LMFDB - Embedded newform 8015.2.a.i.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$1$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.631186 q^{2} +1.05743 q^{3} -1.60160 q^{4} +1.00000 q^{5} -0.667437 q^{6} -1.00000 q^{7} +2.27328 q^{8} -1.88184 q^{9} +O(q^{10})$	\(q-0.631186 q^{2} +1.05743 q^{3} -1.60160 q^{4} +1.00000 q^{5} -0.667437 q^{6} -1.00000 q^{7} +2.27328 q^{8} -1.88184 q^{9} -0.631186 q^{10} -4.12439 q^{11} -1.69359 q^{12} +0.155496 q^{13} +0.631186 q^{14} +1.05743 q^{15} +1.76835 q^{16} +3.66855 q^{17} +1.18779 q^{18} +4.15195 q^{19} -1.60160 q^{20} -1.05743 q^{21} +2.60326 q^{22} +4.93949 q^{23} +2.40384 q^{24} +1.00000 q^{25} -0.0981468 q^{26} -5.16221 q^{27} +1.60160 q^{28} -4.73271 q^{29} -0.667437 q^{30} -4.81108 q^{31} -5.66272 q^{32} -4.36127 q^{33} -2.31554 q^{34} -1.00000 q^{35} +3.01396 q^{36} -5.09445 q^{37} -2.62065 q^{38} +0.164426 q^{39} +2.27328 q^{40} -0.486008 q^{41} +0.667437 q^{42} +9.96928 q^{43} +6.60564 q^{44} -1.88184 q^{45} -3.11774 q^{46} +9.22653 q^{47} +1.86991 q^{48} +1.00000 q^{49} -0.631186 q^{50} +3.87924 q^{51} -0.249043 q^{52} -9.20792 q^{53} +3.25832 q^{54} -4.12439 q^{55} -2.27328 q^{56} +4.39041 q^{57} +2.98722 q^{58} -3.94485 q^{59} -1.69359 q^{60} +11.1307 q^{61} +3.03668 q^{62} +1.88184 q^{63} +0.0375382 q^{64} +0.155496 q^{65} +2.75277 q^{66} -13.5825 q^{67} -5.87557 q^{68} +5.22318 q^{69} +0.631186 q^{70} +12.0128 q^{71} -4.27794 q^{72} -2.92228 q^{73} +3.21555 q^{74} +1.05743 q^{75} -6.64979 q^{76} +4.12439 q^{77} -0.103784 q^{78} -7.74082 q^{79} +1.76835 q^{80} +0.186816 q^{81} +0.306762 q^{82} +2.98305 q^{83} +1.69359 q^{84} +3.66855 q^{85} -6.29247 q^{86} -5.00452 q^{87} -9.37591 q^{88} -1.51795 q^{89} +1.18779 q^{90} -0.155496 q^{91} -7.91111 q^{92} -5.08739 q^{93} -5.82366 q^{94} +4.15195 q^{95} -5.98794 q^{96} -3.54620 q^{97} -0.631186 q^{98} +7.76143 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) $ 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9 - 2 * q^10 - 15 * q^11 - 3 * q^12 - 17 * q^13 + 2 * q^14 + 10 * q^16 - 7 * q^17 - 16 * q^18 - 32 * q^19 + 30 * q^20 - 14 * q^22 + 8 * q^23 - 35 * q^24 + 44 * q^25 - 27 * q^26 + 6 * q^27 - 30 * q^28 - 42 * q^29 - 7 * q^30 - 43 * q^31 - 8 * q^32 - 33 * q^33 - 33 * q^34 - 44 * q^35 - 11 * q^36 - 44 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 - 62 * q^41 + 7 * q^42 - 7 * q^43 - 45 * q^44 + 16 * q^45 - 15 * q^46 + 2 * q^47 - 26 * q^48 + 44 * q^49 - 2 * q^50 - 25 * q^51 - 35 * q^52 - 25 * q^53 - 76 * q^54 - 15 * q^55 + 3 * q^56 - 7 * q^57 - 2 * q^58 - 35 * q^59 - 3 * q^60 - 86 * q^61 - 23 * q^62 - 16 * q^63 - 5 * q^64 - 17 * q^65 - 6 * q^66 + 2 * q^67 - q^68 - 75 * q^69 + 2 * q^70 - 54 * q^71 - 3 * q^72 - 52 * q^73 - 22 * q^74 - 77 * q^76 + 15 * q^77 + 2 * q^78 + 46 * q^79 + 10 * q^80 - 72 * q^81 - 16 * q^82 + 26 * q^83 + 3 * q^84 - 7 * q^85 - 33 * q^86 - 8 * q^87 - 23 * q^88 - 105 * q^89 - 16 * q^90 + 17 * q^91 - 41 * q^92 - 11 * q^93 - 47 * q^94 - 32 * q^95 - 39 * q^96 - 80 * q^97 - 2 * q^98 - 53 * 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 $

$2$	−0.631186	−0.446316	−0.223158	−	0.974782i	$-0.571637\pi$
$2$	−0.631186	−0.446316	−0.223158	+	0.974782i	$0.571637\pi$
$3$	1.05743	0.610509	0.305255	−	0.952271i	$-0.401258\pi$
$3$	1.05743	0.610509	0.305255	+	0.952271i	$0.401258\pi$
$4$	−1.60160	−0.800802
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.667437	−0.272480
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.27328	0.803727
$9$	−1.88184	−0.627279
$10$	−0.631186	−0.199599
$11$	−4.12439	−1.24355	−0.621775	−	0.783196i	$-0.713588\pi$
$11$	−4.12439	−1.24355	−0.621775	+	0.783196i	$0.713588\pi$
$12$	−1.69359	−0.488897
$13$	0.155496	0.0431268	0.0215634	−	0.999767i	$-0.493136\pi$
$13$	0.155496	0.0431268	0.0215634	+	0.999767i	$0.493136\pi$
$14$	0.631186	0.168692
$15$	1.05743	0.273028
$16$	1.76835	0.442086
$17$	3.66855	0.889754	0.444877	−	0.895592i	$-0.353247\pi$
$17$	3.66855	0.889754	0.444877	+	0.895592i	$0.353247\pi$
$18$	1.18779	0.279964
$19$	4.15195	0.952523	0.476262	−	0.879304i	$-0.341992\pi$
$19$	4.15195	0.952523	0.476262	+	0.879304i	$0.341992\pi$
$20$	−1.60160	−0.358130
$21$	−1.05743	−0.230751
$22$	2.60326	0.555016
$23$	4.93949	1.02996	0.514978	−	0.857204i	$-0.327800\pi$
$23$	4.93949	1.02996	0.514978	+	0.857204i	$0.327800\pi$
$24$	2.40384	0.490682
$25$	1.00000	0.200000
$26$	−0.0981468	−0.0192482
$27$	−5.16221	−0.993468
$28$	1.60160	0.302675
$29$	−4.73271	−0.878841	−0.439421	−	0.898281i	$-0.644816\pi$
$29$	−4.73271	−0.878841	−0.439421	+	0.898281i	$0.644816\pi$
$30$	−0.667437	−0.121857
$31$	−4.81108	−0.864095	−0.432047	−	0.901851i	$-0.642209\pi$
$31$	−4.81108	−0.864095	−0.432047	+	0.901851i	$0.642209\pi$
$32$	−5.66272	−1.00104
$33$	−4.36127	−0.759199
$34$	−2.31554	−0.397111
$35$	−1.00000	−0.169031
$36$	3.01396	0.502326
$37$	−5.09445	−0.837522	−0.418761	−	0.908096i	$-0.637536\pi$
$37$	−5.09445	−0.837522	−0.418761	+	0.908096i	$0.637536\pi$
$38$	−2.62065	−0.425126
$39$	0.164426	0.0263293
$40$	2.27328	0.359437
$41$	−0.486008	−0.0759017	−0.0379509	−	0.999280i	$-0.512083\pi$
$41$	−0.486008	−0.0759017	−0.0379509	+	0.999280i	$0.512083\pi$
$42$	0.667437	0.102988
$43$	9.96928	1.52030	0.760150	−	0.649747i	$-0.225125\pi$
$43$	9.96928	1.52030	0.760150	+	0.649747i	$0.225125\pi$
$44$	6.60564	0.995838
$45$	−1.88184	−0.280528
$46$	−3.11774	−0.459685
$47$	9.22653	1.34583	0.672914	−	0.739721i	$-0.265042\pi$
$47$	9.22653	1.34583	0.672914	+	0.739721i	$0.265042\pi$
$48$	1.86991	0.269898
$49$	1.00000	0.142857
$50$	−0.631186	−0.0892632
$51$	3.87924	0.543203
$52$	−0.249043	−0.0345360
$53$	−9.20792	−1.26480	−0.632402	−	0.774640i	$-0.717931\pi$
$53$	−9.20792	−1.26480	−0.632402	+	0.774640i	$0.717931\pi$
$54$	3.25832	0.443401
$55$	−4.12439	−0.556133
$56$	−2.27328	−0.303780
$57$	4.39041	0.581524
$58$	2.98722	0.392241
$59$	−3.94485	−0.513576	−0.256788	−	0.966468i	$-0.582664\pi$
$59$	−3.94485	−0.513576	−0.256788	+	0.966468i	$0.582664\pi$
$60$	−1.69359	−0.218641
$61$	11.1307	1.42514	0.712571	−	0.701600i	$-0.247531\pi$
$61$	11.1307	1.42514	0.712571	+	0.701600i	$0.247531\pi$
$62$	3.03668	0.385659
$63$	1.88184	0.237089
$64$	0.0375382	0.00469228
$65$	0.155496	0.0192869
$66$	2.75277	0.338843
$67$	−13.5825	−1.65937	−0.829684	−	0.558233i	$-0.811480\pi$
$67$	−13.5825	−1.65937	−0.829684	+	0.558233i	$0.811480\pi$
$68$	−5.87557	−0.712517
$69$	5.22318	0.628797
$70$	0.631186	0.0754411
$71$	12.0128	1.42565	0.712827	−	0.701340i	$-0.247415\pi$
$71$	12.0128	1.42565	0.712827	+	0.701340i	$0.247415\pi$
$72$	−4.27794	−0.504161
$73$	−2.92228	−0.342026	−0.171013	−	0.985269i	$-0.554704\pi$
$73$	−2.92228	−0.342026	−0.171013	+	0.985269i	$0.554704\pi$
$74$	3.21555	0.373800
$75$	1.05743	0.122102
$76$	−6.64979	−0.762783
$77$	4.12439	0.470018
$78$	−0.103784	−0.0117512
$79$	−7.74082	−0.870910	−0.435455	−	0.900210i	$-0.643413\pi$
$79$	−7.74082	−0.870910	−0.435455	+	0.900210i	$0.643413\pi$
$80$	1.76835	0.197707
$81$	0.186816	0.0207573
$82$	0.306762	0.0338762
$83$	2.98305	0.327432	0.163716	−	0.986508i	$-0.447652\pi$
$83$	2.98305	0.327432	0.163716	+	0.986508i	$0.447652\pi$
$84$	1.69359	0.184786
$85$	3.66855	0.397910
$86$	−6.29247	−0.678534
$87$	−5.00452	−0.536541
$88$	−9.37591	−0.999475
$89$	−1.51795	−0.160903	−0.0804514	−	0.996759i	$-0.525636\pi$
$89$	−1.51795	−0.160903	−0.0804514	+	0.996759i	$0.525636\pi$
$90$	1.18779	0.125204
$91$	−0.155496	−0.0163004
$92$	−7.91111	−0.824791
$93$	−5.08739	−0.527538
$94$	−5.82366	−0.600664
$95$	4.15195	0.425981
$96$	−5.98794	−0.611142
$97$	−3.54620	−0.360062	−0.180031	−	0.983661i	$-0.557620\pi$
$97$	−3.54620	−0.360062	−0.180031	+	0.983661i	$0.557620\pi$
$98$	−0.631186	−0.0637594
$99$	7.76143	0.780053
$100$	−1.60160	−0.160160
$101$	−6.02064	−0.599076	−0.299538	−	0.954084i	$-0.596833\pi$
$101$	−6.02064	−0.599076	−0.299538	+	0.954084i	$0.596833\pi$
$102$	−2.44852	−0.242440
$103$	−1.53436	−0.151185	−0.0755923	−	0.997139i	$-0.524085\pi$
$103$	−1.53436	−0.151185	−0.0755923	+	0.997139i	$0.524085\pi$
$104$	0.353486	0.0346622
$105$	−1.05743	−0.103195
$106$	5.81191	0.564502
$107$	−16.6271	−1.60740	−0.803701	−	0.595034i	$-0.797139\pi$
$107$	−16.6271	−1.60740	−0.803701	+	0.595034i	$0.797139\pi$
$108$	8.26782	0.795572
$109$	14.6734	1.40545	0.702727	−	0.711460i	$-0.251966\pi$
$109$	14.6734	1.40545	0.702727	+	0.711460i	$0.251966\pi$
$110$	2.60326	0.248211
$111$	−5.38704	−0.511315
$112$	−1.76835	−0.167093
$113$	11.7566	1.10597	0.552985	−	0.833191i	$-0.313489\pi$
$113$	11.7566	1.10597	0.552985	+	0.833191i	$0.313489\pi$
$114$	−2.77117	−0.259543
$115$	4.93949	0.460610
$116$	7.57992	0.703778
$117$	−0.292618	−0.0270525
$118$	2.48994	0.229217
$119$	−3.66855	−0.336295
$120$	2.40384	0.219440
$121$	6.01061	0.546419
$122$	−7.02555	−0.636064
$123$	−0.513921	−0.0463387
$124$	7.70544	0.691969
$125$	1.00000	0.0894427
$126$	−1.18779	−0.105817
$127$	−4.99379	−0.443127	−0.221564	−	0.975146i	$-0.571116\pi$
$127$	−4.99379	−0.443127	−0.221564	+	0.975146i	$0.571116\pi$
$128$	11.3017	0.998942
$129$	10.5418	0.928157
$130$	−0.0981468	−0.00860805
$131$	4.24553	0.370934	0.185467	−	0.982650i	$-0.440620\pi$
$131$	4.24553	0.370934	0.185467	+	0.982650i	$0.440620\pi$
$132$	6.98502	0.607968
$133$	−4.15195	−0.360020
$134$	8.57309	0.740602
$135$	−5.16221	−0.444293
$136$	8.33965	0.715119
$137$	17.0753	1.45884	0.729422	−	0.684064i	$-0.239789\pi$
$137$	17.0753	1.45884	0.729422	+	0.684064i	$0.239789\pi$
$138$	−3.29680	−0.280642
$139$	17.6669	1.49848	0.749242	−	0.662297i	$-0.230418\pi$
$139$	17.6669	1.49848	0.749242	+	0.662297i	$0.230418\pi$
$140$	1.60160	0.135360
$141$	9.75644	0.821640
$142$	−7.58229	−0.636292
$143$	−0.641326	−0.0536304
$144$	−3.32774	−0.277311
$145$	−4.73271	−0.393030
$146$	1.84450	0.152652
$147$	1.05743	0.0872156
$148$	8.15929	0.670690
$149$	−13.0096	−1.06579	−0.532896	−	0.846181i	$-0.678896\pi$
$149$	−13.0096	−1.06579	−0.532896	+	0.846181i	$0.678896\pi$
$150$	−0.667437	−0.0544960
$151$	3.09437	0.251816	0.125908	−	0.992042i	$-0.459816\pi$
$151$	3.09437	0.251816	0.125908	+	0.992042i	$0.459816\pi$
$152$	9.43856	0.765568
$153$	−6.90361	−0.558124
$154$	−2.60326	−0.209777
$155$	−4.81108	−0.386435
$156$	−0.263346	−0.0210846
$157$	−2.68230	−0.214071	−0.107035	−	0.994255i	$-0.534136\pi$
$157$	−2.68230	−0.214071	−0.107035	+	0.994255i	$0.534136\pi$
$158$	4.88590	0.388701
$159$	−9.73675	−0.772175
$160$	−5.66272	−0.447677
$161$	−4.93949	−0.389287
$162$	−0.117915	−0.00926431
$163$	−4.04971	−0.317197	−0.158599	−	0.987343i	$-0.550698\pi$
$163$	−4.04971	−0.317197	−0.158599	+	0.987343i	$0.550698\pi$
$164$	0.778393	0.0607823
$165$	−4.36127	−0.339524
$166$	−1.88286	−0.146138
$167$	−14.8449	−1.14873	−0.574366	−	0.818599i	$-0.694751\pi$
$167$	−14.8449	−1.14873	−0.574366	+	0.818599i	$0.694751\pi$
$168$	−2.40384	−0.185460
$169$	−12.9758	−0.998140
$170$	−2.31554	−0.177594
$171$	−7.81330	−0.597498
$172$	−15.9668	−1.21746
$173$	4.57063	0.347498	0.173749	−	0.984790i	$-0.444412\pi$
$173$	4.57063	0.347498	0.173749	+	0.984790i	$0.444412\pi$
$174$	3.15878	0.239467
$175$	−1.00000	−0.0755929
$176$	−7.29335	−0.549757
$177$	−4.17142	−0.313543
$178$	0.958111	0.0718135
$179$	−4.11478	−0.307553	−0.153777	−	0.988106i	$-0.549144\pi$
$179$	−4.11478	−0.307553	−0.153777	+	0.988106i	$0.549144\pi$
$180$	3.01396	0.224647
$181$	−9.05231	−0.672853	−0.336427	−	0.941710i	$-0.609218\pi$
$181$	−9.05231	−0.672853	−0.336427	+	0.941710i	$0.609218\pi$
$182$	0.0981468	0.00727513
$183$	11.7700	0.870062
$184$	11.2289	0.827803
$185$	−5.09445	−0.374551
$186$	3.21109	0.235448
$187$	−15.1305	−1.10645
$188$	−14.7773	−1.07774
$189$	5.16221	0.375496
$190$	−2.62065	−0.190122
$191$	−16.7658	−1.21313	−0.606565	−	0.795034i	$-0.707453\pi$
$191$	−16.7658	−1.21313	−0.606565	+	0.795034i	$0.707453\pi$
$192$	0.0396941	0.00286468
$193$	−18.4223	−1.32607	−0.663034	−	0.748589i	$-0.730731\pi$
$193$	−18.4223	−1.32607	−0.663034	+	0.748589i	$0.730731\pi$
$194$	2.23831	0.160701
$195$	0.164426	0.0117748
$196$	−1.60160	−0.114400
$197$	−22.9983	−1.63856	−0.819281	−	0.573392i	$-0.805627\pi$
$197$	−22.9983	−1.63856	−0.819281	+	0.573392i	$0.805627\pi$
$198$	−4.89891	−0.348150
$199$	−5.35344	−0.379495	−0.189748	−	0.981833i	$-0.560767\pi$
$199$	−5.35344	−0.379495	−0.189748	+	0.981833i	$0.560767\pi$
$200$	2.27328	0.160745
$201$	−14.3626	−1.01306
$202$	3.80014	0.267377
$203$	4.73271	0.332171
$204$	−6.21302	−0.434998
$205$	−0.486008	−0.0339443
$206$	0.968464	0.0674761
$207$	−9.29532	−0.646069
$208$	0.274970	0.0190658
$209$	−17.1243	−1.18451
$210$	0.667437	0.0460575
$211$	−14.5673	−1.00286	−0.501428	−	0.865199i	$-0.667192\pi$
$211$	−14.5673	−1.00286	−0.501428	+	0.865199i	$0.667192\pi$
$212$	14.7474	1.01286
$213$	12.7027	0.870374
$214$	10.4948	0.717409
$215$	9.96928	0.679899
$216$	−11.7352	−0.798477
$217$	4.81108	0.326597
$218$	−9.26162	−0.627276
$219$	−3.09011	−0.208810
$220$	6.60564	0.445352
$221$	0.570445	0.0383723
$222$	3.40022	0.228208
$223$	−9.32119	−0.624193	−0.312096	−	0.950050i	$-0.601031\pi$
$223$	−9.32119	−0.624193	−0.312096	+	0.950050i	$0.601031\pi$
$224$	5.66272	0.378356
$225$	−1.88184	−0.125456
$226$	−7.42061	−0.493612
$227$	−11.6321	−0.772049	−0.386024	−	0.922489i	$-0.626152\pi$
$227$	−11.6321	−0.772049	−0.386024	+	0.922489i	$0.626152\pi$
$228$	−7.03170	−0.465686
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−3.11774	−0.205578
$231$	4.36127	0.286950
$232$	−10.7588	−0.706348
$233$	3.74962	0.245646	0.122823	−	0.992429i	$-0.460805\pi$
$233$	3.74962	0.245646	0.122823	+	0.992429i	$0.460805\pi$
$234$	0.184696	0.0120740
$235$	9.22653	0.601873
$236$	6.31809	0.411273
$237$	−8.18540	−0.531699
$238$	2.31554	0.150094
$239$	−2.28881	−0.148051	−0.0740255	−	0.997256i	$-0.523585\pi$
$239$	−2.28881	−0.148051	−0.0740255	+	0.997256i	$0.523585\pi$
$240$	1.86991	0.120702
$241$	5.25975	0.338810	0.169405	−	0.985547i	$-0.445815\pi$
$241$	5.25975	0.338810	0.169405	+	0.985547i	$0.445815\pi$
$242$	−3.79381	−0.243875
$243$	15.6842	1.00614
$244$	−17.8270	−1.14126
$245$	1.00000	0.0638877
$246$	0.324380	0.0206817
$247$	0.645612	0.0410793
$248$	−10.9369	−0.694496
$249$	3.15437	0.199900
$250$	−0.631186	−0.0399197
$251$	−8.99995	−0.568072	−0.284036	−	0.958814i	$-0.591673\pi$
$251$	−8.99995	−0.568072	−0.284036	+	0.958814i	$0.591673\pi$
$252$	−3.01396	−0.189861
$253$	−20.3724	−1.28080
$254$	3.15201	0.197775
$255$	3.87924	0.242928
$256$	−7.20858	−0.450536
$257$	11.1184	0.693546	0.346773	−	0.937949i	$-0.387277\pi$
$257$	11.1184	0.693546	0.346773	+	0.937949i	$0.387277\pi$
$258$	−6.65386	−0.414251
$259$	5.09445	0.316554
$260$	−0.249043	−0.0154450
$261$	8.90618	0.551279
$262$	−2.67972	−0.165554
$263$	−27.9148	−1.72130	−0.860650	−	0.509197i	$-0.829943\pi$
$263$	−27.9148	−1.72130	−0.860650	+	0.509197i	$0.829943\pi$
$264$	−9.91439	−0.610188
$265$	−9.20792	−0.565638
$266$	2.62065	0.160683
$267$	−1.60513	−0.0982326
$268$	21.7538	1.32883
$269$	13.4547	0.820349	0.410175	−	0.912007i	$-0.365468\pi$
$269$	13.4547	0.820349	0.410175	+	0.912007i	$0.365468\pi$
$270$	3.25832	0.198295
$271$	−12.8327	−0.779533	−0.389767	−	0.920914i	$-0.627444\pi$
$271$	−12.8327	−0.779533	−0.389767	+	0.920914i	$0.627444\pi$
$272$	6.48726	0.393348
$273$	−0.164426	−0.00995154
$274$	−10.7777	−0.651105
$275$	−4.12439	−0.248710
$276$	−8.36547	−0.503542
$277$	−5.36425	−0.322307	−0.161153	−	0.986929i	$-0.551521\pi$
$277$	−5.36425	−0.322307	−0.161153	+	0.986929i	$0.551521\pi$
$278$	−11.1511	−0.668797
$279$	9.05366	0.542028
$280$	−2.27328	−0.135855
$281$	6.64804	0.396589	0.198294	−	0.980143i	$-0.436460\pi$
$281$	6.64804	0.396589	0.198294	+	0.980143i	$0.436460\pi$
$282$	−6.15813	−0.366711
$283$	−12.4164	−0.738079	−0.369039	−	0.929414i	$-0.620313\pi$
$283$	−12.4164	−0.738079	−0.369039	+	0.929414i	$0.620313\pi$
$284$	−19.2397	−1.14167
$285$	4.39041	0.260065
$286$	0.404796	0.0239361
$287$	0.486008	0.0286882
$288$	10.6563	0.627929
$289$	−3.54174	−0.208338
$290$	2.98722	0.175415
$291$	−3.74987	−0.219821
$292$	4.68033	0.273896
$293$	1.51997	0.0887976	0.0443988	−	0.999014i	$-0.485863\pi$
$293$	1.51997	0.0887976	0.0443988	+	0.999014i	$0.485863\pi$
$294$	−0.667437	−0.0389257
$295$	−3.94485	−0.229678
$296$	−11.5811	−0.673139
$297$	21.2910	1.23543
$298$	8.21150	0.475680
$299$	0.768071	0.0444187
$300$	−1.69359	−0.0977794
$301$	−9.96928	−0.574620
$302$	−1.95312	−0.112390
$303$	−6.36642	−0.365741
$304$	7.34209	0.421097
$305$	11.1307	0.637343
$306$	4.35746	0.249100
$307$	−26.7736	−1.52805	−0.764025	−	0.645186i	$-0.776780\pi$
$307$	−26.7736	−1.52805	−0.764025	+	0.645186i	$0.776780\pi$
$308$	−6.60564	−0.376391
$309$	−1.62248	−0.0922996
$310$	3.03668	0.172472
$311$	5.44805	0.308931	0.154465	−	0.987998i	$-0.450635\pi$
$311$	5.44805	0.308931	0.154465	+	0.987998i	$0.450635\pi$
$312$	0.373788	0.0211616
$313$	−14.3115	−0.808933	−0.404467	−	0.914553i	$-0.632543\pi$
$313$	−14.3115	−0.808933	−0.404467	+	0.914553i	$0.632543\pi$
$314$	1.69303	0.0955432
$315$	1.88184	0.106029
$316$	12.3977	0.697427
$317$	12.5181	0.703085	0.351542	−	0.936172i	$-0.385657\pi$
$317$	12.5181	0.703085	0.351542	+	0.936172i	$0.385657\pi$
$318$	6.14570	0.344634
$319$	19.5195	1.09288
$320$	0.0375382	0.00209845
$321$	−17.5820	−0.981333
$322$	3.11774	0.173745
$323$	15.2316	0.847512
$324$	−0.299205	−0.0166225
$325$	0.155496	0.00862536
$326$	2.55612	0.141570
$327$	15.5161	0.858042
$328$	−1.10483	−0.0610042
$329$	−9.22653	−0.508675
$330$	2.75277	0.151535
$331$	−25.3049	−1.39088	−0.695441	−	0.718583i	$-0.744791\pi$
$331$	−25.3049	−1.39088	−0.695441	+	0.718583i	$0.744791\pi$
$332$	−4.77766	−0.262208
$333$	9.58692	0.525360
$334$	9.36988	0.512697
$335$	−13.5825	−0.742092
$336$	−1.86991	−0.102012
$337$	−23.6313	−1.28728	−0.643639	−	0.765330i	$-0.722576\pi$
$337$	−23.6313	−1.28728	−0.643639	+	0.765330i	$0.722576\pi$
$338$	8.19016	0.445486
$339$	12.4318	0.675205
$340$	−5.87557	−0.318647
$341$	19.8428	1.07455
$342$	4.93164	0.266673
$343$	−1.00000	−0.0539949
$344$	22.6630	1.22191
$345$	5.22318	0.281207
$346$	−2.88492	−0.155094
$347$	−23.2283	−1.24696	−0.623481	−	0.781839i	$-0.714282\pi$
$347$	−23.2283	−1.24696	−0.623481	+	0.781839i	$0.714282\pi$
$348$	8.01526	0.429663
$349$	35.2511	1.88695	0.943474	−	0.331446i	$-0.107537\pi$
$349$	35.2511	1.88695	0.943474	+	0.331446i	$0.107537\pi$
$350$	0.631186	0.0337383
$351$	−0.802703	−0.0428451
$352$	23.3553	1.24484
$353$	−31.5472	−1.67909	−0.839544	−	0.543292i	$-0.817178\pi$
$353$	−31.5472	−1.67909	−0.839544	+	0.543292i	$0.817178\pi$
$354$	2.63294	0.139939
$355$	12.0128	0.637572
$356$	2.43116	0.128851
$357$	−3.87924	−0.205311
$358$	2.59719	0.137266
$359$	−5.47504	−0.288961	−0.144481	−	0.989508i	$-0.546151\pi$
$359$	−5.47504	−0.288961	−0.144481	+	0.989508i	$0.546151\pi$
$360$	−4.27794	−0.225467
$361$	−1.76129	−0.0926993
$362$	5.71369	0.300305
$363$	6.35581	0.333594
$364$	0.249043	0.0130534
$365$	−2.92228	−0.152959
$366$	−7.42905	−0.388323
$367$	31.6054	1.64979	0.824895	−	0.565286i	$-0.191234\pi$
$367$	31.6054	1.64979	0.824895	+	0.565286i	$0.191234\pi$
$368$	8.73473	0.455329
$369$	0.914588	0.0476116
$370$	3.21555	0.167168
$371$	9.20792	0.478051
$372$	8.14799	0.422453
$373$	4.92386	0.254948	0.127474	−	0.991842i	$-0.459313\pi$
$373$	4.92386	0.254948	0.127474	+	0.991842i	$0.459313\pi$
$374$	9.55018	0.493828
$375$	1.05743	0.0546056
$376$	20.9745	1.08168
$377$	−0.735917	−0.0379016
$378$	−3.25832	−0.167590
$379$	−3.59537	−0.184682	−0.0923409	−	0.995727i	$-0.529435\pi$
$379$	−3.59537	−0.184682	−0.0923409	+	0.995727i	$0.529435\pi$
$380$	−6.64979	−0.341127
$381$	−5.28059	−0.270533
$382$	10.5823	0.541439
$383$	−14.8009	−0.756292	−0.378146	−	0.925746i	$-0.623438\pi$
$383$	−14.8009	−0.756292	−0.378146	+	0.925746i	$0.623438\pi$
$384$	11.9508	0.609863
$385$	4.12439	0.210198
$386$	11.6279	0.591845
$387$	−18.7605	−0.953652
$388$	5.67961	0.288339
$389$	−25.2151	−1.27846	−0.639229	−	0.769016i	$-0.720746\pi$
$389$	−25.2151	−1.27846	−0.639229	+	0.769016i	$0.720746\pi$
$390$	−0.103784	−0.00525529
$391$	18.1208	0.916407
$392$	2.27328	0.114818
$393$	4.48937	0.226459
$394$	14.5162	0.731316
$395$	−7.74082	−0.389483
$396$	−12.4307	−0.624668
$397$	19.5116	0.979260	0.489630	−	0.871930i	$-0.337132\pi$
$397$	19.5116	0.979260	0.489630	+	0.871930i	$0.337132\pi$
$398$	3.37901	0.169375
$399$	−4.39041	−0.219795
$400$	1.76835	0.0884173
$401$	−12.6353	−0.630975	−0.315488	−	0.948930i	$-0.602168\pi$
$401$	−12.6353	−0.630975	−0.315488	+	0.948930i	$0.602168\pi$
$402$	9.06547	0.452144
$403$	−0.748103	−0.0372657
$404$	9.64268	0.479741
$405$	0.186816	0.00928294
$406$	−2.98722	−0.148253
$407$	21.0115	1.04150
$408$	8.81862	0.436587
$409$	13.5705	0.671020	0.335510	−	0.942037i	$-0.391091\pi$
$409$	13.5705	0.671020	0.335510	+	0.942037i	$0.391091\pi$
$410$	0.306762	0.0151499
$411$	18.0560	0.890637
$412$	2.45743	0.121069
$413$	3.94485	0.194114
$414$	5.86707	0.288351
$415$	2.98305	0.146432
$416$	−0.880530	−0.0431715
$417$	18.6815	0.914838
$418$	10.8086	0.528666
$419$	28.3293	1.38398	0.691990	−	0.721907i	$-0.256734\pi$
$419$	28.3293	1.38398	0.691990	+	0.721907i	$0.256734\pi$
$420$	1.69359	0.0826387
$421$	−10.2553	−0.499813	−0.249906	−	0.968270i	$-0.580400\pi$
$421$	−10.2553	−0.499813	−0.249906	+	0.968270i	$0.580400\pi$
$422$	9.19469	0.447591
$423$	−17.3628	−0.844209
$424$	−20.9322	−1.01656
$425$	3.66855	0.177951
$426$	−8.01776	−0.388462
$427$	−11.1307	−0.538653
$428$	26.6300	1.28721
$429$	−0.678159	−0.0327418
$430$	−6.29247	−0.303450
$431$	−4.00030	−0.192688	−0.0963439	−	0.995348i	$-0.530715\pi$
$431$	−4.00030	−0.192688	−0.0963439	+	0.995348i	$0.530715\pi$
$432$	−9.12857	−0.439199
$433$	1.15925	0.0557100	0.0278550	−	0.999612i	$-0.491132\pi$
$433$	1.15925	0.0557100	0.0278550	+	0.999612i	$0.491132\pi$
$434$	−3.03668	−0.145766
$435$	−5.00452	−0.239948
$436$	−23.5009	−1.12549
$437$	20.5085	0.981057
$438$	1.95043	0.0931953
$439$	5.37075	0.256332	0.128166	−	0.991753i	$-0.459091\pi$
$439$	5.37075	0.256332	0.128166	+	0.991753i	$0.459091\pi$
$440$	−9.37591	−0.446979
$441$	−1.88184	−0.0896112
$442$	−0.360057	−0.0171261
$443$	4.53117	0.215283	0.107641	−	0.994190i	$-0.465670\pi$
$443$	4.53117	0.215283	0.107641	+	0.994190i	$0.465670\pi$
$444$	8.62790	0.409462
$445$	−1.51795	−0.0719579
$446$	5.88340	0.278587
$447$	−13.7568	−0.650675
$448$	−0.0375382	−0.00177351
$449$	−11.7245	−0.553313	−0.276656	−	0.960969i	$-0.589226\pi$
$449$	−11.7245	−0.553313	−0.276656	+	0.960969i	$0.589226\pi$
$450$	1.18779	0.0559929
$451$	2.00449	0.0943877
$452$	−18.8295	−0.885663
$453$	3.27209	0.153736
$454$	7.34201	0.344578
$455$	−0.155496	−0.00728976
$456$	9.98064	0.467386
$457$	28.1303	1.31588	0.657941	−	0.753070i	$-0.271428\pi$
$457$	28.1303	1.31588	0.657941	+	0.753070i	$0.271428\pi$
$458$	−0.631186	−0.0294934
$459$	−18.9378	−0.883943
$460$	−7.91111	−0.368858
$461$	−13.5167	−0.629534	−0.314767	−	0.949169i	$-0.601926\pi$
$461$	−13.5167	−0.629534	−0.314767	+	0.949169i	$0.601926\pi$
$462$	−2.75277	−0.128070
$463$	−6.39518	−0.297209	−0.148605	−	0.988897i	$-0.547478\pi$
$463$	−6.39518	−0.297209	−0.148605	+	0.988897i	$0.547478\pi$
$464$	−8.36906	−0.388524
$465$	−5.08739	−0.235922
$466$	−2.36671	−0.109636
$467$	−10.8806	−0.503495	−0.251748	−	0.967793i	$-0.581005\pi$
$467$	−10.8806	−0.503495	−0.251748	+	0.967793i	$0.581005\pi$
$468$	0.468658	0.0216637
$469$	13.5825	0.627182
$470$	−5.82366	−0.268625
$471$	−2.83635	−0.130692
$472$	−8.96776	−0.412775
$473$	−41.1172	−1.89057
$474$	5.16651	0.237306
$475$	4.15195	0.190505
$476$	5.87557	0.269306
$477$	17.3278	0.793385
$478$	1.44467	0.0660775
$479$	37.0620	1.69340	0.846702	−	0.532067i	$-0.178584\pi$
$479$	37.0620	1.69340	0.846702	+	0.532067i	$0.178584\pi$
$480$	−5.98794	−0.273311
$481$	−0.792166	−0.0361197
$482$	−3.31988	−0.151216
$483$	−5.22318	−0.237663
$484$	−9.62661	−0.437573
$485$	−3.54620	−0.161025
$486$	−9.89964	−0.449057
$487$	4.19236	0.189974	0.0949870	−	0.995479i	$-0.469719\pi$
$487$	4.19236	0.189974	0.0949870	+	0.995479i	$0.469719\pi$
$488$	25.3033	1.14542
$489$	−4.28229	−0.193652
$490$	−0.631186	−0.0285141
$491$	−25.3750	−1.14516	−0.572579	−	0.819849i	$-0.694057\pi$
$491$	−25.3750	−1.14516	−0.572579	+	0.819849i	$0.694057\pi$
$492$	0.823098	0.0371081
$493$	−17.3622	−0.781953
$494$	−0.407501	−0.0183343
$495$	7.76143	0.348850
$496$	−8.50764	−0.382005
$497$	−12.0128	−0.538846
$498$	−1.99099	−0.0892186
$499$	33.3118	1.49124	0.745620	−	0.666372i	$-0.232154\pi$
$499$	33.3118	1.49124	0.745620	+	0.666372i	$0.232154\pi$
$500$	−1.60160	−0.0716259
$501$	−15.6975	−0.701311
$502$	5.68064	0.253539
$503$	−14.9494	−0.666560	−0.333280	−	0.942828i	$-0.608155\pi$
$503$	−14.9494	−0.666560	−0.333280	+	0.942828i	$0.608155\pi$
$504$	4.27794	0.190555
$505$	−6.02064	−0.267915
$506$	12.8588	0.571642
$507$	−13.7211	−0.609374
$508$	7.99807	0.354857
$509$	8.82759	0.391276	0.195638	−	0.980676i	$-0.437322\pi$
$509$	8.82759	0.391276	0.195638	+	0.980676i	$0.437322\pi$
$510$	−2.44852	−0.108423
$511$	2.92228	0.129274
$512$	−18.0535	−0.797861
$513$	−21.4333	−0.946302
$514$	−7.01777	−0.309540
$515$	−1.53436	−0.0676118
$516$	−16.8839	−0.743270
$517$	−38.0538	−1.67361
$518$	−3.21555	−0.141283
$519$	4.83313	0.212151
$520$	0.353486	0.0155014
$521$	−8.33136	−0.365004	−0.182502	−	0.983206i	$-0.558420\pi$
$521$	−8.33136	−0.365004	−0.182502	+	0.983206i	$0.558420\pi$
$522$	−5.62145	−0.246044
$523$	28.9732	1.26691	0.633455	−	0.773780i	$-0.281636\pi$
$523$	28.9732	1.26691	0.633455	+	0.773780i	$0.281636\pi$
$524$	−6.79967	−0.297045
$525$	−1.05743	−0.0461501
$526$	17.6194	0.768244
$527$	−17.6497	−0.768832
$528$	−7.71222	−0.335631
$529$	1.39859	0.0608081
$530$	5.81191	0.252453
$531$	7.42357	0.322155
$532$	6.64979	0.288305
$533$	−0.0755723	−0.00327340
$534$	1.01314	0.0438428
$535$	−16.6271	−0.718852
$536$	−30.8769	−1.33368
$537$	−4.35111	−0.187764
$538$	−8.49244	−0.366135
$539$	−4.12439	−0.177650
$540$	8.26782	0.355790
$541$	−4.14953	−0.178402	−0.0892012	−	0.996014i	$-0.528431\pi$
$541$	−4.14953	−0.178402	−0.0892012	+	0.996014i	$0.528431\pi$
$542$	8.09984	0.347918
$543$	−9.57221	−0.410783
$544$	−20.7740	−0.890677
$545$	14.6734	0.628538
$546$	0.103784	0.00444153
$547$	−6.48659	−0.277347	−0.138673	−	0.990338i	$-0.544284\pi$
$547$	−6.48659	−0.277347	−0.138673	+	0.990338i	$0.544284\pi$
$548$	−27.3479	−1.16824
$549$	−20.9462	−0.893961
$550$	2.60326	0.111003
$551$	−19.6500	−0.837117
$552$	11.8738	0.505381
$553$	7.74082	0.329173
$554$	3.38584	0.143851
$555$	−5.38704	−0.228667
$556$	−28.2953	−1.19999
$557$	−16.1233	−0.683167	−0.341584	−	0.939851i	$-0.610963\pi$
$557$	−16.1233	−0.683167	−0.341584	+	0.939851i	$0.610963\pi$
$558$	−5.71454	−0.241916
$559$	1.55018	0.0655657
$560$	−1.76835	−0.0747262
$561$	−15.9995	−0.675501
$562$	−4.19615	−0.177004
$563$	40.5760	1.71008	0.855038	−	0.518566i	$-0.173534\pi$
$563$	40.5760	1.71008	0.855038	+	0.518566i	$0.173534\pi$
$564$	−15.6260	−0.657971
$565$	11.7566	0.494605
$566$	7.83706	0.329416
$567$	−0.186816	−0.00784552
$568$	27.3084	1.14584
$569$	−21.5439	−0.903166	−0.451583	−	0.892229i	$-0.649141\pi$
$569$	−21.5439	−0.903166	−0.451583	+	0.892229i	$0.649141\pi$
$570$	−2.77117	−0.116071
$571$	12.4368	0.520462	0.260231	−	0.965546i	$-0.416201\pi$
$571$	12.4368	0.520462	0.260231	+	0.965546i	$0.416201\pi$
$572$	1.02715	0.0429473
$573$	−17.7287	−0.740627
$574$	−0.306762	−0.0128040
$575$	4.93949	0.205991
$576$	−0.0706408	−0.00294336
$577$	−33.2520	−1.38430	−0.692150	−	0.721754i	$-0.743336\pi$
$577$	−33.2520	−1.38430	−0.692150	+	0.721754i	$0.743336\pi$
$578$	2.23550	0.0929844
$579$	−19.4804	−0.809576
$580$	7.57992	0.314739
$581$	−2.98305	−0.123758
$582$	2.36686	0.0981097
$583$	37.9771	1.57285
$584$	−6.64316	−0.274896
$585$	−0.292618	−0.0120983
$586$	−0.959384	−0.0396318
$587$	−0.873056	−0.0360349	−0.0180174	−	0.999838i	$-0.505735\pi$
$587$	−0.873056	−0.0360349	−0.0180174	+	0.999838i	$0.505735\pi$
$588$	−1.69359	−0.0698424
$589$	−19.9754	−0.823071
$590$	2.48994	0.102509
$591$	−24.3192	−1.00036
$592$	−9.00875	−0.370257
$593$	21.3961	0.878634	0.439317	−	0.898332i	$-0.355220\pi$
$593$	21.3961	0.878634	0.439317	+	0.898332i	$0.355220\pi$
$594$	−13.4386	−0.551391
$595$	−3.66855	−0.150396
$596$	20.8363	0.853488
$597$	−5.66090	−0.231685
$598$	−0.484796	−0.0198248
$599$	−10.0110	−0.409039	−0.204520	−	0.978862i	$-0.565563\pi$
$599$	−10.0110	−0.409039	−0.204520	+	0.978862i	$0.565563\pi$
$600$	2.40384	0.0981365
$601$	−26.6303	−1.08627	−0.543136	−	0.839645i	$-0.682763\pi$
$601$	−26.6303	−1.08627	−0.543136	+	0.839645i	$0.682763\pi$
$602$	6.29247	0.256462
$603$	25.5601	1.04089
$604$	−4.95596	−0.201655
$605$	6.01061	0.244366
$606$	4.01839	0.163236
$607$	−20.8981	−0.848227	−0.424114	−	0.905609i	$-0.639414\pi$
$607$	−20.8981	−0.848227	−0.424114	+	0.905609i	$0.639414\pi$
$608$	−23.5113	−0.953511
$609$	5.00452	0.202793
$610$	−7.02555	−0.284456
$611$	1.43469	0.0580413
$612$	11.0569	0.446947
$613$	−35.2806	−1.42497	−0.712485	−	0.701688i	$-0.752430\pi$
$613$	−35.2806	−1.42497	−0.712485	+	0.701688i	$0.752430\pi$
$614$	16.8991	0.681993
$615$	−0.513921	−0.0207233
$616$	9.37591	0.377766
$617$	−38.3629	−1.54443	−0.772216	−	0.635360i	$-0.780852\pi$
$617$	−38.3629	−1.54443	−0.772216	+	0.635360i	$0.780852\pi$
$618$	1.02409	0.0411948
$619$	9.30271	0.373908	0.186954	−	0.982369i	$-0.440139\pi$
$619$	9.30271	0.373908	0.186954	+	0.982369i	$0.440139\pi$
$620$	7.70544	0.309458
$621$	−25.4987	−1.02323
$622$	−3.43873	−0.137881
$623$	1.51795	0.0608155
$624$	0.290763	0.0116398
$625$	1.00000	0.0400000
$626$	9.03321	0.361040
$627$	−18.1078	−0.723155
$628$	4.29598	0.171428
$629$	−18.6892	−0.745189
$630$	−1.18779	−0.0473226
$631$	−30.2538	−1.20439	−0.602193	−	0.798351i	$-0.705706\pi$
$631$	−30.2538	−1.20439	−0.602193	+	0.798351i	$0.705706\pi$
$632$	−17.5971	−0.699974
$633$	−15.4040	−0.612253
$634$	−7.90123	−0.313798
$635$	−4.99379	−0.198172
$636$	15.5944	0.618359
$637$	0.155496	0.00616097
$638$	−12.3205	−0.487772
$639$	−22.6061	−0.894282
$640$	11.3017	0.446741
$641$	−15.5447	−0.613979	−0.306989	−	0.951713i	$-0.599322\pi$
$641$	−15.5447	−0.613979	−0.306989	+	0.951713i	$0.599322\pi$
$642$	11.0975	0.437984
$643$	30.2741	1.19389	0.596947	−	0.802281i	$-0.296380\pi$
$643$	30.2741	1.19389	0.596947	+	0.802281i	$0.296380\pi$
$644$	7.91111	0.311742
$645$	10.5418	0.415084
$646$	−9.61400	−0.378258
$647$	−0.741913	−0.0291676	−0.0145838	−	0.999894i	$-0.504642\pi$
$647$	−0.741913	−0.0291676	−0.0145838	+	0.999894i	$0.504642\pi$
$648$	0.424684	0.0166832
$649$	16.2701	0.638658
$650$	−0.0981468	−0.00384964
$651$	5.08739	0.199391
$652$	6.48603	0.254012
$653$	11.3678	0.444857	0.222429	−	0.974949i	$-0.428602\pi$
$653$	11.3678	0.444857	0.222429	+	0.974949i	$0.428602\pi$
$654$	−9.79354	−0.382958
$655$	4.24553	0.165887
$656$	−0.859430	−0.0335551
$657$	5.49924	0.214546
$658$	5.82366	0.227030
$659$	26.4671	1.03101	0.515507	−	0.856886i	$-0.327604\pi$
$659$	26.4671	1.03101	0.515507	+	0.856886i	$0.327604\pi$
$660$	6.98502	0.271892
$661$	25.3085	0.984386	0.492193	−	0.870486i	$-0.336195\pi$
$661$	25.3085	0.984386	0.492193	+	0.870486i	$0.336195\pi$
$662$	15.9721	0.620773
$663$	0.603207	0.0234266
$664$	6.78131	0.263166
$665$	−4.15195	−0.161006
$666$	−6.05113	−0.234476
$667$	−23.3772	−0.905168
$668$	23.7756	0.919907
$669$	−9.85653	−0.381075
$670$	8.57309	0.331207
$671$	−45.9074	−1.77224
$672$	5.98794	0.230990
$673$	18.6292	0.718102	0.359051	−	0.933318i	$-0.383100\pi$
$673$	18.6292	0.718102	0.359051	+	0.933318i	$0.383100\pi$
$674$	14.9157	0.574532
$675$	−5.16221	−0.198694
$676$	20.7821	0.799313
$677$	−0.825568	−0.0317292	−0.0158646	−	0.999874i	$-0.505050\pi$
$677$	−0.825568	−0.0317292	−0.0158646	+	0.999874i	$0.505050\pi$
$678$	−7.84680	−0.301354
$679$	3.54620	0.136091
$680$	8.33965	0.319811
$681$	−12.3002	−0.471343
$682$	−12.5245	−0.479587
$683$	−12.8199	−0.490541	−0.245270	−	0.969455i	$-0.578877\pi$
$683$	−12.8199	−0.490541	−0.245270	+	0.969455i	$0.578877\pi$
$684$	12.5138	0.478477
$685$	17.0753	0.652415
$686$	0.631186	0.0240988
$687$	1.05743	0.0403436
$688$	17.6291	0.672104
$689$	−1.43179	−0.0545470
$690$	−3.29680	−0.125507
$691$	6.75798	0.257086	0.128543	−	0.991704i	$-0.458970\pi$
$691$	6.75798	0.257086	0.128543	+	0.991704i	$0.458970\pi$
$692$	−7.32034	−0.278277
$693$	−7.76143	−0.294832
$694$	14.6614	0.556539
$695$	17.6669	0.670142
$696$	−11.3767	−0.431232
$697$	−1.78295	−0.0675339
$698$	−22.2500	−0.842175
$699$	3.96497	0.149969
$700$	1.60160	0.0605350
$701$	−28.4838	−1.07582	−0.537909	−	0.843003i	$-0.680785\pi$
$701$	−28.4838	−1.07582	−0.537909	+	0.843003i	$0.680785\pi$
$702$	0.506655	0.0191225
$703$	−21.1519	−0.797760
$704$	−0.154822	−0.00583508
$705$	9.75644	0.367449
$706$	19.9121	0.749403
$707$	6.02064	0.226429
$708$	6.68096	0.251086
$709$	28.9199	1.08611	0.543055	−	0.839697i	$-0.317268\pi$
$709$	28.9199	1.08611	0.543055	+	0.839697i	$0.317268\pi$
$710$	−7.58229	−0.284558
$711$	14.5670	0.546304
$712$	−3.45074	−0.129322
$713$	−23.7643	−0.889979
$714$	2.44852	0.0916337
$715$	−0.641326	−0.0239842
$716$	6.59026	0.246289
$717$	−2.42026	−0.0903865
$718$	3.45577	0.128968
$719$	44.2040	1.64853	0.824266	−	0.566203i	$-0.191588\pi$
$719$	44.2040	1.64853	0.824266	+	0.566203i	$0.191588\pi$
$720$	−3.32774	−0.124017
$721$	1.53436	0.0571424
$722$	1.11170	0.0413732
$723$	5.56183	0.206847
$724$	14.4982	0.538822
$725$	−4.73271	−0.175768
$726$	−4.01170	−0.148888
$727$	27.6202	1.02438	0.512188	−	0.858873i	$-0.328835\pi$
$727$	27.6202	1.02438	0.512188	+	0.858873i	$0.328835\pi$
$728$	−0.353486	−0.0131011
$729$	16.0245	0.593501
$730$	1.84450	0.0682680
$731$	36.5728	1.35269
$732$	−18.8509	−0.696748
$733$	−41.6537	−1.53851	−0.769257	−	0.638940i	$-0.779373\pi$
$733$	−41.6537	−1.53851	−0.769257	+	0.638940i	$0.779373\pi$
$734$	−19.9489	−0.736327
$735$	1.05743	0.0390040
$736$	−27.9710	−1.03102
$737$	56.0196	2.06351
$738$	−0.577275	−0.0212498
$739$	22.2885	0.819897	0.409948	−	0.912109i	$-0.365547\pi$
$739$	22.2885	0.819897	0.409948	+	0.912109i	$0.365547\pi$
$740$	8.15929	0.299942
$741$	0.682691	0.0250793
$742$	−5.81191	−0.213362
$743$	−29.0387	−1.06533	−0.532664	−	0.846327i	$-0.678809\pi$
$743$	−29.0387	−1.06533	−0.532664	+	0.846327i	$0.678809\pi$
$744$	−11.5651	−0.423996
$745$	−13.0096	−0.476636
$746$	−3.10787	−0.113787
$747$	−5.61361	−0.205391
$748$	24.2331	0.886051
$749$	16.6271	0.607540
$750$	−0.667437	−0.0243713
$751$	−37.9209	−1.38375	−0.691877	−	0.722016i	$-0.743216\pi$
$751$	−37.9209	−1.38375	−0.691877	+	0.722016i	$0.743216\pi$
$752$	16.3157	0.594972
$753$	−9.51684	−0.346813
$754$	0.464500	0.0169161
$755$	3.09437	0.112616
$756$	−8.26782	−0.300698
$757$	−26.5258	−0.964097	−0.482048	−	0.876145i	$-0.660107\pi$
$757$	−26.5258	−0.964097	−0.482048	+	0.876145i	$0.660107\pi$
$758$	2.26935	0.0824265
$759$	−21.5424	−0.781941
$760$	9.43856	0.342373
$761$	−46.0910	−1.67080	−0.835399	−	0.549644i	$-0.814763\pi$
$761$	−46.0910	−1.67080	−0.835399	+	0.549644i	$0.814763\pi$
$762$	3.33304	0.120743
$763$	−14.6734	−0.531212
$764$	26.8522	0.971477
$765$	−6.90361	−0.249601
$766$	9.34214	0.337545
$767$	−0.613409	−0.0221489
$768$	−7.62259	−0.275056
$769$	−34.4574	−1.24257	−0.621283	−	0.783586i	$-0.713388\pi$
$769$	−34.4574	−1.24257	−0.621283	+	0.783586i	$0.713388\pi$
$770$	−2.60326	−0.0938149
$771$	11.7569	0.423416
$772$	29.5053	1.06192
$773$	8.44735	0.303830	0.151915	−	0.988394i	$-0.451456\pi$
$773$	8.44735	0.303830	0.151915	+	0.988394i	$0.451456\pi$
$774$	11.8414	0.425630
$775$	−4.81108	−0.172819
$776$	−8.06152	−0.289392
$777$	5.38704	0.193259
$778$	15.9154	0.570596
$779$	−2.01788	−0.0722982
$780$	−0.263346	−0.00942930
$781$	−49.5454	−1.77287
$782$	−11.4376	−0.409007
$783$	24.4312	0.873101
$784$	1.76835	0.0631552
$785$	−2.68230	−0.0957354
$786$	−2.83362	−0.101072
$787$	51.0462	1.81960	0.909801	−	0.415045i	$-0.136234\pi$
$787$	51.0462	1.81960	0.909801	+	0.415045i	$0.136234\pi$
$788$	36.8342	1.31216
$789$	−29.5180	−1.05087
$790$	4.88590	0.173832
$791$	−11.7566	−0.418017
$792$	17.6439	0.626949
$793$	1.73078	0.0614618
$794$	−12.3155	−0.437059
$795$	−9.73675	−0.345327
$796$	8.57409	0.303900
$797$	−2.78603	−0.0986864	−0.0493432	−	0.998782i	$-0.515713\pi$
$797$	−2.78603	−0.0986864	−0.0493432	+	0.998782i	$0.515713\pi$
$798$	2.77117	0.0980982
$799$	33.8480	1.19746
$800$	−5.66272	−0.200207
$801$	2.85654	0.100931
$802$	7.97520	0.281614
$803$	12.0526	0.425327
$804$	23.0032	0.811260
$805$	−4.93949	−0.174094
$806$	0.472192	0.0166323
$807$	14.2275	0.500831
$808$	−13.6866	−0.481493
$809$	−38.1443	−1.34108	−0.670542	−	0.741872i	$-0.733938\pi$
$809$	−38.1443	−1.34108	−0.670542	+	0.741872i	$0.733938\pi$
$810$	−0.117915	−0.00414312
$811$	−19.0538	−0.669069	−0.334534	−	0.942384i	$-0.608579\pi$
$811$	−19.0538	−0.669069	−0.334534	+	0.942384i	$0.608579\pi$
$812$	−7.57992	−0.266003
$813$	−13.5698	−0.475912
$814$	−13.2622	−0.464839
$815$	−4.04971	−0.141855
$816$	6.85984	0.240143
$817$	41.3920	1.44812
$818$	−8.56554	−0.299487
$819$	0.292618	0.0102249
$820$	0.778393	0.0271827
$821$	7.48424	0.261202	0.130601	−	0.991435i	$-0.458309\pi$
$821$	7.48424	0.261202	0.130601	+	0.991435i	$0.458309\pi$
$822$	−11.3967	−0.397505
$823$	9.79715	0.341507	0.170754	−	0.985314i	$-0.445380\pi$
$823$	9.79715	0.341507	0.170754	+	0.985314i	$0.445380\pi$
$824$	−3.48803	−0.121511
$825$	−4.36127	−0.151840
$826$	−2.48994	−0.0866359
$827$	−9.87984	−0.343556	−0.171778	−	0.985136i	$-0.554951\pi$
$827$	−9.87984	−0.343556	−0.171778	+	0.985136i	$0.554951\pi$
$828$	14.8874	0.517374
$829$	−16.3048	−0.566291	−0.283145	−	0.959077i	$-0.591378\pi$
$829$	−16.3048	−0.566291	−0.283145	+	0.959077i	$0.591378\pi$
$830$	−1.88286	−0.0653549
$831$	−5.67234	−0.196771
$832$	0.00583704	0.000202363 0
$833$	3.66855	0.127108
$834$	−11.7915	−0.408306
$835$	−14.8449	−0.513728
$836$	27.4263	0.948559
$837$	24.8358	0.858451
$838$	−17.8811	−0.617692
$839$	−36.3165	−1.25378	−0.626892	−	0.779106i	$-0.715673\pi$
$839$	−36.3165	−1.25378	−0.626892	+	0.779106i	$0.715673\pi$
$840$	−2.40384	−0.0829405
$841$	−6.60149	−0.227638
$842$	6.47300	0.223074
$843$	7.02985	0.242121
$844$	23.3311	0.803090
$845$	−12.9758	−0.446382
$846$	10.9592	0.376784
$847$	−6.01061	−0.206527
$848$	−16.2828	−0.559153
$849$	−13.1295	−0.450604
$850$	−2.31554	−0.0794223
$851$	−25.1640	−0.862611
$852$	−20.3447	−0.696998
$853$	−10.4773	−0.358737	−0.179368	−	0.983782i	$-0.557405\pi$
$853$	−10.4773	−0.358737	−0.179368	+	0.983782i	$0.557405\pi$
$854$	7.02555	0.240409
$855$	−7.81330	−0.267209
$856$	−37.7981	−1.29191
$857$	13.4306	0.458780	0.229390	−	0.973335i	$-0.426327\pi$
$857$	13.4306	0.458780	0.229390	+	0.973335i	$0.426327\pi$
$858$	0.428045	0.0146132
$859$	10.9598	0.373945	0.186972	−	0.982365i	$-0.440133\pi$
$859$	10.9598	0.373945	0.186972	+	0.982365i	$0.440133\pi$
$860$	−15.9668	−0.544465
$861$	0.513921	0.0175144
$862$	2.52493	0.0859996
$863$	18.3341	0.624101	0.312051	−	0.950065i	$-0.398984\pi$
$863$	18.3341	0.624101	0.312051	+	0.950065i	$0.398984\pi$
$864$	29.2322	0.994498
$865$	4.57063	0.155406
$866$	−0.731702	−0.0248642
$867$	−3.74515	−0.127192
$868$	−7.70544	−0.261540
$869$	31.9262	1.08302
$870$	3.15878	0.107093
$871$	−2.11203	−0.0715633
$872$	33.3567	1.12960
$873$	6.67337	0.225859
$874$	−12.9447	−0.437861
$875$	−1.00000	−0.0338062
$876$	4.94913	0.167216
$877$	31.7716	1.07285	0.536425	−	0.843948i	$-0.319774\pi$
$877$	31.7716	1.07285	0.536425	+	0.843948i	$0.319774\pi$
$878$	−3.38994	−0.114405
$879$	1.60727	0.0542117
$880$	−7.29335	−0.245859
$881$	22.4519	0.756422	0.378211	−	0.925719i	$-0.376539\pi$
$881$	22.4519	0.756422	0.378211	+	0.925719i	$0.376539\pi$
$882$	1.18779	0.0399949
$883$	−20.1533	−0.678214	−0.339107	−	0.940748i	$-0.610125\pi$
$883$	−20.1533	−0.678214	−0.339107	+	0.940748i	$0.610125\pi$
$884$	−0.913627	−0.0307286
$885$	−4.17142	−0.140221
$886$	−2.86001	−0.0960840
$887$	3.76101	0.126282	0.0631412	−	0.998005i	$-0.479888\pi$
$887$	3.76101	0.126282	0.0631412	+	0.998005i	$0.479888\pi$
$888$	−12.2463	−0.410957
$889$	4.99379	0.167486
$890$	0.958111	0.0321160
$891$	−0.770501	−0.0258127
$892$	14.9289	0.499855
$893$	38.3081	1.28193
$894$	8.68311	0.290407
$895$	−4.11478	−0.137542
$896$	−11.3017	−0.377565
$897$	0.812183	0.0271180
$898$	7.40033	0.246952
$899$	22.7694	0.759402
$900$	3.01396	0.100465
$901$	−33.7797	−1.12537
$902$	−1.26521	−0.0421267
$903$	−10.5418	−0.350810
$904$	26.7261	0.888897
$905$	−9.05231	−0.300909
$906$	−2.06530	−0.0686149
$907$	16.2364	0.539120	0.269560	−	0.962984i	$-0.413122\pi$
$907$	16.2364	0.539120	0.269560	+	0.962984i	$0.413122\pi$
$908$	18.6300	0.618258
$909$	11.3299	0.375788
$910$	0.0981468	0.00325354
$911$	0.430752	0.0142714	0.00713572	−	0.999975i	$-0.497729\pi$
$911$	0.430752	0.0142714	0.00713572	+	0.999975i	$0.497729\pi$
$912$	7.76376	0.257084
$913$	−12.3033	−0.407178
$914$	−17.7555	−0.587299
$915$	11.7700	0.389104
$916$	−1.60160	−0.0529185
$917$	−4.24553	−0.140200
$918$	11.9533	0.394518
$919$	−2.17181	−0.0716416	−0.0358208	−	0.999358i	$-0.511405\pi$
$919$	−2.17181	−0.0716416	−0.0358208	+	0.999358i	$0.511405\pi$
$920$	11.2289	0.370205
$921$	−28.3113	−0.932889
$922$	8.53153	0.280971
$923$	1.86794	0.0614839
$924$	−6.98502	−0.229790
$925$	−5.09445	−0.167504
$926$	4.03655	0.132649
$927$	2.88741	0.0948349
$928$	26.8000	0.879753
$929$	−19.4379	−0.637737	−0.318868	−	0.947799i	$-0.603303\pi$
$929$	−19.4379	−0.637737	−0.318868	+	0.947799i	$0.603303\pi$
$930$	3.21109	0.105296
$931$	4.15195	0.136075
$932$	−6.00541	−0.196714
$933$	5.76095	0.188605
$934$	6.86770	0.224718
$935$	−15.1305	−0.494822
$936$	−0.665203	−0.0217428
$937$	−33.5877	−1.09726	−0.548632	−	0.836064i	$-0.684851\pi$
$937$	−33.5877	−1.09726	−0.548632	+	0.836064i	$0.684851\pi$
$938$	−8.57309	−0.279921
$939$	−15.1334	−0.493861
$940$	−14.7773	−0.481981
$941$	−12.9558	−0.422347	−0.211173	−	0.977449i	$-0.567728\pi$
$941$	−12.9558	−0.422347	−0.211173	+	0.977449i	$0.567728\pi$
$942$	1.79027	0.0583300
$943$	−2.40063	−0.0781754
$944$	−6.97586	−0.227045
$945$	5.16221	0.167927
$946$	25.9526	0.843792
$947$	−0.184491	−0.00599516	−0.00299758	−	0.999996i	$-0.500954\pi$
$947$	−0.184491	−0.00599516	−0.00299758	+	0.999996i	$0.500954\pi$
$948$	13.1098	0.425785
$949$	−0.454402	−0.0147505
$950$	−2.62065	−0.0850253
$951$	13.2370	0.429239
$952$	−8.33965	−0.270290
$953$	16.6567	0.539565	0.269782	−	0.962921i	$-0.413048\pi$
$953$	16.6567	0.539565	0.269782	+	0.962921i	$0.413048\pi$
$954$	−10.9371	−0.354100
$955$	−16.7658	−0.542528
$956$	3.66577	0.118560
$957$	20.6406	0.667216
$958$	−23.3930	−0.755793
$959$	−17.0753	−0.551391
$960$	0.0396941	0.00128112
$961$	−7.85354	−0.253340
$962$	0.500004	0.0161208
$963$	31.2895	1.00829
$964$	−8.42403	−0.271320
$965$	−18.4223	−0.593036
$966$	3.29680	0.106073
$967$	−25.9005	−0.832904	−0.416452	−	0.909158i	$-0.636727\pi$
$967$	−25.9005	−0.832904	−0.416452	+	0.909158i	$0.636727\pi$
$968$	13.6638	0.439171
$969$	16.1064	0.517413
$970$	2.23831	0.0718679
$971$	53.5899	1.71978	0.859891	−	0.510478i	$-0.170532\pi$
$971$	53.5899	1.71978	0.859891	+	0.510478i	$0.170532\pi$
$972$	−25.1199	−0.805720
$973$	−17.6669	−0.566373
$974$	−2.64616	−0.0847884
$975$	0.164426	0.00526586
$976$	19.6829	0.630036
$977$	17.3413	0.554796	0.277398	−	0.960755i	$-0.410528\pi$
$977$	17.3413	0.554796	0.277398	+	0.960755i	$0.410528\pi$
$978$	2.70292	0.0864299
$979$	6.26064	0.200091
$980$	−1.60160	−0.0511614
$981$	−27.6129	−0.881611
$982$	16.0164	0.511102
$983$	6.76950	0.215914	0.107957	−	0.994156i	$-0.465569\pi$
$983$	6.76950	0.215914	0.107957	+	0.994156i	$0.465569\pi$
$984$	−1.16829	−0.0372436
$985$	−22.9983	−0.732787
$986$	10.9588	0.348998
$987$	−9.75644	−0.310551
$988$	−1.03401	−0.0328964
$989$	49.2432	1.56584
$990$	−4.89891	−0.155697
$991$	−32.1461	−1.02115	−0.510577	−	0.859832i	$-0.670568\pi$
$991$	−32.1461	−1.02115	−0.510577	+	0.859832i	$0.670568\pi$
$992$	27.2438	0.864991
$993$	−26.7582	−0.849146
$994$	7.58229	0.240496
$995$	−5.35344	−0.169715
$996$	−5.05205	−0.160080
$997$	−50.4401	−1.59745	−0.798727	−	0.601694i	$-0.794493\pi$
$997$	−50.4401	−1.59745	−0.798727	+	0.601694i	$0.794493\pi$
$998$	−21.0259	−0.665564
$999$	26.2986	0.832052

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.i.1.17	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.i.1.17	✓	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.631186 q^{2} +1.05743 q^{3} -1.60160 q^{4} +1.00000 q^{5} -0.667437 q^{6} -1.00000 q^{7} +2.27328 q^{8} -1.88184 q^{9} +O(q^{10})\)	\(q-0.631186 q^{2} +1.05743 q^{3} -1.60160 q^{4} +1.00000 q^{5} -0.667437 q^{6} -1.00000 q^{7} +2.27328 q^{8} -1.88184 q^{9} -0.631186 q^{10} -4.12439 q^{11} -1.69359 q^{12} +0.155496 q^{13} +0.631186 q^{14} +1.05743 q^{15} +1.76835 q^{16} +3.66855 q^{17} +1.18779 q^{18} +4.15195 q^{19} -1.60160 q^{20} -1.05743 q^{21} +2.60326 q^{22} +4.93949 q^{23} +2.40384 q^{24} +1.00000 q^{25} -0.0981468 q^{26} -5.16221 q^{27} +1.60160 q^{28} -4.73271 q^{29} -0.667437 q^{30} -4.81108 q^{31} -5.66272 q^{32} -4.36127 q^{33} -2.31554 q^{34} -1.00000 q^{35} +3.01396 q^{36} -5.09445 q^{37} -2.62065 q^{38} +0.164426 q^{39} +2.27328 q^{40} -0.486008 q^{41} +0.667437 q^{42} +9.96928 q^{43} +6.60564 q^{44} -1.88184 q^{45} -3.11774 q^{46} +9.22653 q^{47} +1.86991 q^{48} +1.00000 q^{49} -0.631186 q^{50} +3.87924 q^{51} -0.249043 q^{52} -9.20792 q^{53} +3.25832 q^{54} -4.12439 q^{55} -2.27328 q^{56} +4.39041 q^{57} +2.98722 q^{58} -3.94485 q^{59} -1.69359 q^{60} +11.1307 q^{61} +3.03668 q^{62} +1.88184 q^{63} +0.0375382 q^{64} +0.155496 q^{65} +2.75277 q^{66} -13.5825 q^{67} -5.87557 q^{68} +5.22318 q^{69} +0.631186 q^{70} +12.0128 q^{71} -4.27794 q^{72} -2.92228 q^{73} +3.21555 q^{74} +1.05743 q^{75} -6.64979 q^{76} +4.12439 q^{77} -0.103784 q^{78} -7.74082 q^{79} +1.76835 q^{80} +0.186816 q^{81} +0.306762 q^{82} +2.98305 q^{83} +1.69359 q^{84} +3.66855 q^{85} -6.29247 q^{86} -5.00452 q^{87} -9.37591 q^{88} -1.51795 q^{89} +1.18779 q^{90} -0.155496 q^{91} -7.91111 q^{92} -5.08739 q^{93} -5.82366 q^{94} +4.15195 q^{95} -5.98794 q^{96} -3.54620 q^{97} -0.631186 q^{98} +7.76143 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9 - 2 * q^10 - 15 * q^11 - 3 * q^12 - 17 * q^13 + 2 * q^14 + 10 * q^16 - 7 * q^17 - 16 * q^18 - 32 * q^19 + 30 * q^20 - 14 * q^22 + 8 * q^23 - 35 * q^24 + 44 * q^25 - 27 * q^26 + 6 * q^27 - 30 * q^28 - 42 * q^29 - 7 * q^30 - 43 * q^31 - 8 * q^32 - 33 * q^33 - 33 * q^34 - 44 * q^35 - 11 * q^36 - 44 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 - 62 * q^41 + 7 * q^42 - 7 * q^43 - 45 * q^44 + 16 * q^45 - 15 * q^46 + 2 * q^47 - 26 * q^48 + 44 * q^49 - 2 * q^50 - 25 * q^51 - 35 * q^52 - 25 * q^53 - 76 * q^54 - 15 * q^55 + 3 * q^56 - 7 * q^57 - 2 * q^58 - 35 * q^59 - 3 * q^60 - 86 * q^61 - 23 * q^62 - 16 * q^63 - 5 * q^64 - 17 * q^65 - 6 * q^66 + 2 * q^67 - q^68 - 75 * q^69 + 2 * q^70 - 54 * q^71 - 3 * q^72 - 52 * q^73 - 22 * q^74 - 77 * q^76 + 15 * q^77 + 2 * q^78 + 46 * q^79 + 10 * q^80 - 72 * q^81 - 16 * q^82 + 26 * q^83 + 3 * q^84 - 7 * q^85 - 33 * q^86 - 8 * q^87 - 23 * q^88 - 105 * q^89 - 16 * q^90 + 17 * q^91 - 41 * q^92 - 11 * q^93 - 47 * q^94 - 32 * q^95 - 39 * q^96 - 80 * q^97 - 2 * q^98 - 53 * q^99

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