LMFDB - Embedded newform 6001.2.a.a.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$1$
Dimension:	$113$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20707 q^{2} +2.35834 q^{3} +2.87116 q^{4} +2.79748 q^{5} -5.20501 q^{6} -1.23289 q^{7} -1.92271 q^{8} +2.56174 q^{9} +O(q^{10})$	\(q-2.20707 q^{2} +2.35834 q^{3} +2.87116 q^{4} +2.79748 q^{5} -5.20501 q^{6} -1.23289 q^{7} -1.92271 q^{8} +2.56174 q^{9} -6.17423 q^{10} -1.33154 q^{11} +6.77116 q^{12} -1.81240 q^{13} +2.72108 q^{14} +6.59739 q^{15} -1.49876 q^{16} -1.00000 q^{17} -5.65395 q^{18} -5.52454 q^{19} +8.03200 q^{20} -2.90757 q^{21} +2.93881 q^{22} -6.15852 q^{23} -4.53439 q^{24} +2.82588 q^{25} +4.00009 q^{26} -1.03355 q^{27} -3.53983 q^{28} +9.11906 q^{29} -14.5609 q^{30} -1.41537 q^{31} +7.15329 q^{32} -3.14022 q^{33} +2.20707 q^{34} -3.44898 q^{35} +7.35518 q^{36} -1.73366 q^{37} +12.1931 q^{38} -4.27424 q^{39} -5.37874 q^{40} -7.61760 q^{41} +6.41721 q^{42} +7.65919 q^{43} -3.82307 q^{44} +7.16642 q^{45} +13.5923 q^{46} -3.25393 q^{47} -3.53459 q^{48} -5.47998 q^{49} -6.23692 q^{50} -2.35834 q^{51} -5.20368 q^{52} +8.67258 q^{53} +2.28113 q^{54} -3.72496 q^{55} +2.37049 q^{56} -13.0287 q^{57} -20.1264 q^{58} -1.72023 q^{59} +18.9422 q^{60} +3.71209 q^{61} +3.12381 q^{62} -3.15835 q^{63} -12.7903 q^{64} -5.07014 q^{65} +6.93069 q^{66} +7.03971 q^{67} -2.87116 q^{68} -14.5238 q^{69} +7.61215 q^{70} +9.92169 q^{71} -4.92549 q^{72} -6.65198 q^{73} +3.82631 q^{74} +6.66438 q^{75} -15.8618 q^{76} +1.64164 q^{77} +9.43354 q^{78} -2.43758 q^{79} -4.19276 q^{80} -10.1227 q^{81} +16.8126 q^{82} -4.80688 q^{83} -8.34810 q^{84} -2.79748 q^{85} -16.9044 q^{86} +21.5058 q^{87} +2.56017 q^{88} -6.39909 q^{89} -15.8168 q^{90} +2.23449 q^{91} -17.6821 q^{92} -3.33791 q^{93} +7.18165 q^{94} -15.4548 q^{95} +16.8699 q^{96} -15.0322 q^{97} +12.0947 q^{98} -3.41107 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) $ 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * 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 $

$2$	−2.20707	−1.56063	−0.780317	−	0.625384i	$-0.784942\pi$
$2$	−2.20707	−1.56063	−0.780317	+	0.625384i	$0.784942\pi$
$3$	2.35834	1.36159	0.680793	−	0.732476i	$-0.261635\pi$
$3$	2.35834	1.36159	0.680793	+	0.732476i	$0.261635\pi$
$4$	2.87116	1.43558
$5$	2.79748	1.25107	0.625535	−	0.780196i	$-0.284881\pi$
$5$	2.79748	1.25107	0.625535	+	0.780196i	$0.284881\pi$
$6$	−5.20501	−2.12494
$7$	−1.23289	−0.465989	−0.232994	−	0.972478i	$-0.574852\pi$
$7$	−1.23289	−0.465989	−0.232994	+	0.972478i	$0.574852\pi$
$8$	−1.92271	−0.679781
$9$	2.56174	0.853915
$10$	−6.17423	−1.95246
$11$	−1.33154	−0.401475	−0.200737	−	0.979645i	$-0.564334\pi$
$11$	−1.33154	−0.401475	−0.200737	+	0.979645i	$0.564334\pi$
$12$	6.77116	1.95466
$13$	−1.81240	−0.502668	−0.251334	−	0.967900i	$-0.580869\pi$
$13$	−1.81240	−0.502668	−0.251334	+	0.967900i	$0.580869\pi$
$14$	2.72108	0.727238
$15$	6.59739	1.70344
$16$	−1.49876	−0.374691
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−5.65395	−1.33265
$19$	−5.52454	−1.26742	−0.633708	−	0.773572i	$-0.718468\pi$
$19$	−5.52454	−1.26742	−0.633708	+	0.773572i	$0.718468\pi$
$20$	8.03200	1.79601
$21$	−2.90757	−0.634484
$22$	2.93881	0.626555
$23$	−6.15852	−1.28414	−0.642070	−	0.766646i	$-0.721924\pi$
$23$	−6.15852	−1.28414	−0.642070	+	0.766646i	$0.721924\pi$
$24$	−4.53439	−0.925579
$25$	2.82588	0.565176
$26$	4.00009	0.784482
$27$	−1.03355	−0.198907
$28$	−3.53983	−0.668964
$29$	9.11906	1.69337	0.846684	−	0.532096i	$-0.178596\pi$
$29$	9.11906	1.69337	0.846684	+	0.532096i	$0.178596\pi$
$30$	−14.5609	−2.65845
$31$	−1.41537	−0.254207	−0.127104	−	0.991889i	$-0.540568\pi$
$31$	−1.41537	−0.254207	−0.127104	+	0.991889i	$0.540568\pi$
$32$	7.15329	1.26454
$33$	−3.14022	−0.546642
$34$	2.20707	0.378509
$35$	−3.44898	−0.582985
$36$	7.35518	1.22586
$37$	−1.73366	−0.285012	−0.142506	−	0.989794i	$-0.545516\pi$
$37$	−1.73366	−0.285012	−0.142506	+	0.989794i	$0.545516\pi$
$38$	12.1931	1.97797
$39$	−4.27424	−0.684426
$40$	−5.37874	−0.850453
$41$	−7.61760	−1.18967	−0.594835	−	0.803848i	$-0.702782\pi$
$41$	−7.61760	−1.18967	−0.594835	+	0.803848i	$0.702782\pi$
$42$	6.41721	0.990197
$43$	7.65919	1.16802	0.584008	−	0.811748i	$-0.301484\pi$
$43$	7.65919	1.16802	0.584008	+	0.811748i	$0.301484\pi$
$44$	−3.82307	−0.576349
$45$	7.16642	1.06831
$46$	13.5923	2.00407
$47$	−3.25393	−0.474634	−0.237317	−	0.971432i	$-0.576268\pi$
$47$	−3.25393	−0.474634	−0.237317	+	0.971432i	$0.576268\pi$
$48$	−3.53459	−0.510173
$49$	−5.47998	−0.782854
$50$	−6.23692	−0.882034
$51$	−2.35834	−0.330233
$52$	−5.20368	−0.721620
$53$	8.67258	1.19127	0.595636	−	0.803255i	$-0.296900\pi$
$53$	8.67258	1.19127	0.595636	+	0.803255i	$0.296900\pi$
$54$	2.28113	0.310422
$55$	−3.72496	−0.502273
$56$	2.37049	0.316770
$57$	−13.0287	−1.72570
$58$	−20.1264	−2.64273
$59$	−1.72023	−0.223955	−0.111978	−	0.993711i	$-0.535718\pi$
$59$	−1.72023	−0.223955	−0.111978	+	0.993711i	$0.535718\pi$
$60$	18.9422	2.44542
$61$	3.71209	0.475284	0.237642	−	0.971353i	$-0.423626\pi$
$61$	3.71209	0.475284	0.237642	+	0.971353i	$0.423626\pi$
$62$	3.12381	0.396725
$63$	−3.15835	−0.397915
$64$	−12.7903	−1.59879
$65$	−5.07014	−0.628873
$66$	6.93069	0.853109
$67$	7.03971	0.860038	0.430019	−	0.902820i	$-0.358507\pi$
$67$	7.03971	0.860038	0.430019	+	0.902820i	$0.358507\pi$
$68$	−2.87116	−0.348179
$69$	−14.5238	−1.74847
$70$	7.61215	0.909826
$71$	9.92169	1.17749	0.588744	−	0.808319i	$-0.299623\pi$
$71$	9.92169	1.17749	0.588744	+	0.808319i	$0.299623\pi$
$72$	−4.92549	−0.580475
$73$	−6.65198	−0.778555	−0.389278	−	0.921120i	$-0.627275\pi$
$73$	−6.65198	−0.778555	−0.389278	+	0.921120i	$0.627275\pi$
$74$	3.82631	0.444799
$75$	6.66438	0.769536
$76$	−15.8618	−1.81948
$77$	1.64164	0.187083
$78$	9.43354	1.06814
$79$	−2.43758	−0.274250	−0.137125	−	0.990554i	$-0.543786\pi$
$79$	−2.43758	−0.274250	−0.137125	+	0.990554i	$0.543786\pi$
$80$	−4.19276	−0.468764
$81$	−10.1227	−1.12474
$82$	16.8126	1.85664
$83$	−4.80688	−0.527624	−0.263812	−	0.964574i	$-0.584980\pi$
$83$	−4.80688	−0.527624	−0.263812	+	0.964574i	$0.584980\pi$
$84$	−8.34810	−0.910852
$85$	−2.79748	−0.303429
$86$	−16.9044	−1.82284
$87$	21.5058	2.30566
$88$	2.56017	0.272915
$89$	−6.39909	−0.678302	−0.339151	−	0.940732i	$-0.610140\pi$
$89$	−6.39909	−0.678302	−0.339151	+	0.940732i	$0.610140\pi$
$90$	−15.8168	−1.66724
$91$	2.23449	0.234238
$92$	−17.6821	−1.84348
$93$	−3.33791	−0.346125
$94$	7.18165	0.740730
$95$	−15.4548	−1.58563
$96$	16.8699	1.72177
$97$	−15.0322	−1.52629	−0.763146	−	0.646226i	$-0.776346\pi$
$97$	−15.0322	−1.52629	−0.763146	+	0.646226i	$0.776346\pi$
$98$	12.0947	1.22175
$99$	−3.41107	−0.342825
$100$	8.11356	0.811356
$101$	16.3596	1.62784	0.813921	−	0.580975i	$-0.197329\pi$
$101$	16.3596	1.62784	0.813921	+	0.580975i	$0.197329\pi$
$102$	5.20501	0.515373
$103$	−1.31372	−0.129444	−0.0647222	−	0.997903i	$-0.520616\pi$
$103$	−1.31372	−0.129444	−0.0647222	+	0.997903i	$0.520616\pi$
$104$	3.48471	0.341704
$105$	−8.13386	−0.793784
$106$	−19.1410	−1.85914
$107$	11.3092	1.09331	0.546653	−	0.837359i	$-0.315902\pi$
$107$	11.3092	1.09331	0.546653	+	0.837359i	$0.315902\pi$
$108$	−2.96750	−0.285547
$109$	−0.479146	−0.0458939	−0.0229470	−	0.999737i	$-0.507305\pi$
$109$	−0.479146	−0.0458939	−0.0229470	+	0.999737i	$0.507305\pi$
$110$	8.22124	0.783865
$111$	−4.08855	−0.388068
$112$	1.84781	0.174602
$113$	−12.1182	−1.13998	−0.569991	−	0.821651i	$-0.693053\pi$
$113$	−12.1182	−1.13998	−0.569991	+	0.821651i	$0.693053\pi$
$114$	28.7553	2.69318
$115$	−17.2283	−1.60655
$116$	26.1823	2.43096
$117$	−4.64290	−0.429236
$118$	3.79667	0.349512
$119$	1.23289	0.113019
$120$	−12.6849	−1.15796
$121$	−9.22700	−0.838818
$122$	−8.19283	−0.741744
$123$	−17.9649	−1.61984
$124$	−4.06374	−0.364935
$125$	−6.08205	−0.543995
$126$	6.97070	0.621000
$127$	4.13275	0.366722	0.183361	−	0.983046i	$-0.441302\pi$
$127$	4.13275	0.366722	0.183361	+	0.983046i	$0.441302\pi$
$128$	13.9225	1.23059
$129$	18.0629	1.59035
$130$	11.1902	0.981441
$131$	8.82553	0.771090	0.385545	−	0.922689i	$-0.374013\pi$
$131$	8.82553	0.771090	0.385545	+	0.922689i	$0.374013\pi$
$132$	−9.01607	−0.784748
$133$	6.81116	0.590602
$134$	−15.5371	−1.34220
$135$	−2.89134	−0.248847
$136$	1.92271	0.164871
$137$	−13.2184	−1.12933	−0.564663	−	0.825321i	$-0.690994\pi$
$137$	−13.2184	−1.12933	−0.564663	+	0.825321i	$0.690994\pi$
$138$	32.0552	2.72872
$139$	−15.1365	−1.28386	−0.641931	−	0.766762i	$-0.721867\pi$
$139$	−15.1365	−1.28386	−0.641931	+	0.766762i	$0.721867\pi$
$140$	−9.90258	−0.836921
$141$	−7.67385	−0.646255
$142$	−21.8979	−1.83763
$143$	2.41328	0.201809
$144$	−3.83945	−0.319954
$145$	25.5104	2.11852
$146$	14.6814	1.21504
$147$	−12.9236	−1.06592
$148$	−4.97761	−0.409157
$149$	8.62947	0.706954	0.353477	−	0.935443i	$-0.384999\pi$
$149$	8.62947	0.706954	0.353477	+	0.935443i	$0.384999\pi$
$150$	−14.7087	−1.20096
$151$	−17.3517	−1.41207	−0.706033	−	0.708179i	$-0.749517\pi$
$151$	−17.3517	−1.41207	−0.706033	+	0.708179i	$0.749517\pi$
$152$	10.6221	0.861565
$153$	−2.56174	−0.207105
$154$	−3.62323	−0.291968
$155$	−3.95946	−0.318031
$156$	−12.2720	−0.982548
$157$	−11.6405	−0.929011	−0.464505	−	0.885570i	$-0.653768\pi$
$157$	−11.6405	−0.929011	−0.464505	+	0.885570i	$0.653768\pi$
$158$	5.37992	0.428003
$159$	20.4529	1.62202
$160$	20.0112	1.58202
$161$	7.59278	0.598395
$162$	22.3415	1.75531
$163$	−12.4281	−0.973446	−0.486723	−	0.873556i	$-0.661808\pi$
$163$	−12.4281	−0.973446	−0.486723	+	0.873556i	$0.661808\pi$
$164$	−21.8713	−1.70786
$165$	−8.78470	−0.683888
$166$	10.6091	0.823427
$167$	−5.73833	−0.444045	−0.222023	−	0.975042i	$-0.571266\pi$
$167$	−5.73833	−0.444045	−0.222023	+	0.975042i	$0.571266\pi$
$168$	5.59041	0.431310
$169$	−9.71522	−0.747325
$170$	6.17423	0.473542
$171$	−14.1525	−1.08227
$172$	21.9907	1.67678
$173$	−8.19231	−0.622850	−0.311425	−	0.950271i	$-0.600806\pi$
$173$	−8.19231	−0.622850	−0.311425	+	0.950271i	$0.600806\pi$
$174$	−47.4648	−3.59830
$175$	−3.48400	−0.263366
$176$	1.99566	0.150429
$177$	−4.05688	−0.304934
$178$	14.1232	1.05858
$179$	−18.4263	−1.37725	−0.688623	−	0.725119i	$-0.741785\pi$
$179$	−18.4263	−1.37725	−0.688623	+	0.725119i	$0.741785\pi$
$180$	20.5759	1.53364
$181$	19.7349	1.46689	0.733444	−	0.679750i	$-0.237912\pi$
$181$	19.7349	1.46689	0.733444	+	0.679750i	$0.237912\pi$
$182$	−4.93167	−0.365560
$183$	8.75434	0.647140
$184$	11.8410	0.872933
$185$	−4.84987	−0.356570
$186$	7.36700	0.540174
$187$	1.33154	0.0973719
$188$	−9.34254	−0.681375
$189$	1.27426	0.0926887
$190$	34.1098	2.47458
$191$	−17.1406	−1.24025	−0.620124	−	0.784504i	$-0.712918\pi$
$191$	−17.1406	−1.24025	−0.620124	+	0.784504i	$0.712918\pi$
$192$	−30.1638	−2.17689
$193$	−6.36338	−0.458046	−0.229023	−	0.973421i	$-0.573553\pi$
$193$	−6.36338	−0.458046	−0.229023	+	0.973421i	$0.573553\pi$
$194$	33.1772	2.38198
$195$	−11.9571	−0.856265
$196$	−15.7339	−1.12385
$197$	−17.2143	−1.22647	−0.613234	−	0.789901i	$-0.710132\pi$
$197$	−17.2143	−1.22647	−0.613234	+	0.789901i	$0.710132\pi$
$198$	7.52847	0.535025
$199$	−0.477605	−0.0338565	−0.0169282	−	0.999857i	$-0.505389\pi$
$199$	−0.477605	−0.0338565	−0.0169282	+	0.999857i	$0.505389\pi$
$200$	−5.43335	−0.384196
$201$	16.6020	1.17101
$202$	−36.1068	−2.54047
$203$	−11.2428	−0.789091
$204$	−6.77116	−0.474076
$205$	−21.3101	−1.48836
$206$	2.89947	0.202015
$207$	−15.7765	−1.09655
$208$	2.71635	0.188345
$209$	7.35615	0.508836
$210$	17.9520	1.23881
$211$	−23.1437	−1.59328	−0.796640	−	0.604454i	$-0.793391\pi$
$211$	−23.1437	−1.59328	−0.796640	+	0.604454i	$0.793391\pi$
$212$	24.9004	1.71016
$213$	23.3987	1.60325
$214$	−24.9603	−1.70625
$215$	21.4264	1.46127
$216$	1.98722	0.135213
$217$	1.74499	0.118458
$218$	1.05751	0.0716236
$219$	−15.6876	−1.06007
$220$	−10.6949	−0.721053
$221$	1.81240	0.121915
$222$	9.02371	0.605632
$223$	6.20673	0.415634	0.207817	−	0.978168i	$-0.433364\pi$
$223$	6.20673	0.415634	0.207817	+	0.978168i	$0.433364\pi$
$224$	−8.81923	−0.589260
$225$	7.23919	0.482613
$226$	26.7456	1.77909
$227$	−16.4631	−1.09270	−0.546349	−	0.837558i	$-0.683983\pi$
$227$	−16.4631	−1.09270	−0.546349	+	0.837558i	$0.683983\pi$
$228$	−37.4075	−2.47737
$229$	−3.91085	−0.258436	−0.129218	−	0.991616i	$-0.541247\pi$
$229$	−3.91085	−0.258436	−0.129218	+	0.991616i	$0.541247\pi$
$230$	38.0241	2.50724
$231$	3.87155	0.254729
$232$	−17.5333	−1.15112
$233$	1.86606	0.122250	0.0611249	−	0.998130i	$-0.480531\pi$
$233$	1.86606	0.122250	0.0611249	+	0.998130i	$0.480531\pi$
$234$	10.2472	0.669880
$235$	−9.10279	−0.593801
$236$	−4.93906	−0.321505
$237$	−5.74864	−0.373414
$238$	−2.72108	−0.176381
$239$	−12.2171	−0.790256	−0.395128	−	0.918626i	$-0.629300\pi$
$239$	−12.2171	−0.790256	−0.395128	+	0.918626i	$0.629300\pi$
$240$	−9.88792	−0.638263
$241$	1.36396	0.0878602	0.0439301	−	0.999035i	$-0.486012\pi$
$241$	1.36396	0.0878602	0.0439301	+	0.999035i	$0.486012\pi$
$242$	20.3646	1.30909
$243$	−20.7721	−1.33253
$244$	10.6580	0.682308
$245$	−15.3301	−0.979406
$246$	39.6497	2.52797
$247$	10.0127	0.637090
$248$	2.72134	0.172805
$249$	−11.3362	−0.718404
$250$	13.4235	0.848977
$251$	−23.9958	−1.51460	−0.757300	−	0.653067i	$-0.773482\pi$
$251$	−23.9958	−1.51460	−0.757300	+	0.653067i	$0.773482\pi$
$252$	−9.06813	−0.571238
$253$	8.20032	0.515550
$254$	−9.12127	−0.572319
$255$	−6.59739	−0.413145
$256$	−5.14733	−0.321708
$257$	−0.0995257	−0.00620824	−0.00310412	−	0.999995i	$-0.500988\pi$
$257$	−0.0995257	−0.00620824	−0.00310412	+	0.999995i	$0.500988\pi$
$258$	−39.8662	−2.48196
$259$	2.13741	0.132812
$260$	−14.5572	−0.902798
$261$	23.3607	1.44599
$262$	−19.4786	−1.20339
$263$	−25.8495	−1.59395	−0.796975	−	0.604012i	$-0.793568\pi$
$263$	−25.8495	−1.59395	−0.796975	+	0.604012i	$0.793568\pi$
$264$	6.03773	0.371597
$265$	24.2614	1.49036
$266$	−15.0327	−0.921714
$267$	−15.0912	−0.923567
$268$	20.2121	1.23465
$269$	−12.2495	−0.746865	−0.373432	−	0.927657i	$-0.621819\pi$
$269$	−12.2495	−0.746865	−0.373432	+	0.927657i	$0.621819\pi$
$270$	6.38140	0.388359
$271$	8.31871	0.505325	0.252663	−	0.967554i	$-0.418694\pi$
$271$	8.31871	0.505325	0.252663	+	0.967554i	$0.418694\pi$
$272$	1.49876	0.0908759
$273$	5.26967	0.318935
$274$	29.1740	1.76247
$275$	−3.76278	−0.226904
$276$	−41.7003	−2.51006
$277$	7.75815	0.466142	0.233071	−	0.972460i	$-0.425123\pi$
$277$	7.75815	0.466142	0.233071	+	0.972460i	$0.425123\pi$
$278$	33.4074	2.00364
$279$	−3.62581	−0.217071
$280$	6.63140	0.396302
$281$	27.9014	1.66446	0.832228	−	0.554433i	$-0.187065\pi$
$281$	27.9014	1.66446	0.832228	+	0.554433i	$0.187065\pi$
$282$	16.9367	1.00857
$283$	−5.62883	−0.334599	−0.167300	−	0.985906i	$-0.553505\pi$
$283$	−5.62883	−0.334599	−0.167300	+	0.985906i	$0.553505\pi$
$284$	28.4868	1.69038
$285$	−36.4476	−2.15897
$286$	−5.32628	−0.314950
$287$	9.39167	0.554373
$288$	18.3249	1.07981
$289$	1.00000	0.0588235
$290$	−56.3032	−3.30624
$291$	−35.4510	−2.07818
$292$	−19.0989	−1.11768
$293$	21.5405	1.25841	0.629205	−	0.777240i	$-0.283381\pi$
$293$	21.5405	1.25841	0.629205	+	0.777240i	$0.283381\pi$
$294$	28.5234	1.66352
$295$	−4.81231	−0.280184
$296$	3.33332	0.193745
$297$	1.37622	0.0798563
$298$	−19.0458	−1.10330
$299$	11.1617	0.645496
$300$	19.1345	1.10473
$301$	−9.44294	−0.544282
$302$	38.2965	2.20372
$303$	38.5815	2.21645
$304$	8.27998	0.474889
$305$	10.3845	0.594613
$306$	5.65395	0.323215
$307$	−4.31926	−0.246513	−0.123257	−	0.992375i	$-0.539334\pi$
$307$	−4.31926	−0.246513	−0.123257	+	0.992375i	$0.539334\pi$
$308$	4.71342	0.268572
$309$	−3.09819	−0.176250
$310$	8.73880	0.496330
$311$	11.9695	0.678730	0.339365	−	0.940655i	$-0.389788\pi$
$311$	11.9695	0.678730	0.339365	+	0.940655i	$0.389788\pi$
$312$	8.21812	0.465259
$313$	30.8762	1.74523	0.872613	−	0.488413i	$-0.162424\pi$
$313$	30.8762	1.74523	0.872613	+	0.488413i	$0.162424\pi$
$314$	25.6913	1.44985
$315$	−8.83542	−0.497819
$316$	−6.99869	−0.393707
$317$	−0.571646	−0.0321068	−0.0160534	−	0.999871i	$-0.505110\pi$
$317$	−0.571646	−0.0321068	−0.0160534	+	0.999871i	$0.505110\pi$
$318$	−45.1409	−2.53138
$319$	−12.1424	−0.679844
$320$	−35.7806	−2.00020
$321$	26.6710	1.48863
$322$	−16.7578	−0.933876
$323$	5.52454	0.307394
$324$	−29.0639	−1.61466
$325$	−5.12162	−0.284096
$326$	27.4297	1.51919
$327$	−1.12999	−0.0624885
$328$	14.6464	0.808714
$329$	4.01174	0.221174
$330$	19.3884	1.06730
$331$	24.4602	1.34445	0.672227	−	0.740345i	$-0.265338\pi$
$331$	24.4602	1.34445	0.672227	+	0.740345i	$0.265338\pi$
$332$	−13.8013	−0.757446
$333$	−4.44119	−0.243376
$334$	12.6649	0.692992
$335$	19.6934	1.07597
$336$	4.35776	0.237735
$337$	23.1807	1.26273	0.631366	−	0.775485i	$-0.282494\pi$
$337$	23.1807	1.26273	0.631366	+	0.775485i	$0.282494\pi$
$338$	21.4422	1.16630
$339$	−28.5787	−1.55218
$340$	−8.03200	−0.435597
$341$	1.88462	0.102058
$342$	31.2355	1.68902
$343$	15.3865	0.830790
$344$	−14.7264	−0.793994
$345$	−40.6301	−2.18745
$346$	18.0810	0.972041
$347$	33.0656	1.77506	0.887528	−	0.460754i	$-0.152421\pi$
$347$	33.0656	1.77506	0.887528	+	0.460754i	$0.152421\pi$
$348$	61.7466	3.30997
$349$	−1.47006	−0.0786907	−0.0393454	−	0.999226i	$-0.512527\pi$
$349$	−1.47006	−0.0786907	−0.0393454	+	0.999226i	$0.512527\pi$
$350$	7.68944	0.411018
$351$	1.87321	0.0999845
$352$	−9.52491	−0.507679
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	8.95383	0.475891
$355$	27.7557	1.47312
$356$	−18.3728	−0.973757
$357$	2.90757	0.153885
$358$	40.6681	2.14938
$359$	−21.8109	−1.15114	−0.575568	−	0.817754i	$-0.695219\pi$
$359$	−21.8109	−1.15114	−0.575568	+	0.817754i	$0.695219\pi$
$360$	−13.7790	−0.726215
$361$	11.5206	0.606345
$362$	−43.5564	−2.28927
$363$	−21.7604	−1.14212
$364$	6.41557	0.336267
$365$	−18.6088	−0.974027
$366$	−19.3214	−1.00995
$367$	13.3662	0.697709	0.348855	−	0.937177i	$-0.386571\pi$
$367$	13.3662	0.697709	0.348855	+	0.937177i	$0.386571\pi$
$368$	9.23016	0.481155
$369$	−19.5143	−1.01588
$370$	10.7040	0.556475
$371$	−10.6924	−0.555119
$372$	−9.58366	−0.496890
$373$	34.7776	1.80071	0.900357	−	0.435153i	$-0.143306\pi$
$373$	34.7776	1.80071	0.900357	+	0.435153i	$0.143306\pi$
$374$	−2.93881	−0.151962
$375$	−14.3435	−0.740695
$376$	6.25636	0.322647
$377$	−16.5274	−0.851202
$378$	−2.81238	−0.144653
$379$	−23.3832	−1.20111	−0.600557	−	0.799582i	$-0.705054\pi$
$379$	−23.3832	−1.20111	−0.600557	+	0.799582i	$0.705054\pi$
$380$	−44.3731	−2.27629
$381$	9.74641	0.499324
$382$	37.8304	1.93557
$383$	12.6503	0.646399	0.323200	−	0.946331i	$-0.395241\pi$
$383$	12.6503	0.646399	0.323200	+	0.946331i	$0.395241\pi$
$384$	32.8339	1.67555
$385$	4.59247	0.234054
$386$	14.0444	0.714843
$387$	19.6209	0.997385
$388$	−43.1599	−2.19111
$389$	−21.0974	−1.06968	−0.534840	−	0.844953i	$-0.679628\pi$
$389$	−21.0974	−1.06968	−0.534840	+	0.844953i	$0.679628\pi$
$390$	26.3901	1.33632
$391$	6.15852	0.311450
$392$	10.5364	0.532169
$393$	20.8136	1.04991
$394$	37.9932	1.91407
$395$	−6.81909	−0.343105
$396$	−9.79372	−0.492153
$397$	2.99208	0.150168	0.0750842	−	0.997177i	$-0.476077\pi$
$397$	2.99208	0.150168	0.0750842	+	0.997177i	$0.476077\pi$
$398$	1.05411	0.0528376
$399$	16.0630	0.804155
$400$	−4.23533	−0.211766
$401$	−10.1790	−0.508316	−0.254158	−	0.967163i	$-0.581798\pi$
$401$	−10.1790	−0.508316	−0.254158	+	0.967163i	$0.581798\pi$
$402$	−36.6418	−1.82753
$403$	2.56520	0.127782
$404$	46.9711	2.33690
$405$	−28.3180	−1.40713
$406$	24.8137	1.23148
$407$	2.30844	0.114425
$408$	4.53439	0.224486
$409$	22.9998	1.13726	0.568632	−	0.822592i	$-0.307473\pi$
$409$	22.9998	1.13726	0.568632	+	0.822592i	$0.307473\pi$
$410$	47.0328	2.32279
$411$	−31.1735	−1.53767
$412$	−3.77189	−0.185828
$413$	2.12086	0.104361
$414$	34.8199	1.71131
$415$	−13.4471	−0.660094
$416$	−12.9646	−0.635642
$417$	−35.6970	−1.74809
$418$	−16.2356	−0.794107
$419$	−25.8388	−1.26231	−0.631154	−	0.775657i	$-0.717419\pi$
$419$	−25.8388	−1.26231	−0.631154	+	0.775657i	$0.717419\pi$
$420$	−23.3536	−1.13954
$421$	−10.6812	−0.520568	−0.260284	−	0.965532i	$-0.583816\pi$
$421$	−10.6812	−0.520568	−0.260284	+	0.965532i	$0.583816\pi$
$422$	51.0798	2.48653
$423$	−8.33573	−0.405297
$424$	−16.6749	−0.809803
$425$	−2.82588	−0.137075
$426$	−51.6425	−2.50209
$427$	−4.57660	−0.221477
$428$	32.4706	1.56953
$429$	5.69132	0.274780
$430$	−47.2896	−2.28051
$431$	8.24386	0.397093	0.198546	−	0.980091i	$-0.436378\pi$
$431$	8.24386	0.397093	0.198546	+	0.980091i	$0.436378\pi$
$432$	1.54905	0.0745288
$433$	4.87699	0.234373	0.117187	−	0.993110i	$-0.462612\pi$
$433$	4.87699	0.234373	0.117187	+	0.993110i	$0.462612\pi$
$434$	−3.85132	−0.184869
$435$	60.1620	2.88455
$436$	−1.37571	−0.0658844
$437$	34.0230	1.62754
$438$	34.6236	1.65438
$439$	19.8620	0.947963	0.473982	−	0.880535i	$-0.342816\pi$
$439$	19.8620	0.947963	0.473982	+	0.880535i	$0.342816\pi$
$440$	7.16201	0.341435
$441$	−14.0383	−0.668491
$442$	−4.00009	−0.190265
$443$	−14.7371	−0.700182	−0.350091	−	0.936716i	$-0.613849\pi$
$443$	−14.7371	−0.700182	−0.350091	+	0.936716i	$0.613849\pi$
$444$	−11.7389	−0.557102
$445$	−17.9013	−0.848604
$446$	−13.6987	−0.648652
$447$	20.3512	0.962578
$448$	15.7690	0.745017
$449$	20.4097	0.963193	0.481597	−	0.876393i	$-0.340057\pi$
$449$	20.4097	0.963193	0.481597	+	0.876393i	$0.340057\pi$
$450$	−15.9774	−0.753182
$451$	10.1431	0.477622
$452$	−34.7932	−1.63653
$453$	−40.9212	−1.92265
$454$	36.3353	1.70530
$455$	6.25093	0.293048
$456$	25.0504	1.17309
$457$	27.5873	1.29048	0.645239	−	0.763981i	$-0.276758\pi$
$457$	27.5873	1.29048	0.645239	+	0.763981i	$0.276758\pi$
$458$	8.63152	0.403324
$459$	1.03355	0.0482421
$460$	−49.4652	−2.30633
$461$	−16.5925	−0.772788	−0.386394	−	0.922334i	$-0.626280\pi$
$461$	−16.5925	−0.772788	−0.386394	+	0.922334i	$0.626280\pi$
$462$	−8.54478	−0.397539
$463$	20.3239	0.944534	0.472267	−	0.881456i	$-0.343436\pi$
$463$	20.3239	0.944534	0.472267	+	0.881456i	$0.343436\pi$
$464$	−13.6673	−0.634489
$465$	−9.33772	−0.433027
$466$	−4.11853	−0.190787
$467$	0.797815	0.0369185	0.0184592	−	0.999830i	$-0.494124\pi$
$467$	0.797815	0.0369185	0.0184592	+	0.999830i	$0.494124\pi$
$468$	−13.3305	−0.616202
$469$	−8.67920	−0.400768
$470$	20.0905	0.926706
$471$	−27.4521	−1.26493
$472$	3.30751	0.152240
$473$	−10.1985	−0.468929
$474$	12.6876	0.582763
$475$	−15.6117	−0.716314
$476$	3.53983	0.162248
$477$	22.2169	1.01724
$478$	26.9639	1.23330
$479$	−16.8008	−0.767646	−0.383823	−	0.923407i	$-0.625393\pi$
$479$	−16.8008	−0.767646	−0.383823	+	0.923407i	$0.625393\pi$
$480$	47.1931	2.15406
$481$	3.14208	0.143266
$482$	−3.01035	−0.137118
$483$	17.9063	0.814766
$484$	−26.4922	−1.20419
$485$	−42.0523	−1.90950
$486$	45.8454	2.07959
$487$	0.344348	0.0156039	0.00780196	−	0.999970i	$-0.497517\pi$
$487$	0.344348	0.0156039	0.00780196	+	0.999970i	$0.497517\pi$
$488$	−7.13726	−0.323089
$489$	−29.3097	−1.32543
$490$	33.8347	1.52849
$491$	−3.81319	−0.172087	−0.0860433	−	0.996291i	$-0.527422\pi$
$491$	−3.81319	−0.172087	−0.0860433	+	0.996291i	$0.527422\pi$
$492$	−51.5800	−2.32540
$493$	−9.11906	−0.410702
$494$	−22.0986	−0.994265
$495$	−9.54239	−0.428898
$496$	2.12130	0.0952491
$497$	−12.2324	−0.548697
$498$	25.0199	1.12117
$499$	0.379146	0.0169729	0.00848646	−	0.999964i	$-0.497299\pi$
$499$	0.379146	0.0169729	0.00848646	+	0.999964i	$0.497299\pi$
$500$	−17.4625	−0.780948
$501$	−13.5329	−0.604606
$502$	52.9604	2.36374
$503$	−21.3276	−0.950950	−0.475475	−	0.879729i	$-0.657724\pi$
$503$	−21.3276	−0.950950	−0.475475	+	0.879729i	$0.657724\pi$
$504$	6.07259	0.270495
$505$	45.7657	2.03655
$506$	−18.0987	−0.804585
$507$	−22.9117	−1.01755
$508$	11.8658	0.526459
$509$	27.1592	1.20381	0.601904	−	0.798568i	$-0.294409\pi$
$509$	27.1592	1.20381	0.601904	+	0.798568i	$0.294409\pi$
$510$	14.5609	0.644768
$511$	8.20117	0.362798
$512$	−16.4845	−0.728517
$513$	5.70991	0.252099
$514$	0.219660	0.00968879
$515$	−3.67510	−0.161944
$516$	51.8615	2.28308
$517$	4.33274	0.190554
$518$	−4.71742	−0.207271
$519$	−19.3202	−0.848063
$520$	9.74841	0.427496
$521$	39.5359	1.73210	0.866049	−	0.499959i	$-0.166652\pi$
$521$	39.5359	1.73210	0.866049	+	0.499959i	$0.166652\pi$
$522$	−51.5587	−2.25666
$523$	12.3238	0.538882	0.269441	−	0.963017i	$-0.413161\pi$
$523$	12.3238	0.538882	0.269441	+	0.963017i	$0.413161\pi$
$524$	25.3395	1.10696
$525$	−8.21645	−0.358595
$526$	57.0517	2.48757
$527$	1.41537	0.0616543
$528$	4.70645	0.204822
$529$	14.9273	0.649015
$530$	−53.5465	−2.32591
$531$	−4.40679	−0.191239
$532$	19.5559	0.847856
$533$	13.8061	0.598009
$534$	33.3073	1.44135
$535$	31.6374	1.36780
$536$	−13.5353	−0.584637
$537$	−43.4554	−1.87524
$538$	27.0355	1.16558
$539$	7.29682	0.314296
$540$	−8.30151	−0.357240
$541$	22.1750	0.953376	0.476688	−	0.879073i	$-0.341837\pi$
$541$	22.1750	0.953376	0.476688	+	0.879073i	$0.341837\pi$
$542$	−18.3600	−0.788628
$543$	46.5416	1.99729
$544$	−7.15329	−0.306695
$545$	−1.34040	−0.0574165
$546$	−11.6305	−0.497741
$547$	−36.3780	−1.55541	−0.777705	−	0.628629i	$-0.783616\pi$
$547$	−36.3780	−1.55541	−0.777705	+	0.628629i	$0.783616\pi$
$548$	−37.9522	−1.62124
$549$	9.50941	0.405852
$550$	8.30472	0.354114
$551$	−50.3786	−2.14620
$552$	27.9251	1.18857
$553$	3.00527	0.127797
$554$	−17.1228	−0.727477
$555$	−11.4376	−0.485500
$556$	−43.4594	−1.84309
$557$	−40.8516	−1.73094	−0.865469	−	0.500963i	$-0.832979\pi$
$557$	−40.8516	−1.73094	−0.865469	+	0.500963i	$0.832979\pi$
$558$	8.00241	0.338769
$559$	−13.8815	−0.587124
$560$	5.16921	0.218439
$561$	3.14022	0.132580
$562$	−61.5803	−2.59761
$563$	13.4531	0.566981	0.283491	−	0.958975i	$-0.408508\pi$
$563$	13.4531	0.566981	0.283491	+	0.958975i	$0.408508\pi$
$564$	−22.0329	−0.927750
$565$	−33.9003	−1.42620
$566$	12.4232	0.522187
$567$	12.4802	0.524118
$568$	−19.0765	−0.800434
$569$	27.8814	1.16885	0.584425	−	0.811448i	$-0.301320\pi$
$569$	27.8814	1.16885	0.584425	+	0.811448i	$0.301320\pi$
$570$	80.4423	3.36936
$571$	21.5974	0.903825	0.451912	−	0.892062i	$-0.350742\pi$
$571$	21.5974	0.903825	0.451912	+	0.892062i	$0.350742\pi$
$572$	6.92891	0.289712
$573$	−40.4232	−1.68870
$574$	−20.7281	−0.865173
$575$	−17.4032	−0.725766
$576$	−32.7655	−1.36523
$577$	0.832060	0.0346391	0.0173196	−	0.999850i	$-0.494487\pi$
$577$	0.832060	0.0346391	0.0173196	+	0.999850i	$0.494487\pi$
$578$	−2.20707	−0.0918020
$579$	−15.0070	−0.623669
$580$	73.2444	3.04131
$581$	5.92636	0.245867
$582$	78.2429	3.24327
$583$	−11.5479	−0.478265
$584$	12.7898	0.529247
$585$	−12.9884	−0.537004
$586$	−47.5414	−1.96392
$587$	22.2322	0.917623	0.458811	−	0.888534i	$-0.348275\pi$
$587$	22.2322	0.917623	0.458811	+	0.888534i	$0.348275\pi$
$588$	−37.1058	−1.53022
$589$	7.81925	0.322187
$590$	10.6211	0.437264
$591$	−40.5971	−1.66994
$592$	2.59834	0.106791
$593$	−8.17343	−0.335642	−0.167821	−	0.985817i	$-0.553673\pi$
$593$	−8.17343	−0.335642	−0.167821	+	0.985817i	$0.553673\pi$
$594$	−3.03741	−0.124627
$595$	3.44898	0.141395
$596$	24.7766	1.01489
$597$	−1.12635	−0.0460985
$598$	−24.6346	−1.00738
$599$	17.2933	0.706583	0.353292	−	0.935513i	$-0.385062\pi$
$599$	17.2933	0.706583	0.353292	+	0.935513i	$0.385062\pi$
$600$	−12.8137	−0.523116
$601$	10.4479	0.426179	0.213089	−	0.977033i	$-0.431647\pi$
$601$	10.4479	0.426179	0.213089	+	0.977033i	$0.431647\pi$
$602$	20.8412	0.849425
$603$	18.0339	0.734399
$604$	−49.8196	−2.02713
$605$	−25.8123	−1.04942
$606$	−85.1520	−3.45906
$607$	−1.56711	−0.0636071	−0.0318036	−	0.999494i	$-0.510125\pi$
$607$	−1.56711	−0.0636071	−0.0318036	+	0.999494i	$0.510125\pi$
$608$	−39.5187	−1.60269
$609$	−26.5143	−1.07441
$610$	−22.9193	−0.927974
$611$	5.89741	0.238584
$612$	−7.35518	−0.297315
$613$	4.55767	0.184083	0.0920414	−	0.995755i	$-0.470661\pi$
$613$	4.55767	0.184083	0.0920414	+	0.995755i	$0.470661\pi$
$614$	9.53292	0.384717
$615$	−50.2563	−2.02653
$616$	−3.15641	−0.127175
$617$	−36.6941	−1.47725	−0.738625	−	0.674117i	$-0.764524\pi$
$617$	−36.6941	−1.47725	−0.738625	+	0.674117i	$0.764524\pi$
$618$	6.83792	0.275061
$619$	30.2702	1.21666	0.608332	−	0.793683i	$-0.291839\pi$
$619$	30.2702	1.21666	0.608332	+	0.793683i	$0.291839\pi$
$620$	−11.3682	−0.456559
$621$	6.36516	0.255425
$622$	−26.4176	−1.05925
$623$	7.88938	0.316081
$624$	6.40607	0.256448
$625$	−31.1438	−1.24575
$626$	−68.1459	−2.72366
$627$	17.3483	0.692823
$628$	−33.4217	−1.33367
$629$	1.73366	0.0691255
$630$	19.5004	0.776914
$631$	−37.0650	−1.47554	−0.737768	−	0.675055i	$-0.764120\pi$
$631$	−37.0650	−1.47554	−0.737768	+	0.675055i	$0.764120\pi$
$632$	4.68677	0.186430
$633$	−54.5807	−2.16939
$634$	1.26166	0.0501070
$635$	11.5613	0.458795
$636$	58.7234	2.32854
$637$	9.93190	0.393516
$638$	26.7992	1.06099
$639$	25.4168	1.00547
$640$	38.9479	1.53955
$641$	2.82079	0.111415	0.0557073	−	0.998447i	$-0.482259\pi$
$641$	2.82079	0.111415	0.0557073	+	0.998447i	$0.482259\pi$
$642$	−58.8647	−2.32321
$643$	8.68064	0.342331	0.171165	−	0.985242i	$-0.445247\pi$
$643$	8.68064	0.342331	0.171165	+	0.985242i	$0.445247\pi$
$644$	21.8001	0.859043
$645$	50.5306	1.98964
$646$	−12.1931	−0.479729
$647$	32.0125	1.25854	0.629271	−	0.777186i	$-0.283353\pi$
$647$	32.0125	1.25854	0.629271	+	0.777186i	$0.283353\pi$
$648$	19.4630	0.764579
$649$	2.29056	0.0899123
$650$	11.3038	0.443371
$651$	4.11528	0.161290
$652$	−35.6831	−1.39746
$653$	5.34452	0.209147	0.104574	−	0.994517i	$-0.466652\pi$
$653$	5.34452	0.209147	0.104574	+	0.994517i	$0.466652\pi$
$654$	2.49396	0.0975217
$655$	24.6892	0.964688
$656$	11.4170	0.445758
$657$	−17.0407	−0.664820
$658$	−8.85419	−0.345172
$659$	48.7975	1.90088	0.950441	−	0.310905i	$-0.100632\pi$
$659$	48.7975	1.90088	0.950441	+	0.310905i	$0.100632\pi$
$660$	−25.2223	−0.981775
$661$	−3.43450	−0.133586	−0.0667932	−	0.997767i	$-0.521277\pi$
$661$	−3.43450	−0.133586	−0.0667932	+	0.997767i	$0.521277\pi$
$662$	−53.9853	−2.09820
$663$	4.27424	0.165998
$664$	9.24223	0.358668
$665$	19.0541	0.738885
$666$	9.80202	0.379821
$667$	−56.1599	−2.17452
$668$	−16.4757	−0.637462
$669$	14.6376	0.565921
$670$	−43.4648	−1.67919
$671$	−4.94280	−0.190814
$672$	−20.7987	−0.802327
$673$	21.4308	0.826095	0.413047	−	0.910710i	$-0.364464\pi$
$673$	21.4308	0.826095	0.413047	+	0.910710i	$0.364464\pi$
$674$	−51.1614	−1.97066
$675$	−2.92070	−0.112418
$676$	−27.8939	−1.07284
$677$	−46.0798	−1.77099	−0.885495	−	0.464648i	$-0.846181\pi$
$677$	−46.0798	−1.77099	−0.885495	+	0.464648i	$0.846181\pi$
$678$	63.0752	2.42239
$679$	18.5331	0.711235
$680$	5.37874	0.206265
$681$	−38.8256	−1.48780
$682$	−4.15949	−0.159275
$683$	6.87667	0.263128	0.131564	−	0.991308i	$-0.458000\pi$
$683$	6.87667	0.263128	0.131564	+	0.991308i	$0.458000\pi$
$684$	−40.6340	−1.55368
$685$	−36.9783	−1.41287
$686$	−33.9590	−1.29656
$687$	−9.22309	−0.351883
$688$	−11.4793	−0.437644
$689$	−15.7182	−0.598814
$690$	89.6736	3.41381
$691$	−21.0652	−0.801360	−0.400680	−	0.916218i	$-0.631226\pi$
$691$	−21.0652	−0.801360	−0.400680	+	0.916218i	$0.631226\pi$
$692$	−23.5214	−0.894150
$693$	4.20547	0.159753
$694$	−72.9782	−2.77021
$695$	−42.3441	−1.60620
$696$	−41.3494	−1.56735
$697$	7.61760	0.288537
$698$	3.24453	0.122807
$699$	4.40080	0.166454
$700$	−10.0031	−0.378083
$701$	25.7339	0.971956	0.485978	−	0.873971i	$-0.338464\pi$
$701$	25.7339	0.971956	0.485978	+	0.873971i	$0.338464\pi$
$702$	−4.13430	−0.156039
$703$	9.57767	0.361229
$704$	17.0308	0.641873
$705$	−21.4674	−0.808510
$706$	2.20707	0.0830642
$707$	−20.1696	−0.758557
$708$	−11.6480	−0.437757
$709$	11.6009	0.435679	0.217840	−	0.975985i	$-0.430099\pi$
$709$	11.6009	0.435679	0.217840	+	0.975985i	$0.430099\pi$
$710$	−61.2588	−2.29900
$711$	−6.24447	−0.234186
$712$	12.3036	0.461097
$713$	8.71656	0.326438
$714$	−6.41721	−0.240158
$715$	6.75110	0.252477
$716$	−52.9048	−1.97715
$717$	−28.8119	−1.07600
$718$	48.1382	1.79650
$719$	24.4333	0.911208	0.455604	−	0.890183i	$-0.349423\pi$
$719$	24.4333	0.911208	0.455604	+	0.890183i	$0.349423\pi$
$720$	−10.7408	−0.400285
$721$	1.61967	0.0603197
$722$	−25.4267	−0.946283
$723$	3.21667	0.119629
$724$	56.6622	2.10583
$725$	25.7694	0.957052
$726$	48.0266	1.78244
$727$	14.8271	0.549908	0.274954	−	0.961457i	$-0.411337\pi$
$727$	14.8271	0.549908	0.274954	+	0.961457i	$0.411337\pi$
$728$	−4.29627	−0.159230
$729$	−18.6194	−0.689606
$730$	41.0709	1.52010
$731$	−7.65919	−0.283285
$732$	25.1351	0.929020
$733$	50.1795	1.85342	0.926711	−	0.375774i	$-0.122623\pi$
$733$	50.1795	1.85342	0.926711	+	0.375774i	$0.122623\pi$
$734$	−29.5001	−1.08887
$735$	−36.1536	−1.33354
$736$	−44.0537	−1.62384
$737$	−9.37367	−0.345283
$738$	43.0695	1.58541
$739$	−18.4748	−0.679608	−0.339804	−	0.940496i	$-0.610361\pi$
$739$	−18.4748	−0.679608	−0.339804	+	0.940496i	$0.610361\pi$
$740$	−13.9248	−0.511884
$741$	23.6132	0.867453
$742$	23.5988	0.866338
$743$	7.40447	0.271644	0.135822	−	0.990733i	$-0.456633\pi$
$743$	7.40447	0.271644	0.135822	+	0.990733i	$0.456633\pi$
$744$	6.41783	0.235289
$745$	24.1407	0.884449
$746$	−76.7565	−2.81026
$747$	−12.3140	−0.450546
$748$	3.82307	0.139785
$749$	−13.9431	−0.509468
$750$	31.6571	1.15595
$751$	2.06412	0.0753209	0.0376604	−	0.999291i	$-0.488009\pi$
$751$	2.06412	0.0753209	0.0376604	+	0.999291i	$0.488009\pi$
$752$	4.87687	0.177841
$753$	−56.5901	−2.06226
$754$	36.4770	1.32842
$755$	−48.5411	−1.76659
$756$	3.65860	0.133062
$757$	−38.7026	−1.40667	−0.703335	−	0.710859i	$-0.748307\pi$
$757$	−38.7026	−1.40667	−0.703335	+	0.710859i	$0.748307\pi$
$758$	51.6083	1.87450
$759$	19.3391	0.701965
$760$	29.7151	1.07788
$761$	3.47617	0.126011	0.0630055	−	0.998013i	$-0.479931\pi$
$761$	3.47617	0.126011	0.0630055	+	0.998013i	$0.479931\pi$
$762$	−21.5110	−0.779262
$763$	0.590735	0.0213861
$764$	−49.2133	−1.78047
$765$	−7.16642	−0.259103
$766$	−27.9201	−1.00879
$767$	3.11774	0.112575
$768$	−12.1391	−0.438033
$769$	20.7894	0.749687	0.374843	−	0.927088i	$-0.377696\pi$
$769$	20.7894	0.749687	0.374843	+	0.927088i	$0.377696\pi$
$770$	−10.1359	−0.365272
$771$	−0.234715	−0.00845305
$772$	−18.2703	−0.657562
$773$	−27.5295	−0.990169	−0.495085	−	0.868845i	$-0.664863\pi$
$773$	−27.5295	−0.990169	−0.495085	+	0.868845i	$0.664863\pi$
$774$	−43.3047	−1.55655
$775$	−3.99966	−0.143672
$776$	28.9026	1.03754
$777$	5.04073	0.180835
$778$	46.5634	1.66938
$779$	42.0837	1.50781
$780$	−34.3307	−1.22924
$781$	−13.2111	−0.472732
$782$	−13.5923	−0.486059
$783$	−9.42504	−0.336823
$784$	8.21319	0.293328
$785$	−32.5640	−1.16226
$786$	−45.9370	−1.63852
$787$	−39.5151	−1.40856	−0.704280	−	0.709922i	$-0.748730\pi$
$787$	−39.5151	−1.40856	−0.704280	+	0.709922i	$0.748730\pi$
$788$	−49.4250	−1.76069
$789$	−60.9619	−2.17030
$790$	15.0502	0.535462
$791$	14.9404	0.531219
$792$	6.55849	0.233046
$793$	−6.72777	−0.238910
$794$	−6.60374	−0.234358
$795$	57.2164	2.02926
$796$	−1.37128	−0.0486037
$797$	−26.9246	−0.953720	−0.476860	−	0.878979i	$-0.658225\pi$
$797$	−26.9246	−0.953720	−0.476860	+	0.878979i	$0.658225\pi$
$798$	−35.4521	−1.25499
$799$	3.25393	0.115116
$800$	20.2144	0.714686
$801$	−16.3928	−0.579212
$802$	22.4658	0.793296
$803$	8.85739	0.312570
$804$	47.6670	1.68108
$805$	21.2406	0.748634
$806$	−5.66159	−0.199421
$807$	−28.8884	−1.01692
$808$	−31.4548	−1.10658
$809$	−43.0722	−1.51434	−0.757168	−	0.653220i	$-0.773418\pi$
$809$	−43.0722	−1.51434	−0.757168	+	0.653220i	$0.773418\pi$
$810$	62.4999	2.19602
$811$	28.5052	1.00095	0.500476	−	0.865750i	$-0.333158\pi$
$811$	28.5052	1.00095	0.500476	+	0.865750i	$0.333158\pi$
$812$	−32.2799	−1.13280
$813$	19.6183	0.688044
$814$	−5.09489	−0.178576
$815$	−34.7674	−1.21785
$816$	3.53459	0.123735
$817$	−42.3135	−1.48036
$818$	−50.7621	−1.77485
$819$	5.72418	0.200019
$820$	−61.1846	−2.13666
$821$	24.7631	0.864237	0.432118	−	0.901817i	$-0.357766\pi$
$821$	24.7631	0.864237	0.432118	+	0.901817i	$0.357766\pi$
$822$	68.8021	2.39975
$823$	50.5771	1.76301	0.881503	−	0.472178i	$-0.156532\pi$
$823$	50.5771	1.76301	0.881503	+	0.472178i	$0.156532\pi$
$824$	2.52590	0.0879938
$825$	−8.87389	−0.308949
$826$	−4.68088	−0.162869
$827$	−47.0970	−1.63772	−0.818861	−	0.573992i	$-0.805394\pi$
$827$	−47.0970	−1.63772	−0.818861	+	0.573992i	$0.805394\pi$
$828$	−45.2970	−1.57418
$829$	−26.5104	−0.920743	−0.460372	−	0.887726i	$-0.652284\pi$
$829$	−26.5104	−0.920743	−0.460372	+	0.887726i	$0.652284\pi$
$830$	29.6788	1.03017
$831$	18.2963	0.634692
$832$	23.1811	0.803660
$833$	5.47998	0.189870
$834$	78.7857	2.72813
$835$	−16.0529	−0.555532
$836$	21.1207	0.730474
$837$	1.46286	0.0505637
$838$	57.0281	1.97000
$839$	−22.7756	−0.786302	−0.393151	−	0.919474i	$-0.628615\pi$
$839$	−22.7756	−0.786302	−0.393151	+	0.919474i	$0.628615\pi$
$840$	15.6391	0.539599
$841$	54.1573	1.86749
$842$	23.5741	0.812416
$843$	65.8008	2.26630
$844$	−66.4493	−2.28728
$845$	−27.1781	−0.934955
$846$	18.3975	0.632521
$847$	11.3759	0.390880
$848$	−12.9981	−0.446358
$849$	−13.2747	−0.455585
$850$	6.23692	0.213925
$851$	10.6768	0.365995
$852$	67.1813	2.30159
$853$	40.0643	1.37178	0.685888	−	0.727707i	$-0.259414\pi$
$853$	40.0643	1.37178	0.685888	+	0.727707i	$0.259414\pi$
$854$	10.1009	0.345645
$855$	−39.5912	−1.35399
$856$	−21.7444	−0.743208
$857$	−3.77487	−0.128947	−0.0644736	−	0.997919i	$-0.520537\pi$
$857$	−3.77487	−0.128947	−0.0644736	+	0.997919i	$0.520537\pi$
$858$	−12.5612	−0.428831
$859$	−47.6134	−1.62455	−0.812274	−	0.583276i	$-0.801771\pi$
$859$	−47.6134	−1.62455	−0.812274	+	0.583276i	$0.801771\pi$
$860$	61.5186	2.09777
$861$	22.1487	0.754826
$862$	−18.1948	−0.619717
$863$	−6.33683	−0.215708	−0.107854	−	0.994167i	$-0.534398\pi$
$863$	−6.33683	−0.215708	−0.107854	+	0.994167i	$0.534398\pi$
$864$	−7.39331	−0.251526
$865$	−22.9178	−0.779229
$866$	−10.7639	−0.365771
$867$	2.35834	0.0800933
$868$	5.01015	0.170056
$869$	3.24574	0.110104
$870$	−132.782	−4.50173
$871$	−12.7587	−0.432314
$872$	0.921260	0.0311978
$873$	−38.5087	−1.30332
$874$	−75.0911	−2.53999
$875$	7.49850	0.253496
$876$	−45.0416	−1.52181
$877$	19.7306	0.666254	0.333127	−	0.942882i	$-0.391896\pi$
$877$	19.7306	0.666254	0.333127	+	0.942882i	$0.391896\pi$
$878$	−43.8369	−1.47942
$879$	50.7997	1.71343
$880$	5.58283	0.188197
$881$	30.8366	1.03891	0.519456	−	0.854497i	$-0.326135\pi$
$881$	30.8366	1.03891	0.519456	+	0.854497i	$0.326135\pi$
$882$	30.9835	1.04327
$883$	−32.2549	−1.08546	−0.542731	−	0.839906i	$-0.682610\pi$
$883$	−32.2549	−1.08546	−0.542731	+	0.839906i	$0.682610\pi$
$884$	5.20368	0.175019
$885$	−11.3490	−0.381494
$886$	32.5259	1.09273
$887$	−15.3189	−0.514359	−0.257179	−	0.966364i	$-0.582793\pi$
$887$	−15.3189	−0.514359	−0.257179	+	0.966364i	$0.582793\pi$
$888$	7.86109	0.263801
$889$	−5.09523	−0.170889
$890$	39.5095	1.32436
$891$	13.4788	0.451556
$892$	17.8205	0.596675
$893$	17.9765	0.601559
$894$	−44.9165	−1.50223
$895$	−51.5472	−1.72303
$896$	−17.1649	−0.573440
$897$	26.3230	0.878898
$898$	−45.0457	−1.50319
$899$	−12.9068	−0.430466
$900$	20.7849	0.692829
$901$	−8.67258	−0.288926
$902$	−22.3866	−0.745394
$903$	−22.2696	−0.741087
$904$	23.2997	0.774937
$905$	55.2081	1.83518
$906$	90.3160	3.00055
$907$	−6.00921	−0.199533	−0.0997664	−	0.995011i	$-0.531810\pi$
$907$	−6.00921	−0.199533	−0.0997664	+	0.995011i	$0.531810\pi$
$908$	−47.2683	−1.56865
$909$	41.9092	1.39004
$910$	−13.7962	−0.457341
$911$	−13.6514	−0.452289	−0.226145	−	0.974094i	$-0.572612\pi$
$911$	−13.6514	−0.452289	−0.226145	+	0.974094i	$0.572612\pi$
$912$	19.5270	0.646602
$913$	6.40056	0.211828
$914$	−60.8870	−2.01396
$915$	24.4901	0.809617
$916$	−11.2287	−0.371006
$917$	−10.8809	−0.359320
$918$	−2.28113	−0.0752883
$919$	−44.0249	−1.45225	−0.726123	−	0.687564i	$-0.758680\pi$
$919$	−44.0249	−1.45225	−0.726123	+	0.687564i	$0.758680\pi$
$920$	33.1250	1.09210
$921$	−10.1863	−0.335649
$922$	36.6207	1.20604
$923$	−17.9820	−0.591886
$924$	11.1158	0.365684
$925$	−4.89912	−0.161082
$926$	−44.8564	−1.47407
$927$	−3.36541	−0.110535
$928$	65.2314	2.14132
$929$	34.9801	1.14766	0.573829	−	0.818975i	$-0.305457\pi$
$929$	34.9801	1.14766	0.573829	+	0.818975i	$0.305457\pi$
$930$	20.6090	0.675796
$931$	30.2744	0.992203
$932$	5.35776	0.175499
$933$	28.2282	0.924149
$934$	−1.76083	−0.0576162
$935$	3.72496	0.121819
$936$	8.92694	0.291786
$937$	22.5808	0.737684	0.368842	−	0.929492i	$-0.379754\pi$
$937$	22.5808	0.737684	0.368842	+	0.929492i	$0.379754\pi$
$938$	19.1556	0.625452
$939$	72.8164	2.37627
$940$	−26.1356	−0.852448
$941$	−11.0745	−0.361019	−0.180509	−	0.983573i	$-0.557775\pi$
$941$	−11.0745	−0.361019	−0.180509	+	0.983573i	$0.557775\pi$
$942$	60.5888	1.97409
$943$	46.9131	1.52770
$944$	2.57822	0.0839139
$945$	3.56471	0.115960
$946$	22.5089	0.731826
$947$	18.6045	0.604565	0.302283	−	0.953218i	$-0.402251\pi$
$947$	18.6045	0.604565	0.302283	+	0.953218i	$0.402251\pi$
$948$	−16.5053	−0.536066
$949$	12.0560	0.391355
$950$	34.4561	1.11790
$951$	−1.34813	−0.0437162
$952$	−2.37049	−0.0768281
$953$	25.5967	0.829157	0.414578	−	0.910014i	$-0.363929\pi$
$953$	25.5967	0.829157	0.414578	+	0.910014i	$0.363929\pi$
$954$	−49.0344	−1.58755
$955$	−47.9503	−1.55164
$956$	−35.0771	−1.13448
$957$	−28.6359	−0.925666
$958$	37.0805	1.19802
$959$	16.2969	0.526254
$960$	−84.3826	−2.72344
$961$	−28.9967	−0.935379
$962$	−6.93479	−0.223586
$963$	28.9714	0.933590
$964$	3.91614	0.126130
$965$	−17.8014	−0.573048
$966$	−39.5205	−1.27155
$967$	−30.8727	−0.992801	−0.496400	−	0.868094i	$-0.665345\pi$
$967$	−30.8727	−0.992801	−0.496400	+	0.868094i	$0.665345\pi$
$968$	17.7408	0.570212
$969$	13.0287	0.418543
$970$	92.8124	2.98003
$971$	−57.3292	−1.83978	−0.919892	−	0.392173i	$-0.871723\pi$
$971$	−57.3292	−1.83978	−0.919892	+	0.392173i	$0.871723\pi$
$972$	−59.6399	−1.91295
$973$	18.6617	0.598266
$974$	−0.760001	−0.0243520
$975$	−12.0785	−0.386821
$976$	−5.56354	−0.178084
$977$	−6.75834	−0.216218	−0.108109	−	0.994139i	$-0.534480\pi$
$977$	−6.75834	−0.216218	−0.108109	+	0.994139i	$0.534480\pi$
$978$	64.6885	2.06851
$979$	8.52065	0.272321
$980$	−44.0152	−1.40601
$981$	−1.22745	−0.0391895
$982$	8.41597	0.268564
$983$	4.50130	0.143569	0.0717846	−	0.997420i	$-0.477131\pi$
$983$	4.50130	0.143569	0.0717846	+	0.997420i	$0.477131\pi$
$984$	34.5412	1.10113
$985$	−48.1566	−1.53440
$986$	20.1264	0.640956
$987$	9.46102	0.301148
$988$	28.7479	0.914594
$989$	−47.1692	−1.49989
$990$	21.0607	0.669354
$991$	45.4836	1.44484	0.722418	−	0.691457i	$-0.243031\pi$
$991$	45.4836	1.44484	0.722418	+	0.691457i	$0.243031\pi$
$992$	−10.1245	−0.321454
$993$	57.6853	1.83059
$994$	26.9977	0.856315
$995$	−1.33609	−0.0423569
$996$	−32.5481	−1.03133
$997$	57.1775	1.81083	0.905415	−	0.424528i	$-0.139560\pi$
$997$	57.1775	1.81083	0.905415	+	0.424528i	$0.139560\pi$
$998$	−0.836803	−0.0264885
$999$	1.79183	0.0566910

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.a.1.16	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.a.1.16	✓	113	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.20707 q^{2} +2.35834 q^{3} +2.87116 q^{4} +2.79748 q^{5} -5.20501 q^{6} -1.23289 q^{7} -1.92271 q^{8} +2.56174 q^{9} +O(q^{10})\)	\(q-2.20707 q^{2} +2.35834 q^{3} +2.87116 q^{4} +2.79748 q^{5} -5.20501 q^{6} -1.23289 q^{7} -1.92271 q^{8} +2.56174 q^{9} -6.17423 q^{10} -1.33154 q^{11} +6.77116 q^{12} -1.81240 q^{13} +2.72108 q^{14} +6.59739 q^{15} -1.49876 q^{16} -1.00000 q^{17} -5.65395 q^{18} -5.52454 q^{19} +8.03200 q^{20} -2.90757 q^{21} +2.93881 q^{22} -6.15852 q^{23} -4.53439 q^{24} +2.82588 q^{25} +4.00009 q^{26} -1.03355 q^{27} -3.53983 q^{28} +9.11906 q^{29} -14.5609 q^{30} -1.41537 q^{31} +7.15329 q^{32} -3.14022 q^{33} +2.20707 q^{34} -3.44898 q^{35} +7.35518 q^{36} -1.73366 q^{37} +12.1931 q^{38} -4.27424 q^{39} -5.37874 q^{40} -7.61760 q^{41} +6.41721 q^{42} +7.65919 q^{43} -3.82307 q^{44} +7.16642 q^{45} +13.5923 q^{46} -3.25393 q^{47} -3.53459 q^{48} -5.47998 q^{49} -6.23692 q^{50} -2.35834 q^{51} -5.20368 q^{52} +8.67258 q^{53} +2.28113 q^{54} -3.72496 q^{55} +2.37049 q^{56} -13.0287 q^{57} -20.1264 q^{58} -1.72023 q^{59} +18.9422 q^{60} +3.71209 q^{61} +3.12381 q^{62} -3.15835 q^{63} -12.7903 q^{64} -5.07014 q^{65} +6.93069 q^{66} +7.03971 q^{67} -2.87116 q^{68} -14.5238 q^{69} +7.61215 q^{70} +9.92169 q^{71} -4.92549 q^{72} -6.65198 q^{73} +3.82631 q^{74} +6.66438 q^{75} -15.8618 q^{76} +1.64164 q^{77} +9.43354 q^{78} -2.43758 q^{79} -4.19276 q^{80} -10.1227 q^{81} +16.8126 q^{82} -4.80688 q^{83} -8.34810 q^{84} -2.79748 q^{85} -16.9044 q^{86} +21.5058 q^{87} +2.56017 q^{88} -6.39909 q^{89} -15.8168 q^{90} +2.23449 q^{91} -17.6821 q^{92} -3.33791 q^{93} +7.18165 q^{94} -15.4548 q^{95} +16.8699 q^{96} -15.0322 q^{97} +12.0947 q^{98} -3.41107 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * q^99

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