LMFDB - Embedded newform 8014.2.a.e.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8014,2,Mod(1,8014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8014 = 2 \cdot 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8014.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:	$63.9921121799$
Analytic rank:	$0$
Dimension:	$91$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.99318 q^{3} +1.00000 q^{4} +0.808905 q^{5} +1.99318 q^{6} +3.91873 q^{7} -1.00000 q^{8} +0.972766 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.99318 q^{3} +1.00000 q^{4} +0.808905 q^{5} +1.99318 q^{6} +3.91873 q^{7} -1.00000 q^{8} +0.972766 q^{9} -0.808905 q^{10} +4.55361 q^{11} -1.99318 q^{12} -0.447670 q^{13} -3.91873 q^{14} -1.61229 q^{15} +1.00000 q^{16} -1.12110 q^{17} -0.972766 q^{18} -3.87424 q^{19} +0.808905 q^{20} -7.81074 q^{21} -4.55361 q^{22} +7.20171 q^{23} +1.99318 q^{24} -4.34567 q^{25} +0.447670 q^{26} +4.04064 q^{27} +3.91873 q^{28} -8.61640 q^{29} +1.61229 q^{30} -6.28522 q^{31} -1.00000 q^{32} -9.07616 q^{33} +1.12110 q^{34} +3.16988 q^{35} +0.972766 q^{36} +8.65024 q^{37} +3.87424 q^{38} +0.892288 q^{39} -0.808905 q^{40} +2.00767 q^{41} +7.81074 q^{42} -1.17764 q^{43} +4.55361 q^{44} +0.786876 q^{45} -7.20171 q^{46} -11.1578 q^{47} -1.99318 q^{48} +8.35647 q^{49} +4.34567 q^{50} +2.23456 q^{51} -0.447670 q^{52} -2.76686 q^{53} -4.04064 q^{54} +3.68344 q^{55} -3.91873 q^{56} +7.72206 q^{57} +8.61640 q^{58} +4.24799 q^{59} -1.61229 q^{60} +7.85744 q^{61} +6.28522 q^{62} +3.81201 q^{63} +1.00000 q^{64} -0.362123 q^{65} +9.07616 q^{66} +10.5097 q^{67} -1.12110 q^{68} -14.3543 q^{69} -3.16988 q^{70} +14.0173 q^{71} -0.972766 q^{72} -9.14731 q^{73} -8.65024 q^{74} +8.66171 q^{75} -3.87424 q^{76} +17.8444 q^{77} -0.892288 q^{78} +14.2030 q^{79} +0.808905 q^{80} -10.9720 q^{81} -2.00767 q^{82} +14.7991 q^{83} -7.81074 q^{84} -0.906866 q^{85} +1.17764 q^{86} +17.1740 q^{87} -4.55361 q^{88} -14.2609 q^{89} -0.786876 q^{90} -1.75430 q^{91} +7.20171 q^{92} +12.5276 q^{93} +11.1578 q^{94} -3.13389 q^{95} +1.99318 q^{96} +8.91589 q^{97} -8.35647 q^{98} +4.42960 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9}+O(q^{10}) $ 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9} - 22 q^{10} + 59 q^{11} - 2 q^{12} - 15 q^{13} + 14 q^{14} + 23 q^{15} + 91 q^{16} + 25 q^{17} - 123 q^{18} + 2 q^{19} + 22 q^{20} + 20 q^{21} - 59 q^{22} + 36 q^{23} + 2 q^{24} + 121 q^{25} + 15 q^{26} - 8 q^{27} - 14 q^{28} + 71 q^{29} - 23 q^{30} + 13 q^{31} - 91 q^{32} + 24 q^{33} - 25 q^{34} + 27 q^{35} + 123 q^{36} + 5 q^{37} - 2 q^{38} + 48 q^{39} - 22 q^{40} + 77 q^{41} - 20 q^{42} - 36 q^{43} + 59 q^{44} + 62 q^{45} - 36 q^{46} + 41 q^{47} - 2 q^{48} + 137 q^{49} - 121 q^{50} + 13 q^{51} - 15 q^{52} + 33 q^{53} + 8 q^{54} + 12 q^{55} + 14 q^{56} + 52 q^{57} - 71 q^{58} + 76 q^{59} + 23 q^{60} + 18 q^{61} - 13 q^{62} - 18 q^{63} + 91 q^{64} + 84 q^{65} - 24 q^{66} - 59 q^{67} + 25 q^{68} + 64 q^{69} - 27 q^{70} + 124 q^{71} - 123 q^{72} + 43 q^{73} - 5 q^{74} + 9 q^{75} + 2 q^{76} + 50 q^{77} - 48 q^{78} - 20 q^{79} + 22 q^{80} + 227 q^{81} - 77 q^{82} + 29 q^{83} + 20 q^{84} + 3 q^{85} + 36 q^{86} - 25 q^{87} - 59 q^{88} + 148 q^{89} - 62 q^{90} + 27 q^{91} + 36 q^{92} + 65 q^{93} - 41 q^{94} + 54 q^{95} + 2 q^{96} + 38 q^{97} - 137 q^{98} + 157 q^{99}+O(q^{100}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9 - 22 * q^10 + 59 * q^11 - 2 * q^12 - 15 * q^13 + 14 * q^14 + 23 * q^15 + 91 * q^16 + 25 * q^17 - 123 * q^18 + 2 * q^19 + 22 * q^20 + 20 * q^21 - 59 * q^22 + 36 * q^23 + 2 * q^24 + 121 * q^25 + 15 * q^26 - 8 * q^27 - 14 * q^28 + 71 * q^29 - 23 * q^30 + 13 * q^31 - 91 * q^32 + 24 * q^33 - 25 * q^34 + 27 * q^35 + 123 * q^36 + 5 * q^37 - 2 * q^38 + 48 * q^39 - 22 * q^40 + 77 * q^41 - 20 * q^42 - 36 * q^43 + 59 * q^44 + 62 * q^45 - 36 * q^46 + 41 * q^47 - 2 * q^48 + 137 * q^49 - 121 * q^50 + 13 * q^51 - 15 * q^52 + 33 * q^53 + 8 * q^54 + 12 * q^55 + 14 * q^56 + 52 * q^57 - 71 * q^58 + 76 * q^59 + 23 * q^60 + 18 * q^61 - 13 * q^62 - 18 * q^63 + 91 * q^64 + 84 * q^65 - 24 * q^66 - 59 * q^67 + 25 * q^68 + 64 * q^69 - 27 * q^70 + 124 * q^71 - 123 * q^72 + 43 * q^73 - 5 * q^74 + 9 * q^75 + 2 * q^76 + 50 * q^77 - 48 * q^78 - 20 * q^79 + 22 * q^80 + 227 * q^81 - 77 * q^82 + 29 * q^83 + 20 * q^84 + 3 * q^85 + 36 * q^86 - 25 * q^87 - 59 * q^88 + 148 * q^89 - 62 * q^90 + 27 * q^91 + 36 * q^92 + 65 * q^93 - 41 * q^94 + 54 * q^95 + 2 * q^96 + 38 * q^97 - 137 * q^98 + 157 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.99318	−1.15076	−0.575381	−	0.817885i	$-0.695146\pi$
$3$	−1.99318	−1.15076	−0.575381	+	0.817885i	$0.695146\pi$
$4$	1.00000	0.500000
$5$	0.808905	0.361753	0.180877	−	0.983506i	$-0.442107\pi$
$5$	0.808905	0.361753	0.180877	+	0.983506i	$0.442107\pi$
$6$	1.99318	0.813712
$7$	3.91873	1.48114	0.740571	−	0.671978i	$-0.234555\pi$
$7$	3.91873	1.48114	0.740571	+	0.671978i	$0.234555\pi$
$8$	−1.00000	−0.353553
$9$	0.972766	0.324255
$10$	−0.808905	−0.255798
$11$	4.55361	1.37297	0.686483	−	0.727146i	$-0.259154\pi$
$11$	4.55361	1.37297	0.686483	+	0.727146i	$0.259154\pi$
$12$	−1.99318	−0.575381
$13$	−0.447670	−0.124161	−0.0620807	−	0.998071i	$-0.519774\pi$
$13$	−0.447670	−0.124161	−0.0620807	+	0.998071i	$0.519774\pi$
$14$	−3.91873	−1.04733
$15$	−1.61229	−0.416292
$16$	1.00000	0.250000
$17$	−1.12110	−0.271908	−0.135954	−	0.990715i	$-0.543410\pi$
$17$	−1.12110	−0.271908	−0.135954	+	0.990715i	$0.543410\pi$
$18$	−0.972766	−0.229283
$19$	−3.87424	−0.888812	−0.444406	−	0.895825i	$-0.646585\pi$
$19$	−3.87424	−0.888812	−0.444406	+	0.895825i	$0.646585\pi$
$20$	0.808905	0.180877
$21$	−7.81074	−1.70444
$22$	−4.55361	−0.970833
$23$	7.20171	1.50166	0.750830	−	0.660495i	$-0.229654\pi$
$23$	7.20171	1.50166	0.750830	+	0.660495i	$0.229654\pi$
$24$	1.99318	0.406856
$25$	−4.34567	−0.869135
$26$	0.447670	0.0877954
$27$	4.04064	0.777622
$28$	3.91873	0.740571
$29$	−8.61640	−1.60002	−0.800012	−	0.599983i	$-0.795174\pi$
$29$	−8.61640	−1.60002	−0.800012	+	0.599983i	$0.795174\pi$
$30$	1.61229	0.294363
$31$	−6.28522	−1.12886	−0.564430	−	0.825481i	$-0.690904\pi$
$31$	−6.28522	−1.12886	−0.564430	+	0.825481i	$0.690904\pi$
$32$	−1.00000	−0.176777
$33$	−9.07616	−1.57996
$34$	1.12110	0.192268
$35$	3.16988	0.535808
$36$	0.972766	0.162128
$37$	8.65024	1.42209	0.711045	−	0.703146i	$-0.248222\pi$
$37$	8.65024	1.42209	0.711045	+	0.703146i	$0.248222\pi$
$38$	3.87424	0.628485
$39$	0.892288	0.142880
$40$	−0.808905	−0.127899
$41$	2.00767	0.313545	0.156773	−	0.987635i	$-0.449891\pi$
$41$	2.00767	0.313545	0.156773	+	0.987635i	$0.449891\pi$
$42$	7.81074	1.20522
$43$	−1.17764	−0.179589	−0.0897943	−	0.995960i	$-0.528621\pi$
$43$	−1.17764	−0.179589	−0.0897943	+	0.995960i	$0.528621\pi$
$44$	4.55361	0.686483
$45$	0.786876	0.117300
$46$	−7.20171	−1.06183
$47$	−11.1578	−1.62753	−0.813765	−	0.581195i	$-0.802586\pi$
$47$	−11.1578	−1.62753	−0.813765	+	0.581195i	$0.802586\pi$
$48$	−1.99318	−0.287691
$49$	8.35647	1.19378
$50$	4.34567	0.614571
$51$	2.23456	0.312901
$52$	−0.447670	−0.0620807
$53$	−2.76686	−0.380058	−0.190029	−	0.981779i	$-0.560858\pi$
$53$	−2.76686	−0.380058	−0.190029	+	0.981779i	$0.560858\pi$
$54$	−4.04064	−0.549862
$55$	3.68344	0.496675
$56$	−3.91873	−0.523663
$57$	7.72206	1.02281
$58$	8.61640	1.13139
$59$	4.24799	0.553042	0.276521	−	0.961008i	$-0.410819\pi$
$59$	4.24799	0.553042	0.276521	+	0.961008i	$0.410819\pi$
$60$	−1.61229	−0.208146
$61$	7.85744	1.00604	0.503021	−	0.864274i	$-0.332222\pi$
$61$	7.85744	1.00604	0.503021	+	0.864274i	$0.332222\pi$
$62$	6.28522	0.798224
$63$	3.81201	0.480268
$64$	1.00000	0.125000
$65$	−0.362123	−0.0449158
$66$	9.07616	1.11720
$67$	10.5097	1.28397	0.641985	−	0.766717i	$-0.278111\pi$
$67$	10.5097	1.28397	0.641985	+	0.766717i	$0.278111\pi$
$68$	−1.12110	−0.135954
$69$	−14.3543	−1.72806
$70$	−3.16988	−0.378874
$71$	14.0173	1.66355	0.831773	−	0.555116i	$-0.187326\pi$
$71$	14.0173	1.66355	0.831773	+	0.555116i	$0.187326\pi$
$72$	−0.972766	−0.114642
$73$	−9.14731	−1.07061	−0.535306	−	0.844658i	$-0.679804\pi$
$73$	−9.14731	−1.07061	−0.535306	+	0.844658i	$0.679804\pi$
$74$	−8.65024	−1.00557
$75$	8.66171	1.00017
$76$	−3.87424	−0.444406
$77$	17.8444	2.03356
$78$	−0.892288	−0.101032
$79$	14.2030	1.59796	0.798982	−	0.601355i	$-0.205372\pi$
$79$	14.2030	1.59796	0.798982	+	0.601355i	$0.205372\pi$
$80$	0.808905	0.0904383
$81$	−10.9720	−1.21911
$82$	−2.00767	−0.221710
$83$	14.7991	1.62441	0.812205	−	0.583373i	$-0.198267\pi$
$83$	14.7991	1.62441	0.812205	+	0.583373i	$0.198267\pi$
$84$	−7.81074	−0.852222
$85$	−0.906866	−0.0983635
$86$	1.17764	0.126988
$87$	17.1740	1.84125
$88$	−4.55361	−0.485416
$89$	−14.2609	−1.51165	−0.755826	−	0.654773i	$-0.772764\pi$
$89$	−14.2609	−1.51165	−0.755826	+	0.654773i	$0.772764\pi$
$90$	−0.786876	−0.0829440
$91$	−1.75430	−0.183901
$92$	7.20171	0.750830
$93$	12.5276	1.29905
$94$	11.1578	1.15084
$95$	−3.13389	−0.321531
$96$	1.99318	0.203428
$97$	8.91589	0.905271	0.452636	−	0.891696i	$-0.350484\pi$
$97$	8.91589	0.905271	0.452636	+	0.891696i	$0.350484\pi$
$98$	−8.35647	−0.844131
$99$	4.42960	0.445191
$100$	−4.34567	−0.434567
$101$	14.6617	1.45889	0.729447	−	0.684037i	$-0.239777\pi$
$101$	14.6617	1.45889	0.729447	+	0.684037i	$0.239777\pi$
$102$	−2.23456	−0.221255
$103$	−9.25042	−0.911471	−0.455736	−	0.890115i	$-0.650624\pi$
$103$	−9.25042	−0.911471	−0.455736	+	0.890115i	$0.650624\pi$
$104$	0.447670	0.0438977
$105$	−6.31815	−0.616588
$106$	2.76686	0.268741
$107$	−17.7101	−1.71210	−0.856051	−	0.516892i	$-0.827089\pi$
$107$	−17.7101	−1.71210	−0.856051	+	0.516892i	$0.827089\pi$
$108$	4.04064	0.388811
$109$	−12.9827	−1.24351	−0.621756	−	0.783211i	$-0.713581\pi$
$109$	−12.9827	−1.24351	−0.621756	+	0.783211i	$0.713581\pi$
$110$	−3.68344	−0.351202
$111$	−17.2415	−1.63649
$112$	3.91873	0.370286
$113$	3.97407	0.373849	0.186925	−	0.982374i	$-0.440148\pi$
$113$	3.97407	0.373849	0.186925	+	0.982374i	$0.440148\pi$
$114$	−7.72206	−0.723237
$115$	5.82550	0.543231
$116$	−8.61640	−0.800012
$117$	−0.435479	−0.0402600
$118$	−4.24799	−0.391060
$119$	−4.39331	−0.402734
$120$	1.61229	0.147182
$121$	9.73536	0.885033
$122$	−7.85744	−0.711379
$123$	−4.00165	−0.360816
$124$	−6.28522	−0.564430
$125$	−7.55976	−0.676166
$126$	−3.81201	−0.339601
$127$	12.1216	1.07562	0.537809	−	0.843067i	$-0.319252\pi$
$127$	12.1216	1.07562	0.537809	+	0.843067i	$0.319252\pi$
$128$	−1.00000	−0.0883883
$129$	2.34725	0.206664
$130$	0.362123	0.0317603
$131$	17.9537	1.56862	0.784310	−	0.620369i	$-0.213017\pi$
$131$	17.9537	1.56862	0.784310	+	0.620369i	$0.213017\pi$
$132$	−9.07616	−0.789979
$133$	−15.1821	−1.31646
$134$	−10.5097	−0.907904
$135$	3.26850	0.281307
$136$	1.12110	0.0961338
$137$	−3.62069	−0.309336	−0.154668	−	0.987966i	$-0.549431\pi$
$137$	−3.62069	−0.309336	−0.154668	+	0.987966i	$0.549431\pi$
$138$	14.3543	1.22192
$139$	18.1775	1.54179	0.770897	−	0.636960i	$-0.219808\pi$
$139$	18.1775	1.54179	0.770897	+	0.636960i	$0.219808\pi$
$140$	3.16988	0.267904
$141$	22.2395	1.87290
$142$	−14.0173	−1.17630
$143$	−2.03852	−0.170469
$144$	0.972766	0.0810639
$145$	−6.96985	−0.578814
$146$	9.14731	0.757037
$147$	−16.6560	−1.37376
$148$	8.65024	0.711045
$149$	9.84923	0.806880	0.403440	−	0.915006i	$-0.367814\pi$
$149$	9.84923	0.806880	0.403440	+	0.915006i	$0.367814\pi$
$150$	−8.66171	−0.707225
$151$	11.7885	0.959337	0.479669	−	0.877450i	$-0.340757\pi$
$151$	11.7885	0.959337	0.479669	+	0.877450i	$0.340757\pi$
$152$	3.87424	0.314243
$153$	−1.09057	−0.0881675
$154$	−17.8444	−1.43794
$155$	−5.08415	−0.408369
$156$	0.892288	0.0714402
$157$	3.42041	0.272979	0.136489	−	0.990642i	$-0.456418\pi$
$157$	3.42041	0.272979	0.136489	+	0.990642i	$0.456418\pi$
$158$	−14.2030	−1.12993
$159$	5.51485	0.437356
$160$	−0.808905	−0.0639496
$161$	28.2216	2.22417
$162$	10.9720	0.862044
$163$	14.6838	1.15013	0.575063	−	0.818109i	$-0.304977\pi$
$163$	14.6838	1.15013	0.575063	+	0.818109i	$0.304977\pi$
$164$	2.00767	0.156773
$165$	−7.34176	−0.571555
$166$	−14.7991	−1.14863
$167$	9.51995	0.736676	0.368338	−	0.929692i	$-0.379927\pi$
$167$	9.51995	0.736676	0.368338	+	0.929692i	$0.379927\pi$
$168$	7.81074	0.602612
$169$	−12.7996	−0.984584
$170$	0.906866	0.0695535
$171$	−3.76873	−0.288202
$172$	−1.17764	−0.0897943
$173$	7.12870	0.541985	0.270993	−	0.962581i	$-0.412648\pi$
$173$	7.12870	0.541985	0.270993	+	0.962581i	$0.412648\pi$
$174$	−17.1740	−1.30196
$175$	−17.0295	−1.28731
$176$	4.55361	0.343241
$177$	−8.46702	−0.636420
$178$	14.2609	1.06890
$179$	−16.8052	−1.25608	−0.628041	−	0.778180i	$-0.716143\pi$
$179$	−16.8052	−1.25608	−0.628041	+	0.778180i	$0.716143\pi$
$180$	0.786876	0.0586502
$181$	−5.51085	−0.409618	−0.204809	−	0.978802i	$-0.565657\pi$
$181$	−5.51085	−0.409618	−0.204809	+	0.978802i	$0.565657\pi$
$182$	1.75430	0.130037
$183$	−15.6613	−1.15772
$184$	−7.20171	−0.530917
$185$	6.99722	0.514446
$186$	−12.5276	−0.918567
$187$	−5.10507	−0.373320
$188$	−11.1578	−0.813765
$189$	15.8342	1.15177
$190$	3.13389	0.227357
$191$	−13.3735	−0.967669	−0.483835	−	0.875159i	$-0.660756\pi$
$191$	−13.3735	−0.967669	−0.483835	+	0.875159i	$0.660756\pi$
$192$	−1.99318	−0.143845
$193$	12.2460	0.881487	0.440744	−	0.897633i	$-0.354715\pi$
$193$	12.2460	0.881487	0.440744	+	0.897633i	$0.354715\pi$
$194$	−8.91589	−0.640123
$195$	0.721776	0.0516875
$196$	8.35647	0.596891
$197$	4.12568	0.293943	0.146971	−	0.989141i	$-0.453047\pi$
$197$	4.12568	0.293943	0.146971	+	0.989141i	$0.453047\pi$
$198$	−4.42960	−0.314798
$199$	11.0244	0.781497	0.390748	−	0.920498i	$-0.372216\pi$
$199$	11.0244	0.781497	0.390748	+	0.920498i	$0.372216\pi$
$200$	4.34567	0.307285
$201$	−20.9478	−1.47754
$202$	−14.6617	−1.03159
$203$	−33.7654	−2.36986
$204$	2.23456	0.156451
$205$	1.62401	0.113426
$206$	9.25042	0.644508
$207$	7.00558	0.486922
$208$	−0.447670	−0.0310404
$209$	−17.6418	−1.22031
$210$	6.31815	0.435994
$211$	−15.9680	−1.09928	−0.549640	−	0.835401i	$-0.685235\pi$
$211$	−15.9680	−1.09928	−0.549640	+	0.835401i	$0.685235\pi$
$212$	−2.76686	−0.190029
$213$	−27.9390	−1.91435
$214$	17.7101	1.21064
$215$	−0.952600	−0.0649668
$216$	−4.04064	−0.274931
$217$	−24.6301	−1.67200
$218$	12.9827	0.879296
$219$	18.2322	1.23202
$220$	3.68344	0.248337
$221$	0.501885	0.0337604
$222$	17.2415	1.15717
$223$	−18.0502	−1.20873	−0.604364	−	0.796708i	$-0.706573\pi$
$223$	−18.0502	−1.20873	−0.604364	+	0.796708i	$0.706573\pi$
$224$	−3.91873	−0.261831
$225$	−4.22732	−0.281822
$226$	−3.97407	−0.264351
$227$	0.216959	0.0144001	0.00720003	−	0.999974i	$-0.497708\pi$
$227$	0.216959	0.0144001	0.00720003	+	0.999974i	$0.497708\pi$
$228$	7.72206	0.511406
$229$	−21.0060	−1.38812	−0.694058	−	0.719919i	$-0.744179\pi$
$229$	−21.0060	−1.38812	−0.694058	+	0.719919i	$0.744179\pi$
$230$	−5.82550	−0.384122
$231$	−35.5671	−2.34014
$232$	8.61640	0.565694
$233$	27.3248	1.79011	0.895054	−	0.445957i	$-0.147136\pi$
$233$	27.3248	1.79011	0.895054	+	0.445957i	$0.147136\pi$
$234$	0.435479	0.0284681
$235$	−9.02558	−0.588764
$236$	4.24799	0.276521
$237$	−28.3092	−1.83888
$238$	4.39331	0.284776
$239$	−11.6080	−0.750856	−0.375428	−	0.926852i	$-0.622504\pi$
$239$	−11.6080	−0.750856	−0.375428	+	0.926852i	$0.622504\pi$
$240$	−1.61229	−0.104073
$241$	14.3389	0.923647	0.461823	−	0.886972i	$-0.347195\pi$
$241$	14.3389	0.923647	0.461823	+	0.886972i	$0.347195\pi$
$242$	−9.73536	−0.625813
$243$	9.74730	0.625289
$244$	7.85744	0.503021
$245$	6.75959	0.431855
$246$	4.00165	0.255136
$247$	1.73438	0.110356
$248$	6.28522	0.399112
$249$	−29.4972	−1.86931
$250$	7.55976	0.478121
$251$	6.02416	0.380241	0.190121	−	0.981761i	$-0.439112\pi$
$251$	6.02416	0.380241	0.190121	+	0.981761i	$0.439112\pi$
$252$	3.81201	0.240134
$253$	32.7938	2.06173
$254$	−12.1216	−0.760577
$255$	1.80755	0.113193
$256$	1.00000	0.0625000
$257$	−15.8004	−0.985605	−0.492802	−	0.870141i	$-0.664027\pi$
$257$	−15.8004	−0.985605	−0.492802	+	0.870141i	$0.664027\pi$
$258$	−2.34725	−0.146133
$259$	33.8980	2.10632
$260$	−0.362123	−0.0224579
$261$	−8.38174	−0.518817
$262$	−17.9537	−1.10918
$263$	29.2570	1.80407	0.902033	−	0.431668i	$-0.142075\pi$
$263$	29.2570	1.80407	0.902033	+	0.431668i	$0.142075\pi$
$264$	9.07616	0.558599
$265$	−2.23813	−0.137487
$266$	15.1821	0.930876
$267$	28.4245	1.73955
$268$	10.5097	0.641985
$269$	−23.4258	−1.42829	−0.714147	−	0.699996i	$-0.753185\pi$
$269$	−23.4258	−1.42829	−0.714147	+	0.699996i	$0.753185\pi$
$270$	−3.26850	−0.198914
$271$	−4.55804	−0.276881	−0.138441	−	0.990371i	$-0.544209\pi$
$271$	−4.55804	−0.276881	−0.138441	+	0.990371i	$0.544209\pi$
$272$	−1.12110	−0.0679769
$273$	3.49664	0.211626
$274$	3.62069	0.218734
$275$	−19.7885	−1.19329
$276$	−14.3543	−0.864028
$277$	−11.4738	−0.689396	−0.344698	−	0.938714i	$-0.612019\pi$
$277$	−11.4738	−0.689396	−0.344698	+	0.938714i	$0.612019\pi$
$278$	−18.1775	−1.09021
$279$	−6.11405	−0.366039
$280$	−3.16988	−0.189437
$281$	20.7074	1.23530	0.617649	−	0.786454i	$-0.288085\pi$
$281$	20.7074	1.23530	0.617649	+	0.786454i	$0.288085\pi$
$282$	−22.2395	−1.32434
$283$	9.32672	0.554416	0.277208	−	0.960810i	$-0.410591\pi$
$283$	9.32672	0.554416	0.277208	+	0.960810i	$0.410591\pi$
$284$	14.0173	0.831773
$285$	6.24642	0.370006
$286$	2.03852	0.120540
$287$	7.86752	0.464405
$288$	−0.972766	−0.0573208
$289$	−15.7431	−0.926066
$290$	6.96985	0.409284
$291$	−17.7710	−1.04175
$292$	−9.14731	−0.535306
$293$	−17.5635	−1.02607	−0.513036	−	0.858367i	$-0.671479\pi$
$293$	−17.5635	−1.02607	−0.513036	+	0.858367i	$0.671479\pi$
$294$	16.6560	0.971395
$295$	3.43622	0.200065
$296$	−8.65024	−0.502785
$297$	18.3995	1.06765
$298$	−9.84923	−0.570550
$299$	−3.22399	−0.186448
$300$	8.66171	0.500084
$301$	−4.61486	−0.265996
$302$	−11.7885	−0.678354
$303$	−29.2234	−1.67884
$304$	−3.87424	−0.222203
$305$	6.35592	0.363939
$306$	1.09057	0.0623438
$307$	−7.75364	−0.442523	−0.221262	−	0.975214i	$-0.571018\pi$
$307$	−7.75364	−0.442523	−0.221262	+	0.975214i	$0.571018\pi$
$308$	17.8444	1.01678
$309$	18.4378	1.04889
$310$	5.08415	0.288760
$311$	5.17827	0.293633	0.146816	−	0.989164i	$-0.453097\pi$
$311$	5.17827	0.293633	0.146816	+	0.989164i	$0.453097\pi$
$312$	−0.892288	−0.0505158
$313$	19.7705	1.11749	0.558747	−	0.829338i	$-0.311282\pi$
$313$	19.7705	1.11749	0.558747	+	0.829338i	$0.311282\pi$
$314$	−3.42041	−0.193025
$315$	3.08356	0.173739
$316$	14.2030	0.798982
$317$	32.0722	1.80135	0.900677	−	0.434489i	$-0.143071\pi$
$317$	32.0722	1.80135	0.900677	+	0.434489i	$0.143071\pi$
$318$	−5.51485	−0.309258
$319$	−39.2357	−2.19678
$320$	0.808905	0.0452192
$321$	35.2995	1.97022
$322$	−28.2216	−1.57273
$323$	4.34343	0.241675
$324$	−10.9720	−0.609557
$325$	1.94543	0.107913
$326$	−14.6838	−0.813262
$327$	25.8768	1.43099
$328$	−2.00767	−0.110855
$329$	−43.7244	−2.41060
$330$	7.34176	0.404150
$331$	−16.8204	−0.924532	−0.462266	−	0.886741i	$-0.652964\pi$
$331$	−16.8204	−0.924532	−0.462266	+	0.886741i	$0.652964\pi$
$332$	14.7991	0.812205
$333$	8.41466	0.461121
$334$	−9.51995	−0.520909
$335$	8.50139	0.464480
$336$	−7.81074	−0.426111
$337$	25.5937	1.39417	0.697087	−	0.716986i	$-0.254479\pi$
$337$	25.5937	1.39417	0.697087	+	0.716986i	$0.254479\pi$
$338$	12.7996	0.696206
$339$	−7.92104	−0.430212
$340$	−0.906866	−0.0491817
$341$	−28.6205	−1.54988
$342$	3.76873	0.203790
$343$	5.31566	0.287019
$344$	1.17764	0.0634942
$345$	−11.6113	−0.625130
$346$	−7.12870	−0.383242
$347$	−15.3922	−0.826295	−0.413148	−	0.910664i	$-0.635571\pi$
$347$	−15.3922	−0.826295	−0.413148	+	0.910664i	$0.635571\pi$
$348$	17.1740	0.920625
$349$	−3.39382	−0.181667	−0.0908334	−	0.995866i	$-0.528953\pi$
$349$	−3.39382	−0.181667	−0.0908334	+	0.995866i	$0.528953\pi$
$350$	17.0295	0.910267
$351$	−1.80888	−0.0965506
$352$	−4.55361	−0.242708
$353$	−5.97767	−0.318159	−0.159080	−	0.987266i	$-0.550853\pi$
$353$	−5.97767	−0.318159	−0.159080	+	0.987266i	$0.550853\pi$
$354$	8.46702	0.450017
$355$	11.3387	0.601793
$356$	−14.2609	−0.755826
$357$	8.75665	0.463451
$358$	16.8052	0.888184
$359$	30.7308	1.62191	0.810954	−	0.585110i	$-0.198949\pi$
$359$	30.7308	1.62191	0.810954	+	0.585110i	$0.198949\pi$
$360$	−0.786876	−0.0414720
$361$	−3.99024	−0.210013
$362$	5.51085	0.289644
$363$	−19.4043	−1.01846
$364$	−1.75430	−0.0919504
$365$	−7.39930	−0.387297
$366$	15.6613	0.818629
$367$	−13.2224	−0.690202	−0.345101	−	0.938566i	$-0.612155\pi$
$367$	−13.2224	−0.690202	−0.345101	+	0.938566i	$0.612155\pi$
$368$	7.20171	0.375415
$369$	1.95299	0.101669
$370$	−6.99722	−0.363768
$371$	−10.8426	−0.562919
$372$	12.5276	0.649525
$373$	−19.9361	−1.03225	−0.516126	−	0.856513i	$-0.672626\pi$
$373$	−19.9361	−1.03225	−0.516126	+	0.856513i	$0.672626\pi$
$374$	5.10507	0.263977
$375$	15.0680	0.778106
$376$	11.1578	0.575419
$377$	3.85731	0.198661
$378$	−15.8342	−0.814423
$379$	−26.5242	−1.36246	−0.681229	−	0.732071i	$-0.738554\pi$
$379$	−26.5242	−1.36246	−0.681229	+	0.732071i	$0.738554\pi$
$380$	−3.13389	−0.160765
$381$	−24.1605	−1.23778
$382$	13.3735	0.684245
$383$	16.3297	0.834409	0.417204	−	0.908813i	$-0.363010\pi$
$383$	16.3297	0.834409	0.417204	+	0.908813i	$0.363010\pi$
$384$	1.99318	0.101714
$385$	14.4344	0.735646
$386$	−12.2460	−0.623306
$387$	−1.14557	−0.0582326
$388$	8.91589	0.452636
$389$	37.6965	1.91129	0.955644	−	0.294525i	$-0.0951616\pi$
$389$	37.6965	1.91129	0.955644	+	0.294525i	$0.0951616\pi$
$390$	−0.721776	−0.0365485
$391$	−8.07386	−0.408313
$392$	−8.35647	−0.422066
$393$	−35.7849	−1.80511
$394$	−4.12568	−0.207849
$395$	11.4889	0.578069
$396$	4.42960	0.222596
$397$	−13.2921	−0.667112	−0.333556	−	0.942730i	$-0.608249\pi$
$397$	−13.2921	−0.667112	−0.333556	+	0.942730i	$0.608249\pi$
$398$	−11.0244	−0.552602
$399$	30.2607	1.51493
$400$	−4.34567	−0.217284
$401$	6.63396	0.331284	0.165642	−	0.986186i	$-0.447030\pi$
$401$	6.63396	0.331284	0.165642	+	0.986186i	$0.447030\pi$
$402$	20.9478	1.04478
$403$	2.81371	0.140161
$404$	14.6617	0.729447
$405$	−8.87533	−0.441019
$406$	33.7654	1.67575
$407$	39.3898	1.95248
$408$	−2.23456	−0.110627
$409$	21.0900	1.04283	0.521416	−	0.853303i	$-0.325404\pi$
$409$	21.0900	1.04283	0.521416	+	0.853303i	$0.325404\pi$
$410$	−1.62401	−0.0802043
$411$	7.21668	0.355972
$412$	−9.25042	−0.455736
$413$	16.6468	0.819133
$414$	−7.00558	−0.344306
$415$	11.9710	0.587636
$416$	0.447670	0.0219488
$417$	−36.2310	−1.77424
$418$	17.6418	0.862888
$419$	−1.77207	−0.0865715	−0.0432857	−	0.999063i	$-0.513783\pi$
$419$	−1.77207	−0.0865715	−0.0432857	+	0.999063i	$0.513783\pi$
$420$	−6.31815	−0.308294
$421$	10.0345	0.489052	0.244526	−	0.969643i	$-0.421368\pi$
$421$	10.0345	0.489052	0.244526	+	0.969643i	$0.421368\pi$
$422$	15.9680	0.777309
$423$	−10.8539	−0.527735
$424$	2.76686	0.134371
$425$	4.87195	0.236324
$426$	27.9390	1.35365
$427$	30.7912	1.49009
$428$	−17.7101	−0.856051
$429$	4.06313	0.196170
$430$	0.952600	0.0459385
$431$	24.5974	1.18482	0.592408	−	0.805638i	$-0.298177\pi$
$431$	24.5974	1.18482	0.592408	+	0.805638i	$0.298177\pi$
$432$	4.04064	0.194405
$433$	−5.36157	−0.257661	−0.128830	−	0.991667i	$-0.541122\pi$
$433$	−5.36157	−0.257661	−0.128830	+	0.991667i	$0.541122\pi$
$434$	24.6301	1.18228
$435$	13.8922	0.666078
$436$	−12.9827	−0.621756
$437$	−27.9012	−1.33469
$438$	−18.2322	−0.871170
$439$	−12.8922	−0.615309	−0.307654	−	0.951498i	$-0.599544\pi$
$439$	−12.8922	−0.615309	−0.307654	+	0.951498i	$0.599544\pi$
$440$	−3.68344	−0.175601
$441$	8.12890	0.387090
$442$	−0.501885	−0.0238722
$443$	−11.5644	−0.549442	−0.274721	−	0.961524i	$-0.588586\pi$
$443$	−11.5644	−0.549442	−0.274721	+	0.961524i	$0.588586\pi$
$444$	−17.2415	−0.818245
$445$	−11.5357	−0.546845
$446$	18.0502	0.854700
$447$	−19.6313	−0.928528
$448$	3.91873	0.185143
$449$	27.9213	1.31769	0.658844	−	0.752280i	$-0.271046\pi$
$449$	27.9213	1.31769	0.658844	+	0.752280i	$0.271046\pi$
$450$	4.22732	0.199278
$451$	9.14214	0.430487
$452$	3.97407	0.186925
$453$	−23.4967	−1.10397
$454$	−0.216959	−0.0101824
$455$	−1.41906	−0.0665267
$456$	−7.72206	−0.361619
$457$	−15.2267	−0.712276	−0.356138	−	0.934433i	$-0.615907\pi$
$457$	−15.2267	−0.712276	−0.356138	+	0.934433i	$0.615907\pi$
$458$	21.0060	0.981547
$459$	−4.52998	−0.211441
$460$	5.82550	0.271615
$461$	13.0874	0.609539	0.304770	−	0.952426i	$-0.401421\pi$
$461$	13.0874	0.609539	0.304770	+	0.952426i	$0.401421\pi$
$462$	35.5671	1.65473
$463$	19.6828	0.914738	0.457369	−	0.889277i	$-0.348792\pi$
$463$	19.6828	0.914738	0.457369	+	0.889277i	$0.348792\pi$
$464$	−8.61640	−0.400006
$465$	10.1336	0.469936
$466$	−27.3248	−1.26580
$467$	37.4570	1.73330	0.866650	−	0.498916i	$-0.166268\pi$
$467$	37.4570	1.73330	0.866650	+	0.498916i	$0.166268\pi$
$468$	−0.435479	−0.0201300
$469$	41.1849	1.90174
$470$	9.02558	0.416319
$471$	−6.81750	−0.314134
$472$	−4.24799	−0.195530
$473$	−5.36252	−0.246569
$474$	28.3092	1.30028
$475$	16.8362	0.772497
$476$	−4.39331	−0.201367
$477$	−2.69151	−0.123236
$478$	11.6080	0.530935
$479$	26.0191	1.18884	0.594421	−	0.804154i	$-0.297381\pi$
$479$	26.0191	1.18884	0.594421	+	0.804154i	$0.297381\pi$
$480$	1.61229	0.0735908
$481$	−3.87246	−0.176569
$482$	−14.3389	−0.653117
$483$	−56.2507	−2.55950
$484$	9.73536	0.442517
$485$	7.21211	0.327485
$486$	−9.74730	−0.442146
$487$	−25.7164	−1.16532	−0.582660	−	0.812716i	$-0.697988\pi$
$487$	−25.7164	−1.16532	−0.582660	+	0.812716i	$0.697988\pi$
$488$	−7.85744	−0.355690
$489$	−29.2675	−1.32352
$490$	−6.75959	−0.305367
$491$	−16.2926	−0.735277	−0.367638	−	0.929969i	$-0.619834\pi$
$491$	−16.2926	−0.735277	−0.367638	+	0.929969i	$0.619834\pi$
$492$	−4.00165	−0.180408
$493$	9.65988	0.435059
$494$	−1.73438	−0.0780336
$495$	3.58312	0.161049
$496$	−6.28522	−0.282215
$497$	54.9300	2.46395
$498$	29.4972	1.32180
$499$	−12.9830	−0.581198	−0.290599	−	0.956845i	$-0.593855\pi$
$499$	−12.9830	−0.581198	−0.290599	+	0.956845i	$0.593855\pi$
$500$	−7.55976	−0.338083
$501$	−18.9750	−0.847740
$502$	−6.02416	−0.268871
$503$	21.0737	0.939630	0.469815	−	0.882765i	$-0.344321\pi$
$503$	21.0737	0.939630	0.469815	+	0.882765i	$0.344321\pi$
$504$	−3.81201	−0.169801
$505$	11.8599	0.527760
$506$	−32.7938	−1.45786
$507$	25.5119	1.13302
$508$	12.1216	0.537809
$509$	−19.4810	−0.863481	−0.431741	−	0.901998i	$-0.642100\pi$
$509$	−19.4810	−0.863481	−0.431741	+	0.901998i	$0.642100\pi$
$510$	−1.80755	−0.0800396
$511$	−35.8459	−1.58573
$512$	−1.00000	−0.0441942
$513$	−15.6544	−0.691160
$514$	15.8004	0.696928
$515$	−7.48272	−0.329728
$516$	2.34725	0.103332
$517$	−50.8082	−2.23454
$518$	−33.8980	−1.48939
$519$	−14.2088	−0.623697
$520$	0.362123	0.0158801
$521$	28.0584	1.22926	0.614631	−	0.788814i	$-0.289305\pi$
$521$	28.0584	1.22926	0.614631	+	0.788814i	$0.289305\pi$
$522$	8.38174	0.366859
$523$	−7.29283	−0.318893	−0.159447	−	0.987207i	$-0.550971\pi$
$523$	−7.29283	−0.318893	−0.159447	+	0.987207i	$0.550971\pi$
$524$	17.9537	0.784310
$525$	33.9429	1.48139
$526$	−29.2570	−1.27567
$527$	7.04639	0.306945
$528$	−9.07616	−0.394989
$529$	28.8646	1.25498
$530$	2.23813	0.0972181
$531$	4.13231	0.179327
$532$	−15.1821	−0.658229
$533$	−0.898774	−0.0389302
$534$	−28.4245	−1.23005
$535$	−14.3258	−0.619359
$536$	−10.5097	−0.453952
$537$	33.4959	1.44545
$538$	23.4258	1.00996
$539$	38.0521	1.63902
$540$	3.26850	0.140654
$541$	37.7120	1.62137	0.810683	−	0.585485i	$-0.199096\pi$
$541$	37.7120	1.62137	0.810683	+	0.585485i	$0.199096\pi$
$542$	4.55804	0.195785
$543$	10.9841	0.471373
$544$	1.12110	0.0480669
$545$	−10.5017	−0.449845
$546$	−3.49664	−0.149642
$547$	8.58915	0.367246	0.183623	−	0.982997i	$-0.441217\pi$
$547$	8.58915	0.367246	0.183623	+	0.982997i	$0.441217\pi$
$548$	−3.62069	−0.154668
$549$	7.64345	0.326215
$550$	19.7885	0.843784
$551$	33.3820	1.42212
$552$	14.3543	0.610960
$553$	55.6578	2.36681
$554$	11.4738	0.487476
$555$	−13.9467	−0.592006
$556$	18.1775	0.770897
$557$	15.1279	0.640991	0.320495	−	0.947250i	$-0.396151\pi$
$557$	15.1279	0.640991	0.320495	+	0.947250i	$0.396151\pi$
$558$	6.11405	0.258829
$559$	0.527195	0.0222980
$560$	3.16988	0.133952
$561$	10.1753	0.429602
$562$	−20.7074	−0.873487
$563$	−20.5347	−0.865435	−0.432718	−	0.901530i	$-0.642445\pi$
$563$	−20.5347	−0.865435	−0.432718	+	0.901530i	$0.642445\pi$
$564$	22.2395	0.936450
$565$	3.21465	0.135241
$566$	−9.32672	−0.392031
$567$	−42.9964	−1.80568
$568$	−14.0173	−0.588152
$569$	17.4170	0.730159	0.365079	−	0.930976i	$-0.381042\pi$
$569$	17.4170	0.730159	0.365079	+	0.930976i	$0.381042\pi$
$570$	−6.24642	−0.261634
$571$	8.26055	0.345693	0.172847	−	0.984949i	$-0.444703\pi$
$571$	8.26055	0.345693	0.172847	+	0.984949i	$0.444703\pi$
$572$	−2.03852	−0.0852347
$573$	26.6557	1.11356
$574$	−7.86752	−0.328384
$575$	−31.2963	−1.30515
$576$	0.972766	0.0405319
$577$	−2.22554	−0.0926503	−0.0463251	−	0.998926i	$-0.514751\pi$
$577$	−2.22554	−0.0926503	−0.0463251	+	0.998926i	$0.514751\pi$
$578$	15.7431	0.654828
$579$	−24.4085	−1.01438
$580$	−6.96985	−0.289407
$581$	57.9936	2.40598
$582$	17.7710	0.736630
$583$	−12.5992	−0.521806
$584$	9.14731	0.378518
$585$	−0.352261	−0.0145642
$586$	17.5635	0.725542
$587$	7.70603	0.318062	0.159031	−	0.987274i	$-0.449163\pi$
$587$	7.70603	0.318062	0.159031	+	0.987274i	$0.449163\pi$
$588$	−16.6560	−0.686880
$589$	24.3505	1.00334
$590$	−3.43622	−0.141467
$591$	−8.22323	−0.338258
$592$	8.65024	0.355523
$593$	−25.2410	−1.03652	−0.518261	−	0.855222i	$-0.673421\pi$
$593$	−25.2410	−1.03652	−0.518261	+	0.855222i	$0.673421\pi$
$594$	−18.3995	−0.754941
$595$	−3.55377	−0.145690
$596$	9.84923	0.403440
$597$	−21.9736	−0.899318
$598$	3.22399	0.131839
$599$	23.5055	0.960410	0.480205	−	0.877156i	$-0.340562\pi$
$599$	23.5055	0.960410	0.480205	+	0.877156i	$0.340562\pi$
$600$	−8.66171	−0.353613
$601$	23.1270	0.943369	0.471685	−	0.881767i	$-0.343646\pi$
$601$	23.1270	0.943369	0.471685	+	0.881767i	$0.343646\pi$
$602$	4.61486	0.188088
$603$	10.2235	0.416334
$604$	11.7885	0.479669
$605$	7.87499	0.320164
$606$	29.2234	1.18712
$607$	−19.7447	−0.801412	−0.400706	−	0.916207i	$-0.631235\pi$
$607$	−19.7447	−0.801412	−0.400706	+	0.916207i	$0.631235\pi$
$608$	3.87424	0.157121
$609$	67.3005	2.72715
$610$	−6.35592	−0.257344
$611$	4.99501	0.202076
$612$	−1.09057	−0.0440838
$613$	−27.5116	−1.11118	−0.555591	−	0.831456i	$-0.687508\pi$
$613$	−27.5116	−1.11118	−0.555591	+	0.831456i	$0.687508\pi$
$614$	7.75364	0.312911
$615$	−3.23695	−0.130527
$616$	−17.8444	−0.718971
$617$	34.6047	1.39313	0.696567	−	0.717492i	$-0.254710\pi$
$617$	34.6047	1.39313	0.696567	+	0.717492i	$0.254710\pi$
$618$	−18.4378	−0.741676
$619$	14.3040	0.574925	0.287463	−	0.957792i	$-0.407188\pi$
$619$	14.3040	0.574925	0.287463	+	0.957792i	$0.407188\pi$
$620$	−5.08415	−0.204184
$621$	29.0995	1.16772
$622$	−5.17827	−0.207630
$623$	−55.8846	−2.23897
$624$	0.892288	0.0357201
$625$	15.6132	0.624529
$626$	−19.7705	−0.790188
$627$	35.1633	1.40429
$628$	3.42041	0.136489
$629$	−9.69782	−0.386677
$630$	−3.08356	−0.122852
$631$	−11.4153	−0.454434	−0.227217	−	0.973844i	$-0.572963\pi$
$631$	−11.4153	−0.454434	−0.227217	+	0.973844i	$0.572963\pi$
$632$	−14.2030	−0.564965
$633$	31.8270	1.26501
$634$	−32.0722	−1.27375
$635$	9.80522	0.389108
$636$	5.51485	0.218678
$637$	−3.74095	−0.148222
$638$	39.2357	1.55336
$639$	13.6355	0.539414
$640$	−0.808905	−0.0319748
$641$	−9.16782	−0.362107	−0.181054	−	0.983473i	$-0.557951\pi$
$641$	−9.16782	−0.362107	−0.181054	+	0.983473i	$0.557951\pi$
$642$	−35.2995	−1.39316
$643$	26.0887	1.02884	0.514419	−	0.857539i	$-0.328008\pi$
$643$	26.0887	1.02884	0.514419	+	0.857539i	$0.328008\pi$
$644$	28.2216	1.11209
$645$	1.89870	0.0747614
$646$	−4.34343	−0.170890
$647$	−21.1913	−0.833118	−0.416559	−	0.909109i	$-0.636764\pi$
$647$	−21.1913	−0.833118	−0.416559	+	0.909109i	$0.636764\pi$
$648$	10.9720	0.431022
$649$	19.3437	0.759307
$650$	−1.94543	−0.0763060
$651$	49.0923	1.92408
$652$	14.6838	0.575063
$653$	15.4328	0.603931	0.301965	−	0.953319i	$-0.402357\pi$
$653$	15.4328	0.603931	0.301965	+	0.953319i	$0.402357\pi$
$654$	−25.8768	−1.01186
$655$	14.5228	0.567454
$656$	2.00767	0.0783863
$657$	−8.89819	−0.347152
$658$	43.7244	1.70455
$659$	36.8050	1.43372	0.716859	−	0.697218i	$-0.245579\pi$
$659$	36.8050	1.43372	0.716859	+	0.697218i	$0.245579\pi$
$660$	−7.34176	−0.285777
$661$	17.9037	0.696372	0.348186	−	0.937426i	$-0.386798\pi$
$661$	17.9037	0.696372	0.348186	+	0.937426i	$0.386798\pi$
$662$	16.8204	0.653743
$663$	−1.00035	−0.0388503
$664$	−14.7991	−0.574315
$665$	−12.2809	−0.476233
$666$	−8.41466	−0.326062
$667$	−62.0528	−2.40269
$668$	9.51995	0.368338
$669$	35.9772	1.39096
$670$	−8.50139	−0.328437
$671$	35.7797	1.38126
$672$	7.81074	0.301306
$673$	14.5543	0.561027	0.280514	−	0.959850i	$-0.409495\pi$
$673$	14.5543	0.561027	0.280514	+	0.959850i	$0.409495\pi$
$674$	−25.5937	−0.985831
$675$	−17.5593	−0.675858
$676$	−12.7996	−0.492292
$677$	−32.2171	−1.23820	−0.619101	−	0.785311i	$-0.712503\pi$
$677$	−32.2171	−1.23820	−0.619101	+	0.785311i	$0.712503\pi$
$678$	7.92104	0.304206
$679$	34.9390	1.34084
$680$	0.906866	0.0347767
$681$	−0.432438	−0.0165711
$682$	28.6205	1.09593
$683$	17.0946	0.654107	0.327054	−	0.945006i	$-0.393944\pi$
$683$	17.0946	0.654107	0.327054	+	0.945006i	$0.393944\pi$
$684$	−3.76873	−0.144101
$685$	−2.92879	−0.111903
$686$	−5.31566	−0.202953
$687$	41.8688	1.59739
$688$	−1.17764	−0.0448972
$689$	1.23864	0.0471885
$690$	11.6113	0.442034
$691$	−33.4829	−1.27375	−0.636874	−	0.770968i	$-0.719773\pi$
$691$	−33.4829	−1.27375	−0.636874	+	0.770968i	$0.719773\pi$
$692$	7.12870	0.270993
$693$	17.3584	0.659392
$694$	15.3922	0.584279
$695$	14.7039	0.557749
$696$	−17.1740	−0.650980
$697$	−2.25081	−0.0852553
$698$	3.39382	0.128458
$699$	−54.4633	−2.05999
$700$	−17.0295	−0.643656
$701$	6.55191	0.247462	0.123731	−	0.992316i	$-0.460514\pi$
$701$	6.55191	0.247462	0.123731	+	0.992316i	$0.460514\pi$
$702$	1.80888	0.0682716
$703$	−33.5131	−1.26397
$704$	4.55361	0.171621
$705$	17.9896	0.677528
$706$	5.97767	0.224972
$707$	57.4553	2.16083
$708$	−8.46702	−0.318210
$709$	10.5171	0.394977	0.197489	−	0.980305i	$-0.436721\pi$
$709$	10.5171	0.394977	0.197489	+	0.980305i	$0.436721\pi$
$710$	−11.3387	−0.425532
$711$	13.8162	0.518148
$712$	14.2609	0.534450
$713$	−45.2644	−1.69516
$714$	−8.75665	−0.327709
$715$	−1.64897	−0.0616678
$716$	−16.8052	−0.628041
$717$	23.1367	0.864057
$718$	−30.7308	−1.14686
$719$	−1.13450	−0.0423097	−0.0211548	−	0.999776i	$-0.506734\pi$
$719$	−1.13450	−0.0423097	−0.0211548	+	0.999776i	$0.506734\pi$
$720$	0.786876	0.0293251
$721$	−36.2500	−1.35002
$722$	3.99024	0.148502
$723$	−28.5799	−1.06290
$724$	−5.51085	−0.204809
$725$	37.4440	1.39064
$726$	19.4043	0.720162
$727$	−38.4865	−1.42739	−0.713693	−	0.700459i	$-0.752979\pi$
$727$	−38.4865	−1.42739	−0.713693	+	0.700459i	$0.752979\pi$
$728$	1.75430	0.0650187
$729$	13.4880	0.499554
$730$	7.39930	0.273861
$731$	1.32026	0.0488315
$732$	−15.6613	−0.578858
$733$	−30.6684	−1.13276	−0.566381	−	0.824143i	$-0.691657\pi$
$733$	−30.6684	−1.13276	−0.566381	+	0.824143i	$0.691657\pi$
$734$	13.2224	0.488046
$735$	−13.4731	−0.496962
$736$	−7.20171	−0.265459
$737$	47.8573	1.76285
$738$	−1.95299	−0.0718907
$739$	−22.8297	−0.839804	−0.419902	−	0.907569i	$-0.637936\pi$
$739$	−22.8297	−0.839804	−0.419902	+	0.907569i	$0.637936\pi$
$740$	6.99722	0.257223
$741$	−3.45694	−0.126994
$742$	10.8426	0.398044
$743$	−12.3341	−0.452495	−0.226248	−	0.974070i	$-0.572646\pi$
$743$	−12.3341	−0.452495	−0.226248	+	0.974070i	$0.572646\pi$
$744$	−12.5276	−0.459283
$745$	7.96709	0.291892
$746$	19.9361	0.729912
$747$	14.3960	0.526724
$748$	−5.10507	−0.186660
$749$	−69.4012	−2.53587
$750$	−15.0680	−0.550204
$751$	12.2706	0.447760	0.223880	−	0.974617i	$-0.428128\pi$
$751$	12.2706	0.447760	0.223880	+	0.974617i	$0.428128\pi$
$752$	−11.1578	−0.406882
$753$	−12.0072	−0.437568
$754$	−3.85731	−0.140475
$755$	9.53580	0.347043
$756$	15.8342	0.575884
$757$	30.7669	1.11824	0.559122	−	0.829086i	$-0.311138\pi$
$757$	30.7669	1.11824	0.559122	+	0.829086i	$0.311138\pi$
$758$	26.5242	0.963403
$759$	−65.3639	−2.37256
$760$	3.13389	0.113678
$761$	49.0955	1.77971	0.889856	−	0.456242i	$-0.150805\pi$
$761$	49.0955	1.77971	0.889856	+	0.456242i	$0.150805\pi$
$762$	24.1605	0.875243
$763$	−50.8756	−1.84182
$764$	−13.3735	−0.483835
$765$	−0.882169	−0.0318949
$766$	−16.3297	−0.590016
$767$	−1.90170	−0.0686665
$768$	−1.99318	−0.0719227
$769$	31.7527	1.14503	0.572516	−	0.819894i	$-0.305968\pi$
$769$	31.7527	1.14503	0.572516	+	0.819894i	$0.305968\pi$
$770$	−14.4344	−0.520180
$771$	31.4931	1.13420
$772$	12.2460	0.440744
$773$	−6.38294	−0.229578	−0.114789	−	0.993390i	$-0.536619\pi$
$773$	−6.38294	−0.229578	−0.114789	+	0.993390i	$0.536619\pi$
$774$	1.14557	0.0411767
$775$	27.3135	0.981131
$776$	−8.91589	−0.320062
$777$	−67.5648	−2.42387
$778$	−37.6965	−1.35148
$779$	−7.77820	−0.278683
$780$	0.721776	0.0258437
$781$	63.8293	2.28399
$782$	8.07386	0.288721
$783$	−34.8158	−1.24421
$784$	8.35647	0.298446
$785$	2.76679	0.0987510
$786$	35.7849	1.27641
$787$	−48.3995	−1.72526	−0.862628	−	0.505838i	$-0.831183\pi$
$787$	−48.3995	−1.72526	−0.862628	+	0.505838i	$0.831183\pi$
$788$	4.12568	0.146971
$789$	−58.3145	−2.07605
$790$	−11.4889	−0.408756
$791$	15.5733	0.553724
$792$	−4.42960	−0.157399
$793$	−3.51754	−0.124912
$794$	13.2921	0.471720
$795$	4.46099	0.158215
$796$	11.0244	0.390748
$797$	−35.6066	−1.26125	−0.630626	−	0.776087i	$-0.717202\pi$
$797$	−35.6066	−1.26125	−0.630626	+	0.776087i	$0.717202\pi$
$798$	−30.2607	−1.07122
$799$	12.5090	0.442538
$800$	4.34567	0.153643
$801$	−13.8725	−0.490161
$802$	−6.63396	−0.234253
$803$	−41.6533	−1.46991
$804$	−20.9478	−0.738772
$805$	22.8286	0.804602
$806$	−2.81371	−0.0991087
$807$	46.6918	1.64363
$808$	−14.6617	−0.515797
$809$	17.6559	0.620748	0.310374	−	0.950614i	$-0.399546\pi$
$809$	17.6559	0.620748	0.310374	+	0.950614i	$0.399546\pi$
$810$	8.87533	0.311847
$811$	−40.3969	−1.41853	−0.709263	−	0.704944i	$-0.750972\pi$
$811$	−40.3969	−1.41853	−0.709263	+	0.704944i	$0.750972\pi$
$812$	−33.7654	−1.18493
$813$	9.08500	0.318625
$814$	−39.3898	−1.38061
$815$	11.8778	0.416062
$816$	2.23456	0.0782253
$817$	4.56247	0.159621
$818$	−21.0900	−0.737393
$819$	−1.70652	−0.0596308
$820$	1.62401	0.0567130
$821$	54.5361	1.90332	0.951661	−	0.307149i	$-0.0993751\pi$
$821$	54.5361	1.90332	0.951661	+	0.307149i	$0.0993751\pi$
$822$	−7.21668	−0.251711
$823$	−16.4515	−0.573464	−0.286732	−	0.958011i	$-0.592569\pi$
$823$	−16.4515	−0.573464	−0.286732	+	0.958011i	$0.592569\pi$
$824$	9.25042	0.322254
$825$	39.4420	1.37320
$826$	−16.6468	−0.579215
$827$	−11.9857	−0.416783	−0.208392	−	0.978045i	$-0.566823\pi$
$827$	−11.9857	−0.416783	−0.208392	+	0.978045i	$0.566823\pi$
$828$	7.00558	0.243461
$829$	−33.4216	−1.16078	−0.580390	−	0.814339i	$-0.697100\pi$
$829$	−33.4216	−1.16078	−0.580390	+	0.814339i	$0.697100\pi$
$830$	−11.9710	−0.415521
$831$	22.8694	0.793331
$832$	−0.447670	−0.0155202
$833$	−9.36847	−0.324598
$834$	36.2310	1.25458
$835$	7.70074	0.266495
$836$	−17.6418	−0.610154
$837$	−25.3963	−0.877826
$838$	1.77207	0.0612153
$839$	20.4398	0.705662	0.352831	−	0.935687i	$-0.385219\pi$
$839$	20.4398	0.705662	0.352831	+	0.935687i	$0.385219\pi$
$840$	6.31815	0.217997
$841$	45.2423	1.56008
$842$	−10.0345	−0.345812
$843$	−41.2735	−1.42153
$844$	−15.9680	−0.549640
$845$	−10.3537	−0.356177
$846$	10.8539	0.373165
$847$	38.1503	1.31086
$848$	−2.76686	−0.0950144
$849$	−18.5898	−0.638001
$850$	−4.87195	−0.167106
$851$	62.2965	2.13550
$852$	−27.9390	−0.957174
$853$	19.4420	0.665681	0.332841	−	0.942983i	$-0.391993\pi$
$853$	19.4420	0.665681	0.332841	+	0.942983i	$0.391993\pi$
$854$	−30.7912	−1.05365
$855$	−3.04855	−0.104258
$856$	17.7101	0.605319
$857$	−7.69514	−0.262861	−0.131431	−	0.991325i	$-0.541957\pi$
$857$	−7.69514	−0.262861	−0.131431	+	0.991325i	$0.541957\pi$
$858$	−4.06313	−0.138713
$859$	27.1939	0.927843	0.463922	−	0.885876i	$-0.346442\pi$
$859$	27.1939	0.927843	0.463922	+	0.885876i	$0.346442\pi$
$860$	−0.952600	−0.0324834
$861$	−15.6814	−0.534420
$862$	−24.5974	−0.837791
$863$	15.7396	0.535783	0.267891	−	0.963449i	$-0.413673\pi$
$863$	15.7396	0.535783	0.267891	+	0.963449i	$0.413673\pi$
$864$	−4.04064	−0.137465
$865$	5.76645	0.196065
$866$	5.36157	0.182194
$867$	31.3789	1.06568
$868$	−24.6301	−0.836001
$869$	64.6750	2.19395
$870$	−13.8922	−0.470988
$871$	−4.70490	−0.159420
$872$	12.9827	0.439648
$873$	8.67307	0.293539
$874$	27.9012	0.943771
$875$	−29.6247	−1.00150
$876$	18.2322	0.616010
$877$	2.32874	0.0786361	0.0393181	−	0.999227i	$-0.487481\pi$
$877$	2.32874	0.0786361	0.0393181	+	0.999227i	$0.487481\pi$
$878$	12.8922	0.435089
$879$	35.0072	1.18076
$880$	3.68344	0.124169
$881$	31.0056	1.04461	0.522303	−	0.852760i	$-0.325073\pi$
$881$	31.0056	1.04461	0.522303	+	0.852760i	$0.325073\pi$
$882$	−8.12890	−0.273714
$883$	−47.8694	−1.61093	−0.805467	−	0.592641i	$-0.798085\pi$
$883$	−47.8694	−1.61093	−0.805467	+	0.592641i	$0.798085\pi$
$884$	0.501885	0.0168802
$885$	−6.84901	−0.230227
$886$	11.5644	0.388514
$887$	35.6877	1.19828	0.599138	−	0.800646i	$-0.295510\pi$
$887$	35.6877	1.19828	0.599138	+	0.800646i	$0.295510\pi$
$888$	17.2415	0.578586
$889$	47.5013	1.59314
$890$	11.5357	0.386678
$891$	−49.9623	−1.67380
$892$	−18.0502	−0.604364
$893$	43.2279	1.44657
$894$	19.6313	0.656568
$895$	−13.5938	−0.454392
$896$	−3.91873	−0.130916
$897$	6.42600	0.214558
$898$	−27.9213	−0.931746
$899$	54.1560	1.80620
$900$	−4.22732	−0.140911
$901$	3.10194	0.103341
$902$	−9.14214	−0.304400
$903$	9.19825	0.306099
$904$	−3.97407	−0.132176
$905$	−4.45775	−0.148181
$906$	23.4967	0.780624
$907$	−22.6345	−0.751566	−0.375783	−	0.926708i	$-0.622626\pi$
$907$	−22.6345	−0.751566	−0.375783	+	0.926708i	$0.622626\pi$
$908$	0.216959	0.00720003
$909$	14.2624	0.473055
$910$	1.41906	0.0470415
$911$	−9.88790	−0.327601	−0.163800	−	0.986494i	$-0.552375\pi$
$911$	−9.88790	−0.327601	−0.163800	+	0.986494i	$0.552375\pi$
$912$	7.72206	0.255703
$913$	67.3892	2.23026
$914$	15.2267	0.503655
$915$	−12.6685	−0.418808
$916$	−21.0060	−0.694058
$917$	70.3557	2.32335
$918$	4.52998	0.149512
$919$	−50.6978	−1.67236	−0.836182	−	0.548452i	$-0.815217\pi$
$919$	−50.6978	−1.67236	−0.836182	+	0.548452i	$0.815217\pi$
$920$	−5.82550	−0.192061
$921$	15.4544	0.509240
$922$	−13.0874	−0.431009
$923$	−6.27513	−0.206548
$924$	−35.5671	−1.17007
$925$	−37.5911	−1.23599
$926$	−19.6828	−0.646817
$927$	−8.99850	−0.295550
$928$	8.61640	0.282847
$929$	54.2744	1.78069	0.890343	−	0.455291i	$-0.150465\pi$
$929$	54.2744	1.78069	0.890343	+	0.455291i	$0.150465\pi$
$930$	−10.1336	−0.332295
$931$	−32.3750	−1.06105
$932$	27.3248	0.895054
$933$	−10.3212	−0.337902
$934$	−37.4570	−1.22563
$935$	−4.12952	−0.135050
$936$	0.435479	0.0142341
$937$	−49.0959	−1.60389	−0.801947	−	0.597395i	$-0.796203\pi$
$937$	−49.0959	−1.60389	−0.801947	+	0.597395i	$0.796203\pi$
$938$	−41.1849	−1.34473
$939$	−39.4061	−1.28597
$940$	−9.02558	−0.294382
$941$	−2.29871	−0.0749358	−0.0374679	−	0.999298i	$-0.511929\pi$
$941$	−2.29871	−0.0749358	−0.0374679	+	0.999298i	$0.511929\pi$
$942$	6.81750	0.222126
$943$	14.4587	0.470839
$944$	4.24799	0.138260
$945$	12.8084	0.416656
$946$	5.36252	0.174351
$947$	48.1285	1.56396	0.781982	−	0.623301i	$-0.214209\pi$
$947$	48.1285	1.56396	0.781982	+	0.623301i	$0.214209\pi$
$948$	−28.3092	−0.919439
$949$	4.09498	0.132929
$950$	−16.8362	−0.546238
$951$	−63.9257	−2.07293
$952$	4.39331	0.142388
$953$	22.3781	0.724897	0.362449	−	0.932004i	$-0.381941\pi$
$953$	22.3781	0.724897	0.362449	+	0.932004i	$0.381941\pi$
$954$	2.69151	0.0871409
$955$	−10.8179	−0.350058
$956$	−11.6080	−0.375428
$957$	78.2038	2.52797
$958$	−26.0191	−0.840638
$959$	−14.1885	−0.458171
$960$	−1.61229	−0.0520365
$961$	8.50404	0.274324
$962$	3.87246	0.124853
$963$	−17.2278	−0.555158
$964$	14.3389	0.461823
$965$	9.90586	0.318881
$966$	56.2507	1.80984
$967$	−51.0968	−1.64316	−0.821582	−	0.570091i	$-0.806908\pi$
$967$	−51.0968	−1.64316	−0.821582	+	0.570091i	$0.806908\pi$
$968$	−9.73536	−0.312906
$969$	−8.65723	−0.278110
$970$	−7.21211	−0.231567
$971$	0.906946	0.0291053	0.0145526	−	0.999894i	$-0.495368\pi$
$971$	0.906946	0.0291053	0.0145526	+	0.999894i	$0.495368\pi$
$972$	9.74730	0.312645
$973$	71.2327	2.28362
$974$	25.7164	0.824005
$975$	−3.87759	−0.124182
$976$	7.85744	0.251510
$977$	−2.29775	−0.0735114	−0.0367557	−	0.999324i	$-0.511702\pi$
$977$	−2.29775	−0.0735114	−0.0367557	+	0.999324i	$0.511702\pi$
$978$	29.2675	0.935872
$979$	−64.9385	−2.07544
$980$	6.75959	0.215927
$981$	−12.6291	−0.403216
$982$	16.2926	0.519919
$983$	25.9695	0.828299	0.414149	−	0.910209i	$-0.364079\pi$
$983$	25.9695	0.828299	0.414149	+	0.910209i	$0.364079\pi$
$984$	4.00165	0.127568
$985$	3.33729	0.106335
$986$	−9.65988	−0.307633
$987$	87.1505	2.77403
$988$	1.73438	0.0551781
$989$	−8.48103	−0.269681
$990$	−3.58312	−0.113879
$991$	45.3293	1.43993	0.719966	−	0.694009i	$-0.244157\pi$
$991$	45.3293	1.43993	0.719966	+	0.694009i	$0.244157\pi$
$992$	6.28522	0.199556
$993$	33.5261	1.06392
$994$	−54.9300	−1.74227
$995$	8.91767	0.282709
$996$	−29.4972	−0.934655
$997$	16.2359	0.514196	0.257098	−	0.966385i	$-0.417234\pi$
$997$	16.2359	0.514196	0.257098	+	0.966385i	$0.417234\pi$
$998$	12.9830	0.410969
$999$	34.9525	1.10585

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8014.2.a.e.1.20	✓	91

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8014.2.a.e.1.20	✓	91	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:	\( N \)	\(=\)	\( 8014 = 2 \cdot 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.99318 q^{3} +1.00000 q^{4} +0.808905 q^{5} +1.99318 q^{6} +3.91873 q^{7} -1.00000 q^{8} +0.972766 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.99318 q^{3} +1.00000 q^{4} +0.808905 q^{5} +1.99318 q^{6} +3.91873 q^{7} -1.00000 q^{8} +0.972766 q^{9} -0.808905 q^{10} +4.55361 q^{11} -1.99318 q^{12} -0.447670 q^{13} -3.91873 q^{14} -1.61229 q^{15} +1.00000 q^{16} -1.12110 q^{17} -0.972766 q^{18} -3.87424 q^{19} +0.808905 q^{20} -7.81074 q^{21} -4.55361 q^{22} +7.20171 q^{23} +1.99318 q^{24} -4.34567 q^{25} +0.447670 q^{26} +4.04064 q^{27} +3.91873 q^{28} -8.61640 q^{29} +1.61229 q^{30} -6.28522 q^{31} -1.00000 q^{32} -9.07616 q^{33} +1.12110 q^{34} +3.16988 q^{35} +0.972766 q^{36} +8.65024 q^{37} +3.87424 q^{38} +0.892288 q^{39} -0.808905 q^{40} +2.00767 q^{41} +7.81074 q^{42} -1.17764 q^{43} +4.55361 q^{44} +0.786876 q^{45} -7.20171 q^{46} -11.1578 q^{47} -1.99318 q^{48} +8.35647 q^{49} +4.34567 q^{50} +2.23456 q^{51} -0.447670 q^{52} -2.76686 q^{53} -4.04064 q^{54} +3.68344 q^{55} -3.91873 q^{56} +7.72206 q^{57} +8.61640 q^{58} +4.24799 q^{59} -1.61229 q^{60} +7.85744 q^{61} +6.28522 q^{62} +3.81201 q^{63} +1.00000 q^{64} -0.362123 q^{65} +9.07616 q^{66} +10.5097 q^{67} -1.12110 q^{68} -14.3543 q^{69} -3.16988 q^{70} +14.0173 q^{71} -0.972766 q^{72} -9.14731 q^{73} -8.65024 q^{74} +8.66171 q^{75} -3.87424 q^{76} +17.8444 q^{77} -0.892288 q^{78} +14.2030 q^{79} +0.808905 q^{80} -10.9720 q^{81} -2.00767 q^{82} +14.7991 q^{83} -7.81074 q^{84} -0.906866 q^{85} +1.17764 q^{86} +17.1740 q^{87} -4.55361 q^{88} -14.2609 q^{89} -0.786876 q^{90} -1.75430 q^{91} +7.20171 q^{92} +12.5276 q^{93} +11.1578 q^{94} -3.13389 q^{95} +1.99318 q^{96} +8.91589 q^{97} -8.35647 q^{98} +4.42960 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9}+O(q^{10}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9} - 22 q^{10} + 59 q^{11} - 2 q^{12} - 15 q^{13} + 14 q^{14} + 23 q^{15} + 91 q^{16} + 25 q^{17} - 123 q^{18} + 2 q^{19} + 22 q^{20} + 20 q^{21} - 59 q^{22} + 36 q^{23} + 2 q^{24} + 121 q^{25} + 15 q^{26} - 8 q^{27} - 14 q^{28} + 71 q^{29} - 23 q^{30} + 13 q^{31} - 91 q^{32} + 24 q^{33} - 25 q^{34} + 27 q^{35} + 123 q^{36} + 5 q^{37} - 2 q^{38} + 48 q^{39} - 22 q^{40} + 77 q^{41} - 20 q^{42} - 36 q^{43} + 59 q^{44} + 62 q^{45} - 36 q^{46} + 41 q^{47} - 2 q^{48} + 137 q^{49} - 121 q^{50} + 13 q^{51} - 15 q^{52} + 33 q^{53} + 8 q^{54} + 12 q^{55} + 14 q^{56} + 52 q^{57} - 71 q^{58} + 76 q^{59} + 23 q^{60} + 18 q^{61} - 13 q^{62} - 18 q^{63} + 91 q^{64} + 84 q^{65} - 24 q^{66} - 59 q^{67} + 25 q^{68} + 64 q^{69} - 27 q^{70} + 124 q^{71} - 123 q^{72} + 43 q^{73} - 5 q^{74} + 9 q^{75} + 2 q^{76} + 50 q^{77} - 48 q^{78} - 20 q^{79} + 22 q^{80} + 227 q^{81} - 77 q^{82} + 29 q^{83} + 20 q^{84} + 3 q^{85} + 36 q^{86} - 25 q^{87} - 59 q^{88} + 148 q^{89} - 62 q^{90} + 27 q^{91} + 36 q^{92} + 65 q^{93} - 41 q^{94} + 54 q^{95} + 2 q^{96} + 38 q^{97} - 137 q^{98} + 157 q^{99}+O(q^{100}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9 - 22 * q^10 + 59 * q^11 - 2 * q^12 - 15 * q^13 + 14 * q^14 + 23 * q^15 + 91 * q^16 + 25 * q^17 - 123 * q^18 + 2 * q^19 + 22 * q^20 + 20 * q^21 - 59 * q^22 + 36 * q^23 + 2 * q^24 + 121 * q^25 + 15 * q^26 - 8 * q^27 - 14 * q^28 + 71 * q^29 - 23 * q^30 + 13 * q^31 - 91 * q^32 + 24 * q^33 - 25 * q^34 + 27 * q^35 + 123 * q^36 + 5 * q^37 - 2 * q^38 + 48 * q^39 - 22 * q^40 + 77 * q^41 - 20 * q^42 - 36 * q^43 + 59 * q^44 + 62 * q^45 - 36 * q^46 + 41 * q^47 - 2 * q^48 + 137 * q^49 - 121 * q^50 + 13 * q^51 - 15 * q^52 + 33 * q^53 + 8 * q^54 + 12 * q^55 + 14 * q^56 + 52 * q^57 - 71 * q^58 + 76 * q^59 + 23 * q^60 + 18 * q^61 - 13 * q^62 - 18 * q^63 + 91 * q^64 + 84 * q^65 - 24 * q^66 - 59 * q^67 + 25 * q^68 + 64 * q^69 - 27 * q^70 + 124 * q^71 - 123 * q^72 + 43 * q^73 - 5 * q^74 + 9 * q^75 + 2 * q^76 + 50 * q^77 - 48 * q^78 - 20 * q^79 + 22 * q^80 + 227 * q^81 - 77 * q^82 + 29 * q^83 + 20 * q^84 + 3 * q^85 + 36 * q^86 - 25 * q^87 - 59 * q^88 + 148 * q^89 - 62 * q^90 + 27 * q^91 + 36 * q^92 + 65 * q^93 - 41 * q^94 + 54 * q^95 + 2 * q^96 + 38 * q^97 - 137 * q^98 + 157 * q^99

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