	−33.2587	−1.10191	−0.550954	+	0.834535i	$0.685736\pi$
$912$	19.5436	0.647155
$913$	−41.5400	−1.37477
$914$	−85.0289	−2.81251
$915$	0.0908989	0.00300502
$916$	−36.2740	−1.19853
$917$	−25.5033	−0.842193
$918$	−50.5336	−1.66786
$919$	25.9888	0.857290	0.428645	−	0.903473i	$-0.358991\pi$
$919$	25.9888	0.857290	0.428645	+	0.903473i	$0.358991\pi$
$920$	−2.55281	−0.0841635
$921$	−0.481109	−0.0158531
$922$	−49.8675	−1.64230
$923$	−29.4546	−0.969511
$924$	−89.2211	−2.93516
$925$	43.5627	1.43233
$926$	66.1679	2.17441
$927$	81.9417	2.69132
$928$	53.2292	1.74734
$929$	12.5221	0.410837	0.205418	−	0.978674i	$-0.434144\pi$
$929$	12.5221	0.410837	0.205418	+	0.978674i	$0.434144\pi$
$930$	−8.03554	−0.263496
$931$	−4.00773	−0.131348
$932$	−31.9268	−1.04580
$933$	0.326656	0.0106942
$934$	−46.1829	−1.51115
$935$	−5.23171	−0.171095
$936$	30.3499	0.992017
$937$	1.17257	0.0383061	0.0191530	−	0.999817i	$-0.493903\pi$
$937$	1.17257	0.0383061	0.0191530	+	0.999817i	$0.493903\pi$
$938$	−39.3549	−1.28498
$939$	10.3589	0.338049
$940$	0.175213	0.00571483
$941$	−42.1116	−1.37280	−0.686399	−	0.727225i	$-0.740809\pi$
$941$	−42.1116	−1.37280	−0.686399	+	0.727225i	$0.740809\pi$
$942$	87.9942	2.86701
$943$	16.2213	0.528237
$944$	3.06195	0.0996580
$945$	−3.01082	−0.0979420
$946$	−65.4606	−2.12831
$947$	40.0713	1.30214	0.651072	−	0.759016i	$-0.274320\pi$
$947$	40.0713	1.30214	0.651072	+	0.759016i	$0.274320\pi$
$948$	98.5976	3.20230
$949$	−71.8561	−2.33255
$950$	33.0159	1.07118
$951$	−82.8511	−2.68663
$952$	−21.1331	−0.684926
$953$	12.4569	0.403519	0.201760	−	0.979435i	$-0.435334\pi$
$953$	12.4569	0.403519	0.201760	+	0.979435i	$0.435334\pi$
$954$	120.387	3.89768
$955$	3.30154	0.106835
$956$	−55.5914	−1.79795
$957$	80.6923	2.60841
$958$	76.3305	2.46613
$959$	10.6195	0.342922
$960$	7.81192	0.252128
$961$	2.16295	0.0697726
$962$	−89.5100	−2.88592
$963$	−76.0789	−2.45161
$964$	−23.0263	−0.741627
$965$	−2.04238	−0.0657466
$966$	133.640	4.29979
$967$	−12.0755	−0.388323	−0.194162	−	0.980970i	$-0.562199\pi$
$967$	−12.0755	−0.388323	−0.194162	+	0.980970i	$0.562199\pi$
$968$	9.74588	0.313245
$969$	44.9505	1.44402
$970$	1.25715	0.0403648
$971$	16.5986	0.532674	0.266337	−	0.963880i	$-0.414187\pi$
$971$	16.5986	0.532674	0.266337	+	0.963880i	$0.414187\pi$
$972$	−46.6894	−1.49756
$973$	−16.2951	−0.522396
$974$	−22.2323	−0.712369
$975$	−64.3175	−2.05981
$976$	0.321123	0.0102789
$977$	32.9166	1.05310	0.526548	−	0.850145i	$-0.323486\pi$
$977$	32.9166	1.05310	0.526548	+	0.850145i	$0.323486\pi$
$978$	−19.7584	−0.631802
$979$	−61.0780	−1.95206
$980$	−0.803488	−0.0256665
$981$	−4.10298	−0.130998
$982$	2.84444	0.0907698
$983$	−31.6932	−1.01086	−0.505428	−	0.862869i	$-0.668665\pi$
$983$	−31.6932	−1.01086	−0.505428	+	0.862869i	$0.668665\pi$
$984$	8.00666	0.255243
$985$	2.85741	0.0910447
$986$	78.1747	2.48959
$987$	−2.24257	−0.0713818
$988$	−38.6435	−1.22941
$989$	55.8528	1.77602
$990$	9.89672	0.314538
$991$	−34.2867	−1.08915	−0.544577	−	0.838711i	$-0.683310\pi$
$991$	−34.2867	−1.08915	−0.544577	+	0.838711i	$0.683310\pi$
$992$	−44.4571	−1.41151
$993$	−20.8727	−0.662374
$994$	−38.7977	−1.23059
$995$	−0.373935	−0.0118545
$996$	71.5547	2.26730
$997$	−31.9972	−1.01336	−0.506681	−	0.862134i	$-0.669128\pi$
$997$	−31.9972	−1.01336	−0.506681	+	0.862134i	$0.669128\pi$
$998$	−45.9594	−1.45482
$999$	−39.2644	−1.24227

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1511.2.a.b.1.71	✓	87

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1511.2.a.b.1.71	✓	87	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:	\( N \)	\(=\)	\( 1511 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1511.a (trivial)

\(f(q)\)	\(=\)	\(q+2.15574 q^{2} +2.75955 q^{3} +2.64722 q^{4} -0.234559 q^{5} +5.94888 q^{6} +2.87993 q^{7} +1.39523 q^{8} +4.61514 q^{9} +O(q^{10})\)	\(q+2.15574 q^{2} +2.75955 q^{3} +2.64722 q^{4} -0.234559 q^{5} +5.94888 q^{6} +2.87993 q^{7} +1.39523 q^{8} +4.61514 q^{9} -0.505649 q^{10} -4.24089 q^{11} +7.30514 q^{12} +4.71331 q^{13} +6.20839 q^{14} -0.647280 q^{15} -2.28668 q^{16} -5.25937 q^{17} +9.94905 q^{18} -3.09715 q^{19} -0.620930 q^{20} +7.94733 q^{21} -9.14226 q^{22} +7.80043 q^{23} +3.85022 q^{24} -4.94498 q^{25} +10.1607 q^{26} +4.45707 q^{27} +7.62380 q^{28} -6.89503 q^{29} -1.39537 q^{30} +5.75873 q^{31} -7.71994 q^{32} -11.7030 q^{33} -11.3378 q^{34} -0.675515 q^{35} +12.2173 q^{36} -8.80947 q^{37} -6.67664 q^{38} +13.0066 q^{39} -0.327265 q^{40} +2.07953 q^{41} +17.1324 q^{42} +7.16022 q^{43} -11.2266 q^{44} -1.08253 q^{45} +16.8157 q^{46} -0.282179 q^{47} -6.31021 q^{48} +1.29401 q^{49} -10.6601 q^{50} -14.5135 q^{51} +12.4771 q^{52} +12.1004 q^{53} +9.60830 q^{54} +0.994740 q^{55} +4.01817 q^{56} -8.54674 q^{57} -14.8639 q^{58} -1.33904 q^{59} -1.71349 q^{60} -0.140432 q^{61} +12.4143 q^{62} +13.2913 q^{63} -12.0688 q^{64} -1.10555 q^{65} -25.2286 q^{66} -6.33900 q^{67} -13.9227 q^{68} +21.5257 q^{69} -1.45624 q^{70} -6.24925 q^{71} +6.43919 q^{72} -15.2454 q^{73} -18.9909 q^{74} -13.6459 q^{75} -8.19882 q^{76} -12.2135 q^{77} +28.0389 q^{78} +13.4970 q^{79} +0.536362 q^{80} -1.54589 q^{81} +4.48294 q^{82} +9.79512 q^{83} +21.0383 q^{84} +1.23364 q^{85} +15.4356 q^{86} -19.0272 q^{87} -5.91702 q^{88} +14.4022 q^{89} -2.33364 q^{90} +13.5740 q^{91} +20.6494 q^{92} +15.8915 q^{93} -0.608305 q^{94} +0.726465 q^{95} -21.3036 q^{96} -2.48622 q^{97} +2.78954 q^{98} -19.5723 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 87 q + 6 q^{2} + 4 q^{3} + 110 q^{4} + 10 q^{5} + 8 q^{6} + 21 q^{7} + 15 q^{8} + 133 q^{9}+O(q^{10}) \) 87 * q + 6 * q^2 + 4 * q^3 + 110 * q^4 + 10 * q^5 + 8 * q^6 + 21 * q^7 + 15 * q^8 + 133 * q^9	\( 87 q + 6 q^{2} + 4 q^{3} + 110 q^{4} + 10 q^{5} + 8 q^{6} + 21 q^{7} + 15 q^{8} + 133 q^{9} + 25 q^{10} + 17 q^{11} + 34 q^{13} + 12 q^{14} + 16 q^{15} + 152 q^{16} + 32 q^{17} + 14 q^{18} + 56 q^{19} + 3 q^{20} + 38 q^{21} + 32 q^{22} + 8 q^{23} + 8 q^{24} + 179 q^{25} + 11 q^{26} - 2 q^{27} + 45 q^{28} + 40 q^{29} + 24 q^{30} + 31 q^{31} + 26 q^{32} + 31 q^{33} + 31 q^{34} + 22 q^{35} + 180 q^{36} + 35 q^{37} - 15 q^{38} + 59 q^{39} + 42 q^{40} + 45 q^{41} - 30 q^{42} + 82 q^{43} + 25 q^{44} + 20 q^{45} + 69 q^{46} - 7 q^{47} - 39 q^{48} + 222 q^{49} + 17 q^{50} + 53 q^{51} + 54 q^{52} + 16 q^{53} - 7 q^{54} + 49 q^{55} + 12 q^{56} + 52 q^{57} + 17 q^{58} - 7 q^{59} - 6 q^{60} + 131 q^{61} - 8 q^{62} + 19 q^{63} + 213 q^{64} + 57 q^{65} + 17 q^{66} + 38 q^{67} + 13 q^{68} + 45 q^{69} - 5 q^{71} + 4 q^{72} + 91 q^{73} + q^{74} - 44 q^{75} + 150 q^{76} + 5 q^{77} - 87 q^{78} + 120 q^{79} - 41 q^{80} + 247 q^{81} + 20 q^{82} - 33 q^{83} - 16 q^{84} + 110 q^{85} - 22 q^{86} - 13 q^{87} + 78 q^{88} + 53 q^{89} - 33 q^{90} + 32 q^{91} - 31 q^{92} + 13 q^{93} + 79 q^{94} - 25 q^{95} - 51 q^{96} + 92 q^{97} - 36 q^{98} + 35 q^{99}+O(q^{100}) \) 87 * q + 6 * q^2 + 4 * q^3 + 110 * q^4 + 10 * q^5 + 8 * q^6 + 21 * q^7 + 15 * q^8 + 133 * q^9 + 25 * q^10 + 17 * q^11 + 34 * q^13 + 12 * q^14 + 16 * q^15 + 152 * q^16 + 32 * q^17 + 14 * q^18 + 56 * q^19 + 3 * q^20 + 38 * q^21 + 32 * q^22 + 8 * q^23 + 8 * q^24 + 179 * q^25 + 11 * q^26 - 2 * q^27 + 45 * q^28 + 40 * q^29 + 24 * q^30 + 31 * q^31 + 26 * q^32 + 31 * q^33 + 31 * q^34 + 22 * q^35 + 180 * q^36 + 35 * q^37 - 15 * q^38 + 59 * q^39 + 42 * q^40 + 45 * q^41 - 30 * q^42 + 82 * q^43 + 25 * q^44 + 20 * q^45 + 69 * q^46 - 7 * q^47 - 39 * q^48 + 222 * q^49 + 17 * q^50 + 53 * q^51 + 54 * q^52 + 16 * q^53 - 7 * q^54 + 49 * q^55 + 12 * q^56 + 52 * q^57 + 17 * q^58 - 7 * q^59 - 6 * q^60 + 131 * q^61 - 8 * q^62 + 19 * q^63 + 213 * q^64 + 57 * q^65 + 17 * q^66 + 38 * q^67 + 13 * q^68 + 45 * q^69 - 5 * q^71 + 4 * q^72 + 91 * q^73 + q^74 - 44 * q^75 + 150 * q^76 + 5 * q^77 - 87 * q^78 + 120 * q^79 - 41 * q^80 + 247 * q^81 + 20 * q^82 - 33 * q^83 - 16 * q^84 + 110 * q^85 - 22 * q^86 - 13 * q^87 + 78 * q^88 + 53 * q^89 - 33 * q^90 + 32 * q^91 - 31 * q^92 + 13 * q^93 + 79 * q^94 - 25 * q^95 - 51 * q^96 + 92 * q^97 - 36 * q^98 + 35 * q^99

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