LMFDB - Embedded newform 8043.2.a.q.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.2236783457$
Analytic rank:	$1$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.28577 q^{2} +1.00000 q^{3} -0.346791 q^{4} -1.72364 q^{5} -1.28577 q^{6} -1.00000 q^{7} +3.01744 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.28577 q^{2} +1.00000 q^{3} -0.346791 q^{4} -1.72364 q^{5} -1.28577 q^{6} -1.00000 q^{7} +3.01744 q^{8} +1.00000 q^{9} +2.21621 q^{10} +4.44208 q^{11} -0.346791 q^{12} +3.95687 q^{13} +1.28577 q^{14} -1.72364 q^{15} -3.18615 q^{16} +3.67979 q^{17} -1.28577 q^{18} +3.16642 q^{19} +0.597744 q^{20} -1.00000 q^{21} -5.71150 q^{22} -7.88017 q^{23} +3.01744 q^{24} -2.02905 q^{25} -5.08763 q^{26} +1.00000 q^{27} +0.346791 q^{28} -4.45391 q^{29} +2.21621 q^{30} -7.40231 q^{31} -1.93821 q^{32} +4.44208 q^{33} -4.73137 q^{34} +1.72364 q^{35} -0.346791 q^{36} -7.98661 q^{37} -4.07129 q^{38} +3.95687 q^{39} -5.20099 q^{40} +8.58946 q^{41} +1.28577 q^{42} +2.87790 q^{43} -1.54048 q^{44} -1.72364 q^{45} +10.1321 q^{46} -6.56637 q^{47} -3.18615 q^{48} +1.00000 q^{49} +2.60890 q^{50} +3.67979 q^{51} -1.37221 q^{52} -7.64131 q^{53} -1.28577 q^{54} -7.65656 q^{55} -3.01744 q^{56} +3.16642 q^{57} +5.72671 q^{58} +6.61752 q^{59} +0.597744 q^{60} +2.09088 q^{61} +9.51768 q^{62} -1.00000 q^{63} +8.86440 q^{64} -6.82022 q^{65} -5.71150 q^{66} -11.5390 q^{67} -1.27612 q^{68} -7.88017 q^{69} -2.21621 q^{70} -3.70760 q^{71} +3.01744 q^{72} -12.8338 q^{73} +10.2690 q^{74} -2.02905 q^{75} -1.09809 q^{76} -4.44208 q^{77} -5.08763 q^{78} +11.6666 q^{79} +5.49179 q^{80} +1.00000 q^{81} -11.0441 q^{82} +1.27725 q^{83} +0.346791 q^{84} -6.34265 q^{85} -3.70032 q^{86} -4.45391 q^{87} +13.4037 q^{88} +6.30820 q^{89} +2.21621 q^{90} -3.95687 q^{91} +2.73277 q^{92} -7.40231 q^{93} +8.44286 q^{94} -5.45777 q^{95} -1.93821 q^{96} +4.29604 q^{97} -1.28577 q^{98} +4.44208 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9}+O(q^{10}) $ 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9} - 16 q^{10} - 2 q^{11} + 44 q^{12} - 34 q^{13} + 4 q^{14} - 16 q^{15} + 24 q^{16} - 4 q^{17} - 4 q^{18} - 22 q^{19} - 39 q^{20} - 44 q^{21} - 23 q^{22} - 56 q^{23} - 15 q^{24} + 32 q^{25} - 17 q^{26} + 44 q^{27} - 44 q^{28} - 33 q^{29} - 16 q^{30} - 32 q^{31} - 34 q^{32} - 2 q^{33} - 25 q^{34} + 16 q^{35} + 44 q^{36} - 47 q^{37} - 40 q^{38} - 34 q^{39} - 50 q^{40} + 2 q^{41} + 4 q^{42} - 12 q^{43} - 22 q^{44} - 16 q^{45} + 8 q^{46} - 27 q^{47} + 24 q^{48} + 44 q^{49} - 21 q^{50} - 4 q^{51} - 82 q^{52} - 114 q^{53} - 4 q^{54} - 29 q^{55} + 15 q^{56} - 22 q^{57} - 26 q^{58} - 40 q^{59} - 39 q^{60} - 47 q^{61} - 37 q^{62} - 44 q^{63} - 5 q^{64} - 20 q^{65} - 23 q^{66} - 14 q^{67} - 72 q^{68} - 56 q^{69} + 16 q^{70} - 65 q^{71} - 15 q^{72} - 21 q^{73} - 26 q^{74} + 32 q^{75} - 15 q^{76} + 2 q^{77} - 17 q^{78} + 6 q^{79} - 77 q^{80} + 44 q^{81} - 51 q^{82} - 30 q^{83} - 44 q^{84} - 26 q^{85} - 65 q^{86} - 33 q^{87} - 84 q^{88} - 32 q^{89} - 16 q^{90} + 34 q^{91} - 140 q^{92} - 32 q^{93} - 35 q^{94} - 50 q^{95} - 34 q^{96} - 83 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9 - 16 * q^10 - 2 * q^11 + 44 * q^12 - 34 * q^13 + 4 * q^14 - 16 * q^15 + 24 * q^16 - 4 * q^17 - 4 * q^18 - 22 * q^19 - 39 * q^20 - 44 * q^21 - 23 * q^22 - 56 * q^23 - 15 * q^24 + 32 * q^25 - 17 * q^26 + 44 * q^27 - 44 * q^28 - 33 * q^29 - 16 * q^30 - 32 * q^31 - 34 * q^32 - 2 * q^33 - 25 * q^34 + 16 * q^35 + 44 * q^36 - 47 * q^37 - 40 * q^38 - 34 * q^39 - 50 * q^40 + 2 * q^41 + 4 * q^42 - 12 * q^43 - 22 * q^44 - 16 * q^45 + 8 * q^46 - 27 * q^47 + 24 * q^48 + 44 * q^49 - 21 * q^50 - 4 * q^51 - 82 * q^52 - 114 * q^53 - 4 * q^54 - 29 * q^55 + 15 * q^56 - 22 * q^57 - 26 * q^58 - 40 * q^59 - 39 * q^60 - 47 * q^61 - 37 * q^62 - 44 * q^63 - 5 * q^64 - 20 * q^65 - 23 * q^66 - 14 * q^67 - 72 * q^68 - 56 * q^69 + 16 * q^70 - 65 * q^71 - 15 * q^72 - 21 * q^73 - 26 * q^74 + 32 * q^75 - 15 * q^76 + 2 * q^77 - 17 * q^78 + 6 * q^79 - 77 * q^80 + 44 * q^81 - 51 * q^82 - 30 * q^83 - 44 * q^84 - 26 * q^85 - 65 * q^86 - 33 * q^87 - 84 * q^88 - 32 * q^89 - 16 * q^90 + 34 * q^91 - 140 * q^92 - 32 * q^93 - 35 * q^94 - 50 * q^95 - 34 * q^96 - 83 * q^97 - 4 * q^98 - 2 * 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 $

$2$	−1.28577	−0.909178	−0.454589	−	0.890701i	$-0.650214\pi$
$2$	−1.28577	−0.909178	−0.454589	+	0.890701i	$0.650214\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.346791	−0.173396
$5$	−1.72364	−0.770837	−0.385418	−	0.922742i	$-0.625943\pi$
$5$	−1.72364	−0.770837	−0.385418	+	0.922742i	$0.625943\pi$
$6$	−1.28577	−0.524914
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.01744	1.06683
$9$	1.00000	0.333333
$10$	2.21621	0.700828
$11$	4.44208	1.33934	0.669669	−	0.742660i	$-0.266436\pi$
$11$	4.44208	1.33934	0.669669	+	0.742660i	$0.266436\pi$
$12$	−0.346791	−0.100110
$13$	3.95687	1.09744	0.548719	−	0.836007i	$-0.315116\pi$
$13$	3.95687	1.09744	0.548719	+	0.836007i	$0.315116\pi$
$14$	1.28577	0.343637
$15$	−1.72364	−0.445043
$16$	−3.18615	−0.796538
$17$	3.67979	0.892481	0.446240	−	0.894913i	$-0.352763\pi$
$17$	3.67979	0.892481	0.446240	+	0.894913i	$0.352763\pi$
$18$	−1.28577	−0.303059
$19$	3.16642	0.726426	0.363213	−	0.931706i	$-0.381680\pi$
$19$	3.16642	0.726426	0.363213	+	0.931706i	$0.381680\pi$
$20$	0.597744	0.133660
$21$	−1.00000	−0.218218
$22$	−5.71150	−1.21770
$23$	−7.88017	−1.64313	−0.821565	−	0.570115i	$-0.806899\pi$
$23$	−7.88017	−1.64313	−0.821565	+	0.570115i	$0.806899\pi$
$24$	3.01744	0.615932
$25$	−2.02905	−0.405811
$26$	−5.08763	−0.997765
$27$	1.00000	0.192450
$28$	0.346791	0.0655374
$29$	−4.45391	−0.827071	−0.413535	−	0.910488i	$-0.635706\pi$
$29$	−4.45391	−0.827071	−0.413535	+	0.910488i	$0.635706\pi$
$30$	2.21621	0.404623
$31$	−7.40231	−1.32949	−0.664747	−	0.747069i	$-0.731461\pi$
$31$	−7.40231	−1.32949	−0.664747	+	0.747069i	$0.731461\pi$
$32$	−1.93821	−0.342630
$33$	4.44208	0.773267
$34$	−4.73137	−0.811424
$35$	1.72364	0.291349
$36$	−0.346791	−0.0577985
$37$	−7.98661	−1.31299	−0.656496	−	0.754330i	$-0.727962\pi$
$37$	−7.98661	−1.31299	−0.656496	+	0.754330i	$0.727962\pi$
$38$	−4.07129	−0.660450
$39$	3.95687	0.633606
$40$	−5.20099	−0.822348
$41$	8.58946	1.34145	0.670724	−	0.741707i	$-0.265983\pi$
$41$	8.58946	1.34145	0.670724	+	0.741707i	$0.265983\pi$
$42$	1.28577	0.198399
$43$	2.87790	0.438875	0.219438	−	0.975627i	$-0.429578\pi$
$43$	2.87790	0.438875	0.219438	+	0.975627i	$0.429578\pi$
$44$	−1.54048	−0.232235
$45$	−1.72364	−0.256946
$46$	10.1321	1.49390
$47$	−6.56637	−0.957804	−0.478902	−	0.877868i	$-0.658965\pi$
$47$	−6.56637	−0.957804	−0.478902	+	0.877868i	$0.658965\pi$
$48$	−3.18615	−0.459882
$49$	1.00000	0.142857
$50$	2.60890	0.368954
$51$	3.67979	0.515274
$52$	−1.37221	−0.190291
$53$	−7.64131	−1.04961	−0.524807	−	0.851221i	$-0.675863\pi$
$53$	−7.64131	−1.04961	−0.524807	+	0.851221i	$0.675863\pi$
$54$	−1.28577	−0.174971
$55$	−7.65656	−1.03241
$56$	−3.01744	−0.403222
$57$	3.16642	0.419402
$58$	5.72671	0.751954
$59$	6.61752	0.861528	0.430764	−	0.902465i	$-0.358244\pi$
$59$	6.61752	0.861528	0.430764	+	0.902465i	$0.358244\pi$
$60$	0.597744	0.0771685
$61$	2.09088	0.267710	0.133855	−	0.991001i	$-0.457264\pi$
$61$	2.09088	0.267710	0.133855	+	0.991001i	$0.457264\pi$
$62$	9.51768	1.20875
$63$	−1.00000	−0.125988
$64$	8.86440	1.10805
$65$	−6.82022	−0.845945
$66$	−5.71150	−0.703037
$67$	−11.5390	−1.40971	−0.704857	−	0.709349i	$-0.748989\pi$
$67$	−11.5390	−1.40971	−0.704857	+	0.709349i	$0.748989\pi$
$68$	−1.27612	−0.154752
$69$	−7.88017	−0.948661
$70$	−2.21621	−0.264888
$71$	−3.70760	−0.440011	−0.220005	−	0.975499i	$-0.570608\pi$
$71$	−3.70760	−0.440011	−0.220005	+	0.975499i	$0.570608\pi$
$72$	3.01744	0.355608
$73$	−12.8338	−1.50208	−0.751040	−	0.660257i	$-0.770447\pi$
$73$	−12.8338	−1.50208	−0.751040	+	0.660257i	$0.770447\pi$
$74$	10.2690	1.19374
$75$	−2.02905	−0.234295
$76$	−1.09809	−0.125959
$77$	−4.44208	−0.506222
$78$	−5.08763	−0.576060
$79$	11.6666	1.31260	0.656299	−	0.754501i	$-0.272121\pi$
$79$	11.6666	1.31260	0.656299	+	0.754501i	$0.272121\pi$
$80$	5.49179	0.614001
$81$	1.00000	0.111111
$82$	−11.0441	−1.21962
$83$	1.27725	0.140196	0.0700982	−	0.997540i	$-0.477669\pi$
$83$	1.27725	0.140196	0.0700982	+	0.997540i	$0.477669\pi$
$84$	0.346791	0.0378380
$85$	−6.34265	−0.687957
$86$	−3.70032	−0.399016
$87$	−4.45391	−0.477509
$88$	13.4037	1.42884
$89$	6.30820	0.668668	0.334334	−	0.942455i	$-0.391489\pi$
$89$	6.30820	0.668668	0.334334	+	0.942455i	$0.391489\pi$
$90$	2.21621	0.233609
$91$	−3.95687	−0.414792
$92$	2.73277	0.284911
$93$	−7.40231	−0.767583
$94$	8.44286	0.870814
$95$	−5.45777	−0.559956
$96$	−1.93821	−0.197818
$97$	4.29604	0.436196	0.218098	−	0.975927i	$-0.430015\pi$
$97$	4.29604	0.436196	0.218098	+	0.975927i	$0.430015\pi$
$98$	−1.28577	−0.129883
$99$	4.44208	0.446446
$100$	0.703658	0.0703658
$101$	−8.00310	−0.796339	−0.398169	−	0.917312i	$-0.630354\pi$
$101$	−8.00310	−0.796339	−0.398169	+	0.917312i	$0.630354\pi$
$102$	−4.73137	−0.468476
$103$	−9.20507	−0.907002	−0.453501	−	0.891256i	$-0.649825\pi$
$103$	−9.20507	−0.907002	−0.453501	+	0.891256i	$0.649825\pi$
$104$	11.9396	1.17077
$105$	1.72364	0.168210
$106$	9.82498	0.954286
$107$	−19.6778	−1.90233	−0.951164	−	0.308685i	$-0.900111\pi$
$107$	−19.6778	−1.90233	−0.951164	+	0.308685i	$0.900111\pi$
$108$	−0.346791	−0.0333700
$109$	8.42850	0.807304	0.403652	−	0.914913i	$-0.367741\pi$
$109$	8.42850	0.807304	0.403652	+	0.914913i	$0.367741\pi$
$110$	9.84459	0.938645
$111$	−7.98661	−0.758056
$112$	3.18615	0.301063
$113$	−7.31168	−0.687825	−0.343913	−	0.939002i	$-0.611752\pi$
$113$	−7.31168	−0.687825	−0.343913	+	0.939002i	$0.611752\pi$
$114$	−4.07129	−0.381311
$115$	13.5826	1.26658
$116$	1.54458	0.143410
$117$	3.95687	0.365812
$118$	−8.50862	−0.783282
$119$	−3.67979	−0.337326
$120$	−5.20099	−0.474783
$121$	8.73209	0.793827
$122$	−2.68840	−0.243396
$123$	8.58946	0.774486
$124$	2.56705	0.230528
$125$	12.1156	1.08365
$126$	1.28577	0.114546
$127$	13.8763	1.23132	0.615662	−	0.788010i	$-0.288889\pi$
$127$	13.8763	1.23132	0.615662	+	0.788010i	$0.288889\pi$
$128$	−7.52118	−0.664784
$129$	2.87790	0.253385
$130$	8.76925	0.769114
$131$	6.25371	0.546390	0.273195	−	0.961959i	$-0.411920\pi$
$131$	6.25371	0.546390	0.273195	+	0.961959i	$0.411920\pi$
$132$	−1.54048	−0.134081
$133$	−3.16642	−0.274563
$134$	14.8365	1.28168
$135$	−1.72364	−0.148348
$136$	11.1035	0.952121
$137$	2.21076	0.188878	0.0944388	−	0.995531i	$-0.469894\pi$
$137$	2.21076	0.188878	0.0944388	+	0.995531i	$0.469894\pi$
$138$	10.1321	0.862502
$139$	14.2944	1.21243	0.606217	−	0.795299i	$-0.292686\pi$
$139$	14.2944	1.21243	0.606217	+	0.795299i	$0.292686\pi$
$140$	−0.597744	−0.0505186
$141$	−6.56637	−0.552988
$142$	4.76712	0.400048
$143$	17.5767	1.46984
$144$	−3.18615	−0.265513
$145$	7.67695	0.637536
$146$	16.5013	1.36566
$147$	1.00000	0.0824786
$148$	2.76969	0.227667
$149$	−2.62313	−0.214895	−0.107448	−	0.994211i	$-0.534268\pi$
$149$	−2.62313	−0.214895	−0.107448	+	0.994211i	$0.534268\pi$
$150$	2.60890	0.213016
$151$	−18.5813	−1.51213	−0.756063	−	0.654498i	$-0.772880\pi$
$151$	−18.5813	−1.51213	−0.756063	+	0.654498i	$0.772880\pi$
$152$	9.55447	0.774970
$153$	3.67979	0.297494
$154$	5.71150	0.460246
$155$	12.7589	1.02482
$156$	−1.37221	−0.109864
$157$	6.76992	0.540299	0.270149	−	0.962818i	$-0.412927\pi$
$157$	6.76992	0.540299	0.270149	+	0.962818i	$0.412927\pi$
$158$	−15.0006	−1.19339
$159$	−7.64131	−0.605995
$160$	3.34078	0.264112
$161$	7.88017	0.621045
$162$	−1.28577	−0.101020
$163$	−7.07034	−0.553792	−0.276896	−	0.960900i	$-0.589306\pi$
$163$	−7.07034	−0.553792	−0.276896	+	0.960900i	$0.589306\pi$
$164$	−2.97875	−0.232601
$165$	−7.65656	−0.596063
$166$	−1.64225	−0.127464
$167$	5.13952	0.397708	0.198854	−	0.980029i	$-0.436278\pi$
$167$	5.13952	0.397708	0.198854	+	0.980029i	$0.436278\pi$
$168$	−3.01744	−0.232800
$169$	2.65678	0.204368
$170$	8.15520	0.625475
$171$	3.16642	0.242142
$172$	−0.998030	−0.0760990
$173$	−24.9381	−1.89601	−0.948006	−	0.318253i	$-0.896904\pi$
$173$	−24.9381	−1.89601	−0.948006	+	0.318253i	$0.896904\pi$
$174$	5.72671	0.434141
$175$	2.02905	0.153382
$176$	−14.1532	−1.06683
$177$	6.61752	0.497403
$178$	−8.11091	−0.607938
$179$	−18.1075	−1.35342	−0.676709	−	0.736250i	$-0.736595\pi$
$179$	−18.1075	−1.35342	−0.676709	+	0.736250i	$0.736595\pi$
$180$	0.597744	0.0445532
$181$	3.51070	0.260948	0.130474	−	0.991452i	$-0.458350\pi$
$181$	3.51070	0.260948	0.130474	+	0.991452i	$0.458350\pi$
$182$	5.08763	0.377120
$183$	2.09088	0.154563
$184$	−23.7779	−1.75293
$185$	13.7661	1.01210
$186$	9.51768	0.697870
$187$	16.3459	1.19533
$188$	2.27716	0.166079
$189$	−1.00000	−0.0727393
$190$	7.01745	0.509099
$191$	19.0033	1.37503	0.687514	−	0.726171i	$-0.258702\pi$
$191$	19.0033	1.37503	0.687514	+	0.726171i	$0.258702\pi$
$192$	8.86440	0.639733
$193$	−12.7164	−0.915348	−0.457674	−	0.889120i	$-0.651317\pi$
$193$	−12.7164	−0.915348	−0.457674	+	0.889120i	$0.651317\pi$
$194$	−5.52372	−0.396580
$195$	−6.82022	−0.488406
$196$	−0.346791	−0.0247708
$197$	−0.426875	−0.0304136	−0.0152068	−	0.999884i	$-0.504841\pi$
$197$	−0.426875	−0.0304136	−0.0152068	+	0.999884i	$0.504841\pi$
$198$	−5.71150	−0.405899
$199$	12.8220	0.908927	0.454463	−	0.890765i	$-0.349831\pi$
$199$	12.8220	0.908927	0.454463	+	0.890765i	$0.349831\pi$
$200$	−6.12254	−0.432929
$201$	−11.5390	−0.813899
$202$	10.2902	0.724013
$203$	4.45391	0.312603
$204$	−1.27612	−0.0893462
$205$	−14.8052	−1.03404
$206$	11.8356	0.824626
$207$	−7.88017	−0.547710
$208$	−12.6072	−0.874151
$209$	14.0655	0.972930
$210$	−2.21621	−0.152933
$211$	−12.6391	−0.870110	−0.435055	−	0.900404i	$-0.643271\pi$
$211$	−12.6391	−0.870110	−0.435055	+	0.900404i	$0.643271\pi$
$212$	2.64994	0.181999
$213$	−3.70760	−0.254040
$214$	25.3012	1.72956
$215$	−4.96047	−0.338301
$216$	3.01744	0.205311
$217$	7.40231	0.502501
$218$	−10.8371	−0.733983
$219$	−12.8338	−0.867226
$220$	2.65523	0.179016
$221$	14.5604	0.979441
$222$	10.2690	0.689208
$223$	−2.57624	−0.172518	−0.0862588	−	0.996273i	$-0.527491\pi$
$223$	−2.57624	−0.172518	−0.0862588	+	0.996273i	$0.527491\pi$
$224$	1.93821	0.129502
$225$	−2.02905	−0.135270
$226$	9.40116	0.625356
$227$	6.35588	0.421855	0.210927	−	0.977502i	$-0.432352\pi$
$227$	6.35588	0.421855	0.210927	+	0.977502i	$0.432352\pi$
$228$	−1.09809	−0.0727225
$229$	2.30301	0.152187	0.0760937	−	0.997101i	$-0.475755\pi$
$229$	2.30301	0.152187	0.0760937	+	0.997101i	$0.475755\pi$
$230$	−17.4641	−1.15155
$231$	−4.44208	−0.292268
$232$	−13.4394	−0.882340
$233$	−0.834733	−0.0546852	−0.0273426	−	0.999626i	$-0.508704\pi$
$233$	−0.834733	−0.0546852	−0.0273426	+	0.999626i	$0.508704\pi$
$234$	−5.08763	−0.332588
$235$	11.3181	0.738310
$236$	−2.29490	−0.149385
$237$	11.6666	0.757829
$238$	4.73137	0.306689
$239$	−4.03264	−0.260850	−0.130425	−	0.991458i	$-0.541634\pi$
$239$	−4.03264	−0.260850	−0.130425	+	0.991458i	$0.541634\pi$
$240$	5.49179	0.354494
$241$	11.6714	0.751821	0.375911	−	0.926656i	$-0.377330\pi$
$241$	11.6714	0.751821	0.375911	+	0.926656i	$0.377330\pi$
$242$	−11.2275	−0.721730
$243$	1.00000	0.0641500
$244$	−0.725100	−0.0464198
$245$	−1.72364	−0.110120
$246$	−11.0441	−0.704145
$247$	12.5291	0.797207
$248$	−22.3360	−1.41834
$249$	1.27725	0.0809425
$250$	−15.5779	−0.985231
$251$	22.2731	1.40586	0.702932	−	0.711257i	$-0.251874\pi$
$251$	22.2731	1.40586	0.702932	+	0.711257i	$0.251874\pi$
$252$	0.346791	0.0218458
$253$	−35.0044	−2.20071
$254$	−17.8418	−1.11949
$255$	−6.34265	−0.397192
$256$	−8.05829	−0.503643
$257$	−23.0212	−1.43603	−0.718013	−	0.696030i	$-0.754948\pi$
$257$	−23.0212	−1.43603	−0.718013	+	0.696030i	$0.754948\pi$
$258$	−3.70032	−0.230372
$259$	7.98661	0.496264
$260$	2.36519	0.146683
$261$	−4.45391	−0.275690
$262$	−8.04085	−0.496765
$263$	−5.76488	−0.355478	−0.177739	−	0.984078i	$-0.556878\pi$
$263$	−5.76488	−0.355478	−0.177739	+	0.984078i	$0.556878\pi$
$264$	13.4037	0.824941
$265$	13.1709	0.809081
$266$	4.07129	0.249627
$267$	6.30820	0.386056
$268$	4.00163	0.244438
$269$	−22.7608	−1.38775	−0.693876	−	0.720095i	$-0.744098\pi$
$269$	−22.7608	−1.38775	−0.693876	+	0.720095i	$0.744098\pi$
$270$	2.21621	0.134874
$271$	−16.8459	−1.02331	−0.511657	−	0.859190i	$-0.670968\pi$
$271$	−16.8459	−1.02331	−0.511657	+	0.859190i	$0.670968\pi$
$272$	−11.7244	−0.710895
$273$	−3.95687	−0.239480
$274$	−2.84253	−0.171723
$275$	−9.01322	−0.543518
$276$	2.73277	0.164494
$277$	1.37439	0.0825793	0.0412896	−	0.999147i	$-0.486853\pi$
$277$	1.37439	0.0825793	0.0412896	+	0.999147i	$0.486853\pi$
$278$	−18.3793	−1.10232
$279$	−7.40231	−0.443164
$280$	5.20099	0.310818
$281$	20.6455	1.23161	0.615803	−	0.787900i	$-0.288832\pi$
$281$	20.6455	1.23161	0.615803	+	0.787900i	$0.288832\pi$
$282$	8.44286	0.502765
$283$	14.2129	0.844870	0.422435	−	0.906393i	$-0.361176\pi$
$283$	14.2129	0.844870	0.422435	+	0.906393i	$0.361176\pi$
$284$	1.28576	0.0762960
$285$	−5.45777	−0.323291
$286$	−22.5996	−1.33635
$287$	−8.58946	−0.507020
$288$	−1.93821	−0.114210
$289$	−3.45913	−0.203478
$290$	−9.87081	−0.579634
$291$	4.29604	0.251838
$292$	4.45064	0.260454
$293$	−17.5703	−1.02647	−0.513233	−	0.858250i	$-0.671552\pi$
$293$	−17.5703	−1.02647	−0.513233	+	0.858250i	$0.671552\pi$
$294$	−1.28577	−0.0749877
$295$	−11.4062	−0.664098
$296$	−24.0991	−1.40073
$297$	4.44208	0.257756
$298$	3.37275	0.195378
$299$	−31.1808	−1.80323
$300$	0.703658	0.0406257
$301$	−2.87790	−0.165879
$302$	23.8913	1.37479
$303$	−8.00310	−0.459766
$304$	−10.0887	−0.578626
$305$	−3.60394	−0.206361
$306$	−4.73137	−0.270475
$307$	5.92893	0.338382	0.169191	−	0.985583i	$-0.445885\pi$
$307$	5.92893	0.338382	0.169191	+	0.985583i	$0.445885\pi$
$308$	1.54048	0.0877767
$309$	−9.20507	−0.523658
$310$	−16.4051	−0.931746
$311$	−25.4845	−1.44509	−0.722547	−	0.691322i	$-0.757029\pi$
$311$	−25.4845	−1.44509	−0.722547	+	0.691322i	$0.757029\pi$
$312$	11.9396	0.675946
$313$	9.08064	0.513268	0.256634	−	0.966509i	$-0.417386\pi$
$313$	9.08064	0.513268	0.256634	+	0.966509i	$0.417386\pi$
$314$	−8.70458	−0.491228
$315$	1.72364	0.0971163
$316$	−4.04589	−0.227599
$317$	5.38791	0.302615	0.151307	−	0.988487i	$-0.451652\pi$
$317$	5.38791	0.302615	0.151307	+	0.988487i	$0.451652\pi$
$318$	9.82498	0.550957
$319$	−19.7846	−1.10773
$320$	−15.2791	−0.854126
$321$	−19.6778	−1.09831
$322$	−10.1321	−0.564640
$323$	11.6518	0.648321
$324$	−0.346791	−0.0192662
$325$	−8.02869	−0.445352
$326$	9.09084	0.503495
$327$	8.42850	0.466097
$328$	25.9182	1.43109
$329$	6.56637	0.362016
$330$	9.84459	0.541927
$331$	24.5442	1.34907	0.674534	−	0.738244i	$-0.264344\pi$
$331$	24.5442	1.34907	0.674534	+	0.738244i	$0.264344\pi$
$332$	−0.442939	−0.0243095
$333$	−7.98661	−0.437664
$334$	−6.60825	−0.361587
$335$	19.8891	1.08666
$336$	3.18615	0.173819
$337$	−6.50374	−0.354281	−0.177141	−	0.984186i	$-0.556685\pi$
$337$	−6.50374	−0.354281	−0.177141	+	0.984186i	$0.556685\pi$
$338$	−3.41602	−0.185807
$339$	−7.31168	−0.397116
$340$	2.19958	0.119289
$341$	−32.8816	−1.78064
$342$	−4.07129	−0.220150
$343$	−1.00000	−0.0539949
$344$	8.68388	0.468203
$345$	13.5826	0.731263
$346$	32.0648	1.72381
$347$	−33.0957	−1.77667	−0.888335	−	0.459197i	$-0.848137\pi$
$347$	−33.0957	−1.77667	−0.888335	+	0.459197i	$0.848137\pi$
$348$	1.54458	0.0827980
$349$	22.4048	1.19930	0.599649	−	0.800263i	$-0.295307\pi$
$349$	22.4048	1.19930	0.599649	+	0.800263i	$0.295307\pi$
$350$	−2.60890	−0.139452
$351$	3.95687	0.211202
$352$	−8.60969	−0.458898
$353$	−27.7221	−1.47550	−0.737750	−	0.675074i	$-0.764112\pi$
$353$	−27.7221	−1.47550	−0.737750	+	0.675074i	$0.764112\pi$
$354$	−8.50862	−0.452228
$355$	6.39058	0.339177
$356$	−2.18763	−0.115944
$357$	−3.67979	−0.194755
$358$	23.2821	1.23050
$359$	−33.7994	−1.78387	−0.891933	−	0.452168i	$-0.850651\pi$
$359$	−33.7994	−1.78387	−0.891933	+	0.452168i	$0.850651\pi$
$360$	−5.20099	−0.274116
$361$	−8.97380	−0.472305
$362$	−4.51395	−0.237248
$363$	8.73209	0.458316
$364$	1.37221	0.0719232
$365$	22.1208	1.15786
$366$	−2.68840	−0.140525
$367$	11.4303	0.596656	0.298328	−	0.954463i	$-0.403571\pi$
$367$	11.4303	0.596656	0.298328	+	0.954463i	$0.403571\pi$
$368$	25.1074	1.30882
$369$	8.58946	0.447149
$370$	−17.7000	−0.920181
$371$	7.64131	0.396717
$372$	2.56705	0.133096
$373$	6.65385	0.344523	0.172262	−	0.985051i	$-0.444893\pi$
$373$	6.65385	0.344523	0.172262	+	0.985051i	$0.444893\pi$
$374$	−21.0171	−1.08677
$375$	12.1156	0.625646
$376$	−19.8136	−1.02181
$377$	−17.6235	−0.907658
$378$	1.28577	0.0661330
$379$	−7.34790	−0.377436	−0.188718	−	0.982031i	$-0.560433\pi$
$379$	−7.34790	−0.377436	−0.188718	+	0.982031i	$0.560433\pi$
$380$	1.89271	0.0970939
$381$	13.8763	0.710905
$382$	−24.4339	−1.25015
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	−7.52118	−0.383813
$385$	7.65656	0.390215
$386$	16.3504	0.832214
$387$	2.87790	0.146292
$388$	−1.48983	−0.0756345
$389$	10.0809	0.511124	0.255562	−	0.966793i	$-0.417740\pi$
$389$	10.0809	0.511124	0.255562	+	0.966793i	$0.417740\pi$
$390$	8.76925	0.444048
$391$	−28.9974	−1.46646
$392$	3.01744	0.152404
$393$	6.25371	0.315458
$394$	0.548864	0.0276513
$395$	−20.1091	−1.01180
$396$	−1.54048	−0.0774118
$397$	14.6664	0.736083	0.368042	−	0.929809i	$-0.380028\pi$
$397$	14.6664	0.736083	0.368042	+	0.929809i	$0.380028\pi$
$398$	−16.4862	−0.826376
$399$	−3.16642	−0.158519
$400$	6.46488	0.323244
$401$	−22.3136	−1.11429	−0.557144	−	0.830416i	$-0.688103\pi$
$401$	−22.3136	−1.11429	−0.557144	+	0.830416i	$0.688103\pi$
$402$	14.8365	0.739979
$403$	−29.2899	−1.45904
$404$	2.77541	0.138082
$405$	−1.72364	−0.0856485
$406$	−5.72671	−0.284212
$407$	−35.4772	−1.75854
$408$	11.1035	0.549707
$409$	−24.2478	−1.19898	−0.599489	−	0.800383i	$-0.704630\pi$
$409$	−24.2478	−1.19898	−0.599489	+	0.800383i	$0.704630\pi$
$410$	19.0361	0.940124
$411$	2.21076	0.109049
$412$	3.19224	0.157270
$413$	−6.61752	−0.325627
$414$	10.1321	0.497966
$415$	−2.20152	−0.108069
$416$	−7.66923	−0.376015
$417$	14.2944	0.699999
$418$	−18.0850	−0.884566
$419$	−9.01330	−0.440329	−0.220164	−	0.975463i	$-0.570659\pi$
$419$	−9.01330	−0.440329	−0.220164	+	0.975463i	$0.570659\pi$
$420$	−0.597744	−0.0291669
$421$	−13.3225	−0.649301	−0.324650	−	0.945834i	$-0.605247\pi$
$421$	−13.3225	−0.649301	−0.324650	+	0.945834i	$0.605247\pi$
$422$	16.2510	0.791085
$423$	−6.56637	−0.319268
$424$	−23.0572	−1.11976
$425$	−7.46650	−0.362178
$426$	4.76712	0.230968
$427$	−2.09088	−0.101185
$428$	6.82410	0.329855
$429$	17.5767	0.848612
$430$	6.37803	0.307576
$431$	−12.9764	−0.625053	−0.312527	−	0.949909i	$-0.601175\pi$
$431$	−12.9764	−0.625053	−0.312527	+	0.949909i	$0.601175\pi$
$432$	−3.18615	−0.153294
$433$	19.1894	0.922182	0.461091	−	0.887353i	$-0.347458\pi$
$433$	19.1894	0.922182	0.461091	+	0.887353i	$0.347458\pi$
$434$	−9.51768	−0.456863
$435$	7.67695	0.368082
$436$	−2.92293	−0.139983
$437$	−24.9519	−1.19361
$438$	16.5013	0.788462
$439$	−23.9459	−1.14287	−0.571437	−	0.820646i	$-0.693614\pi$
$439$	−23.9459	−1.14287	−0.571437	+	0.820646i	$0.693614\pi$
$440$	−23.1032	−1.10140
$441$	1.00000	0.0476190
$442$	−18.7214	−0.890486
$443$	10.5588	0.501665	0.250832	−	0.968031i	$-0.419296\pi$
$443$	10.5588	0.501665	0.250832	+	0.968031i	$0.419296\pi$
$444$	2.76969	0.131444
$445$	−10.8731	−0.515434
$446$	3.31245	0.156849
$447$	−2.62313	−0.124070
$448$	−8.86440	−0.418804
$449$	−37.9076	−1.78897	−0.894485	−	0.447099i	$-0.852457\pi$
$449$	−37.9076	−1.78897	−0.894485	+	0.447099i	$0.852457\pi$
$450$	2.60890	0.122985
$451$	38.1551	1.79665
$452$	2.53563	0.119266
$453$	−18.5813	−0.873027
$454$	−8.17222	−0.383541
$455$	6.82022	0.319737
$456$	9.55447	0.447429
$457$	9.22988	0.431756	0.215878	−	0.976420i	$-0.430739\pi$
$457$	9.22988	0.431756	0.215878	+	0.976420i	$0.430739\pi$
$458$	−2.96115	−0.138365
$459$	3.67979	0.171758
$460$	−4.71033	−0.219620
$461$	−33.6450	−1.56700	−0.783502	−	0.621390i	$-0.786568\pi$
$461$	−33.6450	−1.56700	−0.783502	+	0.621390i	$0.786568\pi$
$462$	5.71150	0.265723
$463$	−2.20522	−0.102485	−0.0512427	−	0.998686i	$-0.516318\pi$
$463$	−2.20522	−0.102485	−0.0512427	+	0.998686i	$0.516318\pi$
$464$	14.1908	0.658793
$465$	12.7589	0.591681
$466$	1.07328	0.0497185
$467$	19.0361	0.880885	0.440443	−	0.897781i	$-0.354822\pi$
$467$	19.0361	0.880885	0.440443	+	0.897781i	$0.354822\pi$
$468$	−1.37221	−0.0634303
$469$	11.5390	0.532822
$470$	−14.5525	−0.671256
$471$	6.76992	0.311942
$472$	19.9680	0.919100
$473$	12.7839	0.587802
$474$	−15.0006	−0.689001
$475$	−6.42483	−0.294792
$476$	1.27612	0.0584908
$477$	−7.64131	−0.349871
$478$	5.18505	0.237159
$479$	41.3794	1.89067	0.945337	−	0.326094i	$-0.105733\pi$
$479$	41.3794	1.89067	0.945337	+	0.326094i	$0.105733\pi$
$480$	3.34078	0.152485
$481$	−31.6020	−1.44093
$482$	−15.0068	−0.683539
$483$	7.88017	0.358560
$484$	−3.02821	−0.137646
$485$	−7.40483	−0.336236
$486$	−1.28577	−0.0583238
$487$	4.04288	0.183201	0.0916003	−	0.995796i	$-0.470802\pi$
$487$	4.04288	0.183201	0.0916003	+	0.995796i	$0.470802\pi$
$488$	6.30911	0.285600
$489$	−7.07034	−0.319732
$490$	2.21621	0.100118
$491$	−30.3999	−1.37193	−0.685964	−	0.727636i	$-0.740619\pi$
$491$	−30.3999	−1.37193	−0.685964	+	0.727636i	$0.740619\pi$
$492$	−2.97875	−0.134292
$493$	−16.3895	−0.738145
$494$	−16.1095	−0.724803
$495$	−7.65656	−0.344137
$496$	23.5849	1.05899
$497$	3.70760	0.166308
$498$	−1.64225	−0.0735911
$499$	35.5287	1.59048	0.795241	−	0.606294i	$-0.207344\pi$
$499$	35.5287	1.59048	0.795241	+	0.606294i	$0.207344\pi$
$500$	−4.20158	−0.187900
$501$	5.13952	0.229617
$502$	−28.6381	−1.27818
$503$	0.509870	0.0227340	0.0113670	−	0.999935i	$-0.496382\pi$
$503$	0.509870	0.0227340	0.0113670	+	0.999935i	$0.496382\pi$
$504$	−3.01744	−0.134407
$505$	13.7945	0.613847
$506$	45.0076	2.00083
$507$	2.65678	0.117992
$508$	−4.81219	−0.213506
$509$	−30.5752	−1.35522	−0.677610	−	0.735421i	$-0.736984\pi$
$509$	−30.5752	−1.35522	−0.677610	+	0.735421i	$0.736984\pi$
$510$	8.15520	0.361118
$511$	12.8338	0.567733
$512$	25.4035	1.12269
$513$	3.16642	0.139801
$514$	29.6001	1.30560
$515$	15.8662	0.699150
$516$	−0.998030	−0.0439358
$517$	−29.1684	−1.28282
$518$	−10.2690	−0.451192
$519$	−24.9381	−1.09466
$520$	−20.5796	−0.902475
$521$	34.4165	1.50781	0.753907	−	0.656981i	$-0.228167\pi$
$521$	34.4165	1.50781	0.753907	+	0.656981i	$0.228167\pi$
$522$	5.72671	0.250651
$523$	−21.8239	−0.954294	−0.477147	−	0.878823i	$-0.658329\pi$
$523$	−21.8239	−0.954294	−0.477147	+	0.878823i	$0.658329\pi$
$524$	−2.16873	−0.0947416
$525$	2.02905	0.0885552
$526$	7.41232	0.323193
$527$	−27.2389	−1.18655
$528$	−14.1532	−0.615937
$529$	39.0971	1.69987
$530$	−16.9348	−0.735599
$531$	6.61752	0.287176
$532$	1.09809	0.0476081
$533$	33.9873	1.47215
$534$	−8.11091	−0.350993
$535$	33.9176	1.46638
$536$	−34.8182	−1.50392
$537$	−18.1075	−0.781397
$538$	29.2652	1.26171
$539$	4.44208	0.191334
$540$	0.597744	0.0257228
$541$	17.6374	0.758292	0.379146	−	0.925337i	$-0.376218\pi$
$541$	17.6374	0.758292	0.379146	+	0.925337i	$0.376218\pi$
$542$	21.6600	0.930375
$543$	3.51070	0.150658
$544$	−7.13221	−0.305791
$545$	−14.5277	−0.622299
$546$	5.08763	0.217730
$547$	19.0798	0.815792	0.407896	−	0.913028i	$-0.366263\pi$
$547$	19.0798	0.815792	0.407896	+	0.913028i	$0.366263\pi$
$548$	−0.766671	−0.0327505
$549$	2.09088	0.0892367
$550$	11.5889	0.494154
$551$	−14.1029	−0.600806
$552$	−23.7779	−1.01206
$553$	−11.6666	−0.496116
$554$	−1.76716	−0.0750792
$555$	13.7661	0.584337
$556$	−4.95717	−0.210231
$557$	−29.7095	−1.25883	−0.629417	−	0.777068i	$-0.716706\pi$
$557$	−29.7095	−1.25883	−0.629417	+	0.777068i	$0.716706\pi$
$558$	9.51768	0.402915
$559$	11.3875	0.481638
$560$	−5.49179	−0.232071
$561$	16.3459	0.690126
$562$	−26.5454	−1.11975
$563$	−2.42321	−0.102126	−0.0510630	−	0.998695i	$-0.516261\pi$
$563$	−2.42321	−0.102126	−0.0510630	+	0.998695i	$0.516261\pi$
$564$	2.27716	0.0958858
$565$	12.6027	0.530201
$566$	−18.2746	−0.768137
$567$	−1.00000	−0.0419961
$568$	−11.1874	−0.469415
$569$	40.3488	1.69151	0.845754	−	0.533573i	$-0.179151\pi$
$569$	40.3488	1.69151	0.845754	+	0.533573i	$0.179151\pi$
$570$	7.01745	0.293929
$571$	24.9084	1.04239	0.521193	−	0.853439i	$-0.325487\pi$
$571$	24.9084	1.04239	0.521193	+	0.853439i	$0.325487\pi$
$572$	−6.09545	−0.254864
$573$	19.0033	0.793873
$574$	11.0441	0.460971
$575$	15.9893	0.666800
$576$	8.86440	0.369350
$577$	−31.7599	−1.32218	−0.661091	−	0.750306i	$-0.729906\pi$
$577$	−31.7599	−1.32218	−0.661091	+	0.750306i	$0.729906\pi$
$578$	4.44765	0.184998
$579$	−12.7164	−0.528476
$580$	−2.66230	−0.110546
$581$	−1.27725	−0.0529893
$582$	−5.52372	−0.228966
$583$	−33.9433	−1.40579
$584$	−38.7251	−1.60246
$585$	−6.82022	−0.281982
$586$	22.5913	0.933239
$587$	13.2431	0.546603	0.273301	−	0.961928i	$-0.411884\pi$
$587$	13.2431	0.546603	0.273301	+	0.961928i	$0.411884\pi$
$588$	−0.346791	−0.0143014
$589$	−23.4388	−0.965779
$590$	14.6658	0.603783
$591$	−0.426875	−0.0175593
$592$	25.4466	1.04585
$593$	−1.71998	−0.0706311	−0.0353156	−	0.999376i	$-0.511244\pi$
$593$	−1.71998	−0.0706311	−0.0353156	+	0.999376i	$0.511244\pi$
$594$	−5.71150	−0.234346
$595$	6.34265	0.260023
$596$	0.909680	0.0372619
$597$	12.8220	0.524769
$598$	40.0914	1.63946
$599$	−3.82641	−0.156343	−0.0781714	−	0.996940i	$-0.524908\pi$
$599$	−3.82641	−0.156343	−0.0781714	+	0.996940i	$0.524908\pi$
$600$	−6.12254	−0.249952
$601$	−25.7095	−1.04871	−0.524356	−	0.851499i	$-0.675694\pi$
$601$	−25.7095	−1.04871	−0.524356	+	0.851499i	$0.675694\pi$
$602$	3.70032	0.150814
$603$	−11.5390	−0.469905
$604$	6.44384	0.262196
$605$	−15.0510	−0.611911
$606$	10.2902	0.418009
$607$	17.4469	0.708146	0.354073	−	0.935218i	$-0.384796\pi$
$607$	17.4469	0.708146	0.354073	+	0.935218i	$0.384796\pi$
$608$	−6.13718	−0.248896
$609$	4.45391	0.180482
$610$	4.63384	0.187619
$611$	−25.9823	−1.05113
$612$	−1.27612	−0.0515841
$613$	9.31276	0.376139	0.188069	−	0.982156i	$-0.439777\pi$
$613$	9.31276	0.376139	0.188069	+	0.982156i	$0.439777\pi$
$614$	−7.62325	−0.307649
$615$	−14.8052	−0.597002
$616$	−13.4037	−0.540051
$617$	−32.0776	−1.29140	−0.645698	−	0.763593i	$-0.723433\pi$
$617$	−32.0776	−1.29140	−0.645698	+	0.763593i	$0.723433\pi$
$618$	11.8356	0.476098
$619$	13.8765	0.557744	0.278872	−	0.960328i	$-0.410040\pi$
$619$	13.8765	0.557744	0.278872	+	0.960328i	$0.410040\pi$
$620$	−4.42469	−0.177700
$621$	−7.88017	−0.316220
$622$	32.7673	1.31385
$623$	−6.30820	−0.252733
$624$	−12.6072	−0.504691
$625$	−10.7377	−0.429507
$626$	−11.6756	−0.466652
$627$	14.0655	0.561721
$628$	−2.34775	−0.0936854
$629$	−29.3891	−1.17182
$630$	−2.21621	−0.0882960
$631$	15.4304	0.614275	0.307138	−	0.951665i	$-0.400629\pi$
$631$	15.4304	0.614275	0.307138	+	0.951665i	$0.400629\pi$
$632$	35.2033	1.40031
$633$	−12.6391	−0.502358
$634$	−6.92762	−0.275131
$635$	−23.9178	−0.949150
$636$	2.64994	0.105077
$637$	3.95687	0.156777
$638$	25.4385	1.00712
$639$	−3.70760	−0.146670
$640$	12.9638	0.512440
$641$	19.1516	0.756444	0.378222	−	0.925715i	$-0.376536\pi$
$641$	19.1516	0.756444	0.378222	+	0.925715i	$0.376536\pi$
$642$	25.3012	0.998559
$643$	−15.7267	−0.620201	−0.310100	−	0.950704i	$-0.600363\pi$
$643$	−15.7267	−0.620201	−0.310100	+	0.950704i	$0.600363\pi$
$644$	−2.73277	−0.107686
$645$	−4.96047	−0.195318
$646$	−14.9815	−0.589439
$647$	−10.5602	−0.415164	−0.207582	−	0.978218i	$-0.566559\pi$
$647$	−10.5602	−0.415164	−0.207582	+	0.978218i	$0.566559\pi$
$648$	3.01744	0.118536
$649$	29.3956	1.15388
$650$	10.3231	0.404904
$651$	7.40231	0.290119
$652$	2.45193	0.0960251
$653$	41.8716	1.63856	0.819282	−	0.573391i	$-0.194373\pi$
$653$	41.8716	1.63856	0.819282	+	0.573391i	$0.194373\pi$
$654$	−10.8371	−0.423765
$655$	−10.7792	−0.421177
$656$	−27.3673	−1.06851
$657$	−12.8338	−0.500693
$658$	−8.44286	−0.329137
$659$	−19.9225	−0.776070	−0.388035	−	0.921645i	$-0.626846\pi$
$659$	−19.9225	−0.776070	−0.388035	+	0.921645i	$0.626846\pi$
$660$	2.65523	0.103355
$661$	−14.4339	−0.561412	−0.280706	−	0.959794i	$-0.590569\pi$
$661$	−14.4339	−0.561412	−0.280706	+	0.959794i	$0.590569\pi$
$662$	−31.5582	−1.22654
$663$	14.5604	0.565481
$664$	3.85402	0.149565
$665$	5.45777	0.211643
$666$	10.2690	0.397914
$667$	35.0976	1.35898
$668$	−1.78234	−0.0689608
$669$	−2.57624	−0.0996031
$670$	−25.5729	−0.987967
$671$	9.28787	0.358554
$672$	1.93821	0.0747681
$673$	−18.2105	−0.701962	−0.350981	−	0.936383i	$-0.614152\pi$
$673$	−18.2105	−0.701962	−0.350981	+	0.936383i	$0.614152\pi$
$674$	8.36233	0.322105
$675$	−2.02905	−0.0780983
$676$	−0.921350	−0.0354365
$677$	−32.0732	−1.23267	−0.616336	−	0.787483i	$-0.711384\pi$
$677$	−32.0732	−1.23267	−0.616336	+	0.787483i	$0.711384\pi$
$678$	9.40116	0.361049
$679$	−4.29604	−0.164867
$680$	−19.1385	−0.733930
$681$	6.35588	0.243558
$682$	42.2783	1.61892
$683$	−15.5020	−0.593169	−0.296585	−	0.955007i	$-0.595848\pi$
$683$	−15.5020	−0.593169	−0.296585	+	0.955007i	$0.595848\pi$
$684$	−1.09809	−0.0419864
$685$	−3.81055	−0.145594
$686$	1.28577	0.0490910
$687$	2.30301	0.0878655
$688$	−9.16942	−0.349581
$689$	−30.2356	−1.15189
$690$	−17.4641	−0.664848
$691$	18.0816	0.687855	0.343927	−	0.938996i	$-0.388243\pi$
$691$	18.0816	0.687855	0.343927	+	0.938996i	$0.388243\pi$
$692$	8.64833	0.328760
$693$	−4.44208	−0.168741
$694$	42.5535	1.61531
$695$	−24.6384	−0.934588
$696$	−13.4394	−0.509419
$697$	31.6074	1.19722
$698$	−28.8074	−1.09038
$699$	−0.834733	−0.0315725
$700$	−0.703658	−0.0265958
$701$	17.2830	0.652771	0.326385	−	0.945237i	$-0.394169\pi$
$701$	17.2830	0.652771	0.326385	+	0.945237i	$0.394169\pi$
$702$	−5.08763	−0.192020
$703$	−25.2890	−0.953791
$704$	39.3764	1.48405
$705$	11.3181	0.426264
$706$	35.6443	1.34149
$707$	8.00310	0.300988
$708$	−2.29490	−0.0862476
$709$	45.6534	1.71455	0.857276	−	0.514858i	$-0.172155\pi$
$709$	45.6534	1.71455	0.857276	+	0.514858i	$0.172155\pi$
$710$	−8.21682	−0.308372
$711$	11.6666	0.437533
$712$	19.0346	0.713352
$713$	58.3314	2.18453
$714$	4.73137	0.177067
$715$	−30.2960	−1.13301
$716$	6.27953	0.234677
$717$	−4.03264	−0.150602
$718$	43.4584	1.62185
$719$	−47.9618	−1.78867	−0.894336	−	0.447396i	$-0.852351\pi$
$719$	−47.9618	−1.78867	−0.894336	+	0.447396i	$0.852351\pi$
$720$	5.49179	0.204667
$721$	9.20507	0.342815
$722$	11.5383	0.429409
$723$	11.6714	0.434064
$724$	−1.21748	−0.0452472
$725$	9.03723	0.335634
$726$	−11.2275	−0.416691
$727$	21.3618	0.792266	0.396133	−	0.918193i	$-0.370352\pi$
$727$	21.3618	0.792266	0.396133	+	0.918193i	$0.370352\pi$
$728$	−11.9396	−0.442511
$729$	1.00000	0.0370370
$730$	−28.4423	−1.05270
$731$	10.5901	0.391688
$732$	−0.725100	−0.0268005
$733$	20.2583	0.748256	0.374128	−	0.927377i	$-0.377942\pi$
$733$	20.2583	0.748256	0.374128	+	0.927377i	$0.377942\pi$
$734$	−14.6967	−0.542466
$735$	−1.72364	−0.0635775
$736$	15.2734	0.562986
$737$	−51.2572	−1.88808
$738$	−11.0441	−0.406538
$739$	36.9274	1.35840	0.679198	−	0.733955i	$-0.262328\pi$
$739$	36.9274	1.35840	0.679198	+	0.733955i	$0.262328\pi$
$740$	−4.77395	−0.175494
$741$	12.5291	0.460268
$742$	−9.82498	−0.360686
$743$	−25.9150	−0.950729	−0.475364	−	0.879789i	$-0.657684\pi$
$743$	−25.9150	−0.950729	−0.475364	+	0.879789i	$0.657684\pi$
$744$	−22.3360	−0.818877
$745$	4.52135	0.165649
$746$	−8.55533	−0.313233
$747$	1.27725	0.0467322
$748$	−5.66863	−0.207266
$749$	19.6778	0.719013
$750$	−15.5779	−0.568823
$751$	−38.2339	−1.39517	−0.697587	−	0.716500i	$-0.745743\pi$
$751$	−38.2339	−1.39517	−0.697587	+	0.716500i	$0.745743\pi$
$752$	20.9215	0.762928
$753$	22.2731	0.811676
$754$	22.6598	0.825222
$755$	32.0276	1.16560
$756$	0.346791	0.0126127
$757$	14.7576	0.536375	0.268187	−	0.963367i	$-0.413575\pi$
$757$	14.7576	0.536375	0.268187	+	0.963367i	$0.413575\pi$
$758$	9.44772	0.343157
$759$	−35.0044	−1.27058
$760$	−16.4685	−0.597375
$761$	−20.4168	−0.740108	−0.370054	−	0.929010i	$-0.620661\pi$
$761$	−20.4168	−0.740108	−0.370054	+	0.929010i	$0.620661\pi$
$762$	−17.8418	−0.646339
$763$	−8.42850	−0.305132
$764$	−6.59017	−0.238424
$765$	−6.34265	−0.229319
$766$	−1.28577	−0.0464568
$767$	26.1846	0.945473
$768$	−8.05829	−0.290778
$769$	−2.52420	−0.0910251	−0.0455126	−	0.998964i	$-0.514492\pi$
$769$	−2.52420	−0.0910251	−0.0455126	+	0.998964i	$0.514492\pi$
$770$	−9.84459	−0.354775
$771$	−23.0212	−0.829090
$772$	4.40994	0.158717
$773$	41.0895	1.47789	0.738943	−	0.673768i	$-0.235325\pi$
$773$	41.0895	1.47789	0.738943	+	0.673768i	$0.235325\pi$
$774$	−3.70032	−0.133005
$775$	15.0197	0.539523
$776$	12.9630	0.465345
$777$	7.98661	0.286518
$778$	−12.9618	−0.464703
$779$	27.1978	0.974463
$780$	2.36519	0.0846875
$781$	−16.4695	−0.589323
$782$	37.2840	1.33327
$783$	−4.45391	−0.159170
$784$	−3.18615	−0.113791
$785$	−11.6689	−0.416482
$786$	−8.04085	−0.286808
$787$	22.8342	0.813953	0.406976	−	0.913439i	$-0.366583\pi$
$787$	22.8342	0.813953	0.406976	+	0.913439i	$0.366583\pi$
$788$	0.148036	0.00527358
$789$	−5.76488	−0.205235
$790$	25.8557	0.919905
$791$	7.31168	0.259974
$792$	13.4037	0.476280
$793$	8.27334	0.293795
$794$	−18.8576	−0.669231
$795$	13.1709	0.467123
$796$	−4.44655	−0.157604
$797$	−43.6189	−1.54506	−0.772531	−	0.634978i	$-0.781009\pi$
$797$	−43.6189	−1.54506	−0.772531	+	0.634978i	$0.781009\pi$
$798$	4.07129	0.144122
$799$	−24.1629	−0.854822
$800$	3.93273	0.139043
$801$	6.30820	0.222889
$802$	28.6902	1.01309
$803$	−57.0087	−2.01179
$804$	4.00163	0.141127
$805$	−13.5826	−0.478724
$806$	37.6602	1.32652
$807$	−22.7608	−0.801218
$808$	−24.1489	−0.849554
$809$	−35.1157	−1.23460	−0.617300	−	0.786728i	$-0.711774\pi$
$809$	−35.1157	−1.23460	−0.617300	+	0.786728i	$0.711774\pi$
$810$	2.21621	0.0778697
$811$	−32.2005	−1.13071	−0.565356	−	0.824847i	$-0.691261\pi$
$811$	−32.2005	−1.13071	−0.565356	+	0.824847i	$0.691261\pi$
$812$	−1.54458	−0.0542040
$813$	−16.8459	−0.590811
$814$	45.6156	1.59882
$815$	12.1867	0.426883
$816$	−11.7244	−0.410435
$817$	9.11262	0.318810
$818$	31.1772	1.09009
$819$	−3.95687	−0.138264
$820$	5.13430	0.179298
$821$	25.0443	0.874053	0.437026	−	0.899449i	$-0.356032\pi$
$821$	25.0443	0.874053	0.437026	+	0.899449i	$0.356032\pi$
$822$	−2.84253	−0.0991445
$823$	−0.766448	−0.0267167	−0.0133583	−	0.999911i	$-0.504252\pi$
$823$	−0.766448	−0.0267167	−0.0133583	+	0.999911i	$0.504252\pi$
$824$	−27.7757	−0.967613
$825$	−9.01322	−0.313800
$826$	8.50862	0.296053
$827$	51.9639	1.80696	0.903481	−	0.428627i	$-0.141003\pi$
$827$	51.9639	1.80696	0.903481	+	0.428627i	$0.141003\pi$
$828$	2.73277	0.0949705
$829$	13.0294	0.452530	0.226265	−	0.974066i	$-0.427348\pi$
$829$	13.0294	0.452530	0.226265	+	0.974066i	$0.427348\pi$
$830$	2.83066	0.0982536
$831$	1.37439	0.0476772
$832$	35.0752	1.21602
$833$	3.67979	0.127497
$834$	−18.3793	−0.636423
$835$	−8.85870	−0.306568
$836$	−4.87779	−0.168702
$837$	−7.40231	−0.255861
$838$	11.5891	0.400337
$839$	2.72003	0.0939057	0.0469529	−	0.998897i	$-0.485049\pi$
$839$	2.72003	0.0939057	0.0469529	+	0.998897i	$0.485049\pi$
$840$	5.20099	0.179451
$841$	−9.16267	−0.315954
$842$	17.1297	0.590330
$843$	20.6455	0.711068
$844$	4.38312	0.150873
$845$	−4.57935	−0.157534
$846$	8.44286	0.290271
$847$	−8.73209	−0.300038
$848$	24.3464	0.836058
$849$	14.2129	0.487786
$850$	9.60021	0.329284
$851$	62.9359	2.15741
$852$	1.28576	0.0440495
$853$	−16.8323	−0.576325	−0.288163	−	0.957581i	$-0.593044\pi$
$853$	−16.8323	−0.576325	−0.288163	+	0.957581i	$0.593044\pi$
$854$	2.68840	0.0919951
$855$	−5.45777	−0.186652
$856$	−59.3767	−2.02945
$857$	53.9577	1.84316	0.921580	−	0.388189i	$-0.126899\pi$
$857$	53.9577	1.84316	0.921580	+	0.388189i	$0.126899\pi$
$858$	−22.5996	−0.771539
$859$	−26.5975	−0.907494	−0.453747	−	0.891131i	$-0.649913\pi$
$859$	−26.5975	−0.907494	−0.453747	+	0.891131i	$0.649913\pi$
$860$	1.72025	0.0586599
$861$	−8.58946	−0.292728
$862$	16.6847	0.568285
$863$	−37.4831	−1.27594	−0.637970	−	0.770061i	$-0.720226\pi$
$863$	−37.4831	−1.27594	−0.637970	+	0.770061i	$0.720226\pi$
$864$	−1.93821	−0.0659392
$865$	42.9845	1.46152
$866$	−24.6731	−0.838428
$867$	−3.45913	−0.117478
$868$	−2.56705	−0.0871315
$869$	51.8241	1.75801
$870$	−9.87081	−0.334652
$871$	−45.6583	−1.54707
$872$	25.4325	0.861252
$873$	4.29604	0.145399
$874$	32.0825	1.08521
$875$	−12.1156	−0.409581
$876$	4.45064	0.150373
$877$	−36.8868	−1.24558	−0.622789	−	0.782390i	$-0.714000\pi$
$877$	−36.8868	−1.24558	−0.622789	+	0.782390i	$0.714000\pi$
$878$	30.7889	1.03908
$879$	−17.5703	−0.592630
$880$	24.3950	0.822355
$881$	21.7402	0.732445	0.366223	−	0.930527i	$-0.380651\pi$
$881$	21.7402	0.732445	0.366223	+	0.930527i	$0.380651\pi$
$882$	−1.28577	−0.0432942
$883$	7.03627	0.236789	0.118395	−	0.992967i	$-0.462225\pi$
$883$	7.03627	0.236789	0.118395	+	0.992967i	$0.462225\pi$
$884$	−5.04943	−0.169831
$885$	−11.4062	−0.383417
$886$	−13.5762	−0.456102
$887$	18.7455	0.629414	0.314707	−	0.949189i	$-0.398094\pi$
$887$	18.7455	0.629414	0.314707	+	0.949189i	$0.398094\pi$
$888$	−24.0991	−0.808713
$889$	−13.8763	−0.465397
$890$	13.9803	0.468621
$891$	4.44208	0.148815
$892$	0.893417	0.0299138
$893$	−20.7919	−0.695774
$894$	3.37275	0.112802
$895$	31.2109	1.04327
$896$	7.52118	0.251265
$897$	−31.1808	−1.04110
$898$	48.7405	1.62649
$899$	32.9692	1.09958
$900$	0.703658	0.0234553
$901$	−28.1184	−0.936760
$902$	−49.0587	−1.63348
$903$	−2.87790	−0.0957704
$904$	−22.0626	−0.733790
$905$	−6.05119	−0.201148
$906$	23.8913	0.793737
$907$	29.3094	0.973202	0.486601	−	0.873624i	$-0.338237\pi$
$907$	29.3094	0.973202	0.486601	+	0.873624i	$0.338237\pi$
$908$	−2.20416	−0.0731478
$909$	−8.00310	−0.265446
$910$	−8.76925	−0.290698
$911$	1.21574	0.0402793	0.0201396	−	0.999797i	$-0.493589\pi$
$911$	1.21574	0.0402793	0.0201396	+	0.999797i	$0.493589\pi$
$912$	−10.0887	−0.334070
$913$	5.67365	0.187770
$914$	−11.8675	−0.392543
$915$	−3.60394	−0.119142
$916$	−0.798665	−0.0263886
$917$	−6.25371	−0.206516
$918$	−4.73137	−0.156159
$919$	−6.40569	−0.211304	−0.105652	−	0.994403i	$-0.533693\pi$
$919$	−6.40569	−0.211304	−0.105652	+	0.994403i	$0.533693\pi$
$920$	40.9847	1.35122
$921$	5.92893	0.195365
$922$	43.2598	1.42468
$923$	−14.6705	−0.482884
$924$	1.54048	0.0506779
$925$	16.2053	0.532826
$926$	2.83541	0.0931774
$927$	−9.20507	−0.302334
$928$	8.63261	0.283379
$929$	16.7128	0.548328	0.274164	−	0.961683i	$-0.411599\pi$
$929$	16.7128	0.548328	0.274164	+	0.961683i	$0.411599\pi$
$930$	−16.4051	−0.537944
$931$	3.16642	0.103775
$932$	0.289478	0.00948217
$933$	−25.4845	−0.834326
$934$	−24.4761	−0.800881
$935$	−28.1746	−0.921407
$936$	11.9396	0.390258
$937$	27.7625	0.906962	0.453481	−	0.891266i	$-0.350182\pi$
$937$	27.7625	0.906962	0.453481	+	0.891266i	$0.350182\pi$
$938$	−14.8365	−0.484430
$939$	9.08064	0.296336
$940$	−3.92501	−0.128020
$941$	−45.2173	−1.47404	−0.737021	−	0.675870i	$-0.763768\pi$
$941$	−45.2173	−1.47404	−0.737021	+	0.675870i	$0.763768\pi$
$942$	−8.70458	−0.283610
$943$	−67.6864	−2.20417
$944$	−21.0844	−0.686240
$945$	1.72364	0.0560701
$946$	−16.4371	−0.534417
$947$	37.1778	1.20812	0.604058	−	0.796940i	$-0.293549\pi$
$947$	37.1778	1.20812	0.604058	+	0.796940i	$0.293549\pi$
$948$	−4.04589	−0.131404
$949$	−50.7815	−1.64844
$950$	8.26087	0.268018
$951$	5.38791	0.174715
$952$	−11.1035	−0.359868
$953$	−41.5568	−1.34616	−0.673079	−	0.739571i	$-0.735029\pi$
$953$	−41.5568	−1.34616	−0.673079	+	0.739571i	$0.735029\pi$
$954$	9.82498	0.318095
$955$	−32.7549	−1.05992
$956$	1.39848	0.0452302
$957$	−19.7846	−0.639547
$958$	−53.2045	−1.71896
$959$	−2.21076	−0.0713890
$960$	−15.2791	−0.493130
$961$	23.7941	0.767553
$962$	40.6329	1.31006
$963$	−19.6778	−0.634110
$964$	−4.04754	−0.130363
$965$	21.9186	0.705584
$966$	−10.1321	−0.325995
$967$	28.1570	0.905468	0.452734	−	0.891646i	$-0.350449\pi$
$967$	28.1570	0.905468	0.452734	+	0.891646i	$0.350449\pi$
$968$	26.3485	0.846874
$969$	11.6518	0.374308
$970$	9.52092	0.305698
$971$	−28.9506	−0.929070	−0.464535	−	0.885555i	$-0.653779\pi$
$971$	−28.9506	−0.929070	−0.464535	+	0.885555i	$0.653779\pi$
$972$	−0.346791	−0.0111233
$973$	−14.2944	−0.458257
$974$	−5.19823	−0.166562
$975$	−8.02869	−0.257124
$976$	−6.66187	−0.213241
$977$	−50.2193	−1.60666	−0.803329	−	0.595535i	$-0.796940\pi$
$977$	−50.2193	−1.60666	−0.803329	+	0.595535i	$0.796940\pi$
$978$	9.09084	0.290693
$979$	28.0216	0.895573
$980$	0.597744	0.0190942
$981$	8.42850	0.269101
$982$	39.0873	1.24733
$983$	−54.7181	−1.74524	−0.872618	−	0.488404i	$-0.837579\pi$
$983$	−54.7181	−1.74524	−0.872618	+	0.488404i	$0.837579\pi$
$984$	25.9182	0.826241
$985$	0.735780	0.0234439
$986$	21.0731	0.671105
$987$	6.56637	0.209010
$988$	−4.34498	−0.138232
$989$	−22.6783	−0.721129
$990$	9.84459	0.312882
$991$	33.7106	1.07085	0.535427	−	0.844582i	$-0.320151\pi$
$991$	33.7106	1.07085	0.535427	+	0.844582i	$0.320151\pi$
$992$	14.3472	0.455525
$993$	24.5442	0.778885
$994$	−4.76712	−0.151204
$995$	−22.1005	−0.700634
$996$	−0.442939	−0.0140351
$997$	−44.4195	−1.40678	−0.703389	−	0.710805i	$-0.748331\pi$
$997$	−44.4195	−1.40678	−0.703389	+	0.710805i	$0.748331\pi$
$998$	−45.6818	−1.44603
$999$	−7.98661	−0.252685

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.q.1.14	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.q.1.14	✓	44	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-1.28577 q^{2} +1.00000 q^{3} -0.346791 q^{4} -1.72364 q^{5} -1.28577 q^{6} -1.00000 q^{7} +3.01744 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.28577 q^{2} +1.00000 q^{3} -0.346791 q^{4} -1.72364 q^{5} -1.28577 q^{6} -1.00000 q^{7} +3.01744 q^{8} +1.00000 q^{9} +2.21621 q^{10} +4.44208 q^{11} -0.346791 q^{12} +3.95687 q^{13} +1.28577 q^{14} -1.72364 q^{15} -3.18615 q^{16} +3.67979 q^{17} -1.28577 q^{18} +3.16642 q^{19} +0.597744 q^{20} -1.00000 q^{21} -5.71150 q^{22} -7.88017 q^{23} +3.01744 q^{24} -2.02905 q^{25} -5.08763 q^{26} +1.00000 q^{27} +0.346791 q^{28} -4.45391 q^{29} +2.21621 q^{30} -7.40231 q^{31} -1.93821 q^{32} +4.44208 q^{33} -4.73137 q^{34} +1.72364 q^{35} -0.346791 q^{36} -7.98661 q^{37} -4.07129 q^{38} +3.95687 q^{39} -5.20099 q^{40} +8.58946 q^{41} +1.28577 q^{42} +2.87790 q^{43} -1.54048 q^{44} -1.72364 q^{45} +10.1321 q^{46} -6.56637 q^{47} -3.18615 q^{48} +1.00000 q^{49} +2.60890 q^{50} +3.67979 q^{51} -1.37221 q^{52} -7.64131 q^{53} -1.28577 q^{54} -7.65656 q^{55} -3.01744 q^{56} +3.16642 q^{57} +5.72671 q^{58} +6.61752 q^{59} +0.597744 q^{60} +2.09088 q^{61} +9.51768 q^{62} -1.00000 q^{63} +8.86440 q^{64} -6.82022 q^{65} -5.71150 q^{66} -11.5390 q^{67} -1.27612 q^{68} -7.88017 q^{69} -2.21621 q^{70} -3.70760 q^{71} +3.01744 q^{72} -12.8338 q^{73} +10.2690 q^{74} -2.02905 q^{75} -1.09809 q^{76} -4.44208 q^{77} -5.08763 q^{78} +11.6666 q^{79} +5.49179 q^{80} +1.00000 q^{81} -11.0441 q^{82} +1.27725 q^{83} +0.346791 q^{84} -6.34265 q^{85} -3.70032 q^{86} -4.45391 q^{87} +13.4037 q^{88} +6.30820 q^{89} +2.21621 q^{90} -3.95687 q^{91} +2.73277 q^{92} -7.40231 q^{93} +8.44286 q^{94} -5.45777 q^{95} -1.93821 q^{96} +4.29604 q^{97} -1.28577 q^{98} +4.44208 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9}+O(q^{10}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9} - 16 q^{10} - 2 q^{11} + 44 q^{12} - 34 q^{13} + 4 q^{14} - 16 q^{15} + 24 q^{16} - 4 q^{17} - 4 q^{18} - 22 q^{19} - 39 q^{20} - 44 q^{21} - 23 q^{22} - 56 q^{23} - 15 q^{24} + 32 q^{25} - 17 q^{26} + 44 q^{27} - 44 q^{28} - 33 q^{29} - 16 q^{30} - 32 q^{31} - 34 q^{32} - 2 q^{33} - 25 q^{34} + 16 q^{35} + 44 q^{36} - 47 q^{37} - 40 q^{38} - 34 q^{39} - 50 q^{40} + 2 q^{41} + 4 q^{42} - 12 q^{43} - 22 q^{44} - 16 q^{45} + 8 q^{46} - 27 q^{47} + 24 q^{48} + 44 q^{49} - 21 q^{50} - 4 q^{51} - 82 q^{52} - 114 q^{53} - 4 q^{54} - 29 q^{55} + 15 q^{56} - 22 q^{57} - 26 q^{58} - 40 q^{59} - 39 q^{60} - 47 q^{61} - 37 q^{62} - 44 q^{63} - 5 q^{64} - 20 q^{65} - 23 q^{66} - 14 q^{67} - 72 q^{68} - 56 q^{69} + 16 q^{70} - 65 q^{71} - 15 q^{72} - 21 q^{73} - 26 q^{74} + 32 q^{75} - 15 q^{76} + 2 q^{77} - 17 q^{78} + 6 q^{79} - 77 q^{80} + 44 q^{81} - 51 q^{82} - 30 q^{83} - 44 q^{84} - 26 q^{85} - 65 q^{86} - 33 q^{87} - 84 q^{88} - 32 q^{89} - 16 q^{90} + 34 q^{91} - 140 q^{92} - 32 q^{93} - 35 q^{94} - 50 q^{95} - 34 q^{96} - 83 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9 - 16 * q^10 - 2 * q^11 + 44 * q^12 - 34 * q^13 + 4 * q^14 - 16 * q^15 + 24 * q^16 - 4 * q^17 - 4 * q^18 - 22 * q^19 - 39 * q^20 - 44 * q^21 - 23 * q^22 - 56 * q^23 - 15 * q^24 + 32 * q^25 - 17 * q^26 + 44 * q^27 - 44 * q^28 - 33 * q^29 - 16 * q^30 - 32 * q^31 - 34 * q^32 - 2 * q^33 - 25 * q^34 + 16 * q^35 + 44 * q^36 - 47 * q^37 - 40 * q^38 - 34 * q^39 - 50 * q^40 + 2 * q^41 + 4 * q^42 - 12 * q^43 - 22 * q^44 - 16 * q^45 + 8 * q^46 - 27 * q^47 + 24 * q^48 + 44 * q^49 - 21 * q^50 - 4 * q^51 - 82 * q^52 - 114 * q^53 - 4 * q^54 - 29 * q^55 + 15 * q^56 - 22 * q^57 - 26 * q^58 - 40 * q^59 - 39 * q^60 - 47 * q^61 - 37 * q^62 - 44 * q^63 - 5 * q^64 - 20 * q^65 - 23 * q^66 - 14 * q^67 - 72 * q^68 - 56 * q^69 + 16 * q^70 - 65 * q^71 - 15 * q^72 - 21 * q^73 - 26 * q^74 + 32 * q^75 - 15 * q^76 + 2 * q^77 - 17 * q^78 + 6 * q^79 - 77 * q^80 + 44 * q^81 - 51 * q^82 - 30 * q^83 - 44 * q^84 - 26 * q^85 - 65 * q^86 - 33 * q^87 - 84 * q^88 - 32 * q^89 - 16 * q^90 + 34 * q^91 - 140 * q^92 - 32 * q^93 - 35 * q^94 - 50 * q^95 - 34 * q^96 - 83 * q^97 - 4 * q^98 - 2 * q^99

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