LMFDB - Embedded newform 8007.2.a.j.1.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.29
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.131411 q^{2} -1.00000 q^{3} -1.98273 q^{4} -1.75160 q^{5} +0.131411 q^{6} -3.32975 q^{7} +0.523376 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.131411 q^{2} -1.00000 q^{3} -1.98273 q^{4} -1.75160 q^{5} +0.131411 q^{6} -3.32975 q^{7} +0.523376 q^{8} +1.00000 q^{9} +0.230180 q^{10} +1.63217 q^{11} +1.98273 q^{12} +0.746925 q^{13} +0.437567 q^{14} +1.75160 q^{15} +3.89668 q^{16} +1.00000 q^{17} -0.131411 q^{18} +0.00279817 q^{19} +3.47295 q^{20} +3.32975 q^{21} -0.214485 q^{22} +3.02868 q^{23} -0.523376 q^{24} -1.93189 q^{25} -0.0981544 q^{26} -1.00000 q^{27} +6.60201 q^{28} -9.67725 q^{29} -0.230180 q^{30} +8.99614 q^{31} -1.55882 q^{32} -1.63217 q^{33} -0.131411 q^{34} +5.83240 q^{35} -1.98273 q^{36} +4.98303 q^{37} -0.000367711 q^{38} -0.746925 q^{39} -0.916746 q^{40} -6.91975 q^{41} -0.437567 q^{42} -11.6504 q^{43} -3.23615 q^{44} -1.75160 q^{45} -0.398002 q^{46} +2.19566 q^{47} -3.89668 q^{48} +4.08727 q^{49} +0.253873 q^{50} -1.00000 q^{51} -1.48095 q^{52} +10.6601 q^{53} +0.131411 q^{54} -2.85891 q^{55} -1.74271 q^{56} -0.00279817 q^{57} +1.27170 q^{58} -6.66092 q^{59} -3.47295 q^{60} -11.3075 q^{61} -1.18219 q^{62} -3.32975 q^{63} -7.58852 q^{64} -1.30832 q^{65} +0.214485 q^{66} -7.22729 q^{67} -1.98273 q^{68} -3.02868 q^{69} -0.766443 q^{70} +3.50379 q^{71} +0.523376 q^{72} +4.25786 q^{73} -0.654827 q^{74} +1.93189 q^{75} -0.00554801 q^{76} -5.43472 q^{77} +0.0981544 q^{78} +7.29929 q^{79} -6.82544 q^{80} +1.00000 q^{81} +0.909333 q^{82} -17.2337 q^{83} -6.60201 q^{84} -1.75160 q^{85} +1.53100 q^{86} +9.67725 q^{87} +0.854237 q^{88} +8.66461 q^{89} +0.230180 q^{90} -2.48708 q^{91} -6.00505 q^{92} -8.99614 q^{93} -0.288535 q^{94} -0.00490127 q^{95} +1.55882 q^{96} -3.84649 q^{97} -0.537113 q^{98} +1.63217 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * 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 $

$2$	−0.131411	−0.0929218	−0.0464609	−	0.998920i	$-0.514794\pi$
$2$	−0.131411	−0.0929218	−0.0464609	+	0.998920i	$0.514794\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.98273	−0.991366
$5$	−1.75160	−0.783340	−0.391670	−	0.920106i	$-0.628102\pi$
$5$	−1.75160	−0.783340	−0.391670	+	0.920106i	$0.628102\pi$
$6$	0.131411	0.0536484
$7$	−3.32975	−1.25853	−0.629264	−	0.777191i	$-0.716644\pi$
$7$	−3.32975	−1.25853	−0.629264	+	0.777191i	$0.716644\pi$
$8$	0.523376	0.185041
$9$	1.00000	0.333333
$10$	0.230180	0.0727894
$11$	1.63217	0.492117	0.246058	−	0.969255i	$-0.420864\pi$
$11$	1.63217	0.492117	0.246058	+	0.969255i	$0.420864\pi$
$12$	1.98273	0.572365
$13$	0.746925	0.207160	0.103580	−	0.994621i	$-0.466970\pi$
$13$	0.746925	0.207160	0.103580	+	0.994621i	$0.466970\pi$
$14$	0.437567	0.116945
$15$	1.75160	0.452261
$16$	3.89668	0.974171
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.131411	−0.0309739
$19$	0.00279817	0.000641944 0	0.000320972	−	1.00000i	$-0.499898\pi$
$19$	0.00279817	0.000641944 0	0.000320972		1.00000i	$0.499898\pi$
$20$	3.47295	0.776576
$21$	3.32975	0.726612
$22$	−0.214485	−0.0457284
$23$	3.02868	0.631523	0.315761	−	0.948839i	$-0.397740\pi$
$23$	3.02868	0.631523	0.315761	+	0.948839i	$0.397740\pi$
$24$	−0.523376	−0.106834
$25$	−1.93189	−0.386379
$26$	−0.0981544	−0.0192497
$27$	−1.00000	−0.192450
$28$	6.60201	1.24766
$29$	−9.67725	−1.79702	−0.898511	−	0.438952i	$-0.855350\pi$
$29$	−9.67725	−1.79702	−0.898511	+	0.438952i	$0.855350\pi$
$30$	−0.230180	−0.0420250
$31$	8.99614	1.61575	0.807877	−	0.589351i	$-0.200616\pi$
$31$	8.99614	1.61575	0.807877	+	0.589351i	$0.200616\pi$
$32$	−1.55882	−0.275563
$33$	−1.63217	−0.284124
$34$	−0.131411	−0.0225368
$35$	5.83240	0.985856
$36$	−1.98273	−0.330455
$37$	4.98303	0.819206	0.409603	−	0.912264i	$-0.365667\pi$
$37$	4.98303	0.819206	0.409603	+	0.912264i	$0.365667\pi$
$38$	−0.000367711 0	−5.96506e−5 0
$39$	−0.746925	−0.119604
$40$	−0.916746	−0.144950
$41$	−6.91975	−1.08068	−0.540341	−	0.841446i	$-0.681705\pi$
$41$	−6.91975	−1.08068	−0.540341	+	0.841446i	$0.681705\pi$
$42$	−0.437567	−0.0675181
$43$	−11.6504	−1.77668	−0.888338	−	0.459191i	$-0.848139\pi$
$43$	−11.6504	−1.77668	−0.888338	+	0.459191i	$0.848139\pi$
$44$	−3.23615	−0.487868
$45$	−1.75160	−0.261113
$46$	−0.398002	−0.0586823
$47$	2.19566	0.320271	0.160135	−	0.987095i	$-0.448807\pi$
$47$	2.19566	0.320271	0.160135	+	0.987095i	$0.448807\pi$
$48$	−3.89668	−0.562438
$49$	4.08727	0.583895
$50$	0.253873	0.0359030
$51$	−1.00000	−0.140028
$52$	−1.48095	−0.205371
$53$	10.6601	1.46427	0.732135	−	0.681159i	$-0.238524\pi$
$53$	10.6601	1.46427	0.732135	+	0.681159i	$0.238524\pi$
$54$	0.131411	0.0178828
$55$	−2.85891	−0.385495
$56$	−1.74271	−0.232880
$57$	−0.00279817	−0.000370626 0
$58$	1.27170	0.166982
$59$	−6.66092	−0.867178	−0.433589	−	0.901111i	$-0.642753\pi$
$59$	−6.66092	−0.867178	−0.433589	+	0.901111i	$0.642753\pi$
$60$	−3.47295	−0.448356
$61$	−11.3075	−1.44777	−0.723887	−	0.689918i	$-0.757646\pi$
$61$	−11.3075	−1.44777	−0.723887	+	0.689918i	$0.757646\pi$
$62$	−1.18219	−0.150139
$63$	−3.32975	−0.419510
$64$	−7.58852	−0.948565
$65$	−1.30832	−0.162277
$66$	0.214485	0.0264013
$67$	−7.22729	−0.882954	−0.441477	−	0.897273i	$-0.645545\pi$
$67$	−7.22729	−0.882954	−0.441477	+	0.897273i	$0.645545\pi$
$68$	−1.98273	−0.240441
$69$	−3.02868	−0.364610
$70$	−0.766443	−0.0916075
$71$	3.50379	0.415824	0.207912	−	0.978148i	$-0.433333\pi$
$71$	3.50379	0.415824	0.207912	+	0.978148i	$0.433333\pi$
$72$	0.523376	0.0616804
$73$	4.25786	0.498345	0.249173	−	0.968459i	$-0.419841\pi$
$73$	4.25786	0.498345	0.249173	+	0.968459i	$0.419841\pi$
$74$	−0.654827	−0.0761221
$75$	1.93189	0.223076
$76$	−0.00554801	−0.000636401 0
$77$	−5.43472	−0.619343
$78$	0.0981544	0.0111138
$79$	7.29929	0.821234	0.410617	−	0.911808i	$-0.365313\pi$
$79$	7.29929	0.821234	0.410617	+	0.911808i	$0.365313\pi$
$80$	−6.82544	−0.763107
$81$	1.00000	0.111111
$82$	0.909333	0.100419
$83$	−17.2337	−1.89165	−0.945824	−	0.324681i	$-0.894743\pi$
$83$	−17.2337	−1.89165	−0.945824	+	0.324681i	$0.894743\pi$
$84$	−6.60201	−0.720338
$85$	−1.75160	−0.189988
$86$	1.53100	0.165092
$87$	9.67725	1.03751
$88$	0.854237	0.0910619
$89$	8.66461	0.918447	0.459223	−	0.888321i	$-0.348128\pi$
$89$	8.66461	0.918447	0.459223	+	0.888321i	$0.348128\pi$
$90$	0.230180	0.0242631
$91$	−2.48708	−0.260717
$92$	−6.00505	−0.626070
$93$	−8.99614	−0.932856
$94$	−0.288535	−0.0297601
$95$	−0.00490127	−0.000502860 0
$96$	1.55882	0.159096
$97$	−3.84649	−0.390552	−0.195276	−	0.980748i	$-0.562560\pi$
$97$	−3.84649	−0.390552	−0.195276	+	0.980748i	$0.562560\pi$
$98$	−0.537113	−0.0542566
$99$	1.63217	0.164039
$100$	3.83043	0.383043
$101$	−0.156704	−0.0155926	−0.00779631	−	0.999970i	$-0.502482\pi$
$101$	−0.156704	−0.0155926	−0.00779631	+	0.999970i	$0.502482\pi$
$102$	0.131411	0.0130117
$103$	−4.07346	−0.401370	−0.200685	−	0.979656i	$-0.564317\pi$
$103$	−4.07346	−0.401370	−0.200685	+	0.979656i	$0.564317\pi$
$104$	0.390923	0.0383331
$105$	−5.83240	−0.569184
$106$	−1.40085	−0.136063
$107$	−19.4583	−1.88110	−0.940550	−	0.339654i	$-0.889690\pi$
$107$	−19.4583	−1.88110	−0.940550	+	0.339654i	$0.889690\pi$
$108$	1.98273	0.190788
$109$	−15.4770	−1.48243	−0.741214	−	0.671268i	$-0.765750\pi$
$109$	−15.4770	−1.48243	−0.741214	+	0.671268i	$0.765750\pi$
$110$	0.375692	0.0358209
$111$	−4.98303	−0.472969
$112$	−12.9750	−1.22602
$113$	5.25157	0.494026	0.247013	−	0.969012i	$-0.420551\pi$
$113$	5.25157	0.494026	0.247013	+	0.969012i	$0.420551\pi$
$114$	0.000367711 0	3.44393e−5 0
$115$	−5.30504	−0.494697
$116$	19.1874	1.78150
$117$	0.746925	0.0690533
$118$	0.875320	0.0805797
$119$	−3.32975	−0.305238
$120$	0.916746	0.0836870
$121$	−8.33603	−0.757821
$122$	1.48593	0.134530
$123$	6.91975	0.623933
$124$	−17.8369	−1.60180
$125$	12.1419	1.08601
$126$	0.437567	0.0389816
$127$	4.27016	0.378915	0.189458	−	0.981889i	$-0.439327\pi$
$127$	4.27016	0.378915	0.189458	+	0.981889i	$0.439327\pi$
$128$	4.11486	0.363705
$129$	11.6504	1.02576
$130$	0.171927	0.0150790
$131$	−2.44736	−0.213827	−0.106913	−	0.994268i	$-0.534097\pi$
$131$	−2.44736	−0.213827	−0.106913	+	0.994268i	$0.534097\pi$
$132$	3.23615	0.281671
$133$	−0.00931721	−0.000807904 0
$134$	0.949747	0.0820457
$135$	1.75160	0.150754
$136$	0.523376	0.0448791
$137$	10.4571	0.893408	0.446704	−	0.894682i	$-0.352598\pi$
$137$	10.4571	0.893408	0.446704	+	0.894682i	$0.352598\pi$
$138$	0.398002	0.0338802
$139$	−2.13034	−0.180693	−0.0903467	−	0.995910i	$-0.528798\pi$
$139$	−2.13034	−0.180693	−0.0903467	+	0.995910i	$0.528798\pi$
$140$	−11.5641	−0.977343
$141$	−2.19566	−0.184908
$142$	−0.460438	−0.0386391
$143$	1.21911	0.101947
$144$	3.89668	0.324724
$145$	16.9507	1.40768
$146$	−0.559531	−0.0463071
$147$	−4.08727	−0.337112
$148$	−9.88002	−0.812132
$149$	0.248196	0.0203330	0.0101665	−	0.999948i	$-0.496764\pi$
$149$	0.248196	0.0203330	0.0101665	+	0.999948i	$0.496764\pi$
$150$	−0.253873	−0.0207286
$151$	8.72959	0.710404	0.355202	−	0.934790i	$-0.384412\pi$
$151$	8.72959	0.710404	0.355202	+	0.934790i	$0.384412\pi$
$152$	0.00146449	0.000118786 0
$153$	1.00000	0.0808452
$154$	0.714183	0.0575505
$155$	−15.7576	−1.26568
$156$	1.48095	0.118571
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−0.959209	−0.0763106
$159$	−10.6601	−0.845397
$160$	2.73043	0.215859
$161$	−10.0848	−0.794790
$162$	−0.131411	−0.0103246
$163$	−1.27401	−0.0997883	−0.0498942	−	0.998755i	$-0.515888\pi$
$163$	−1.27401	−0.0997883	−0.0498942	+	0.998755i	$0.515888\pi$
$164$	13.7200	1.07135
$165$	2.85891	0.222565
$166$	2.26471	0.175775
$167$	4.00729	0.310093	0.155047	−	0.987907i	$-0.450447\pi$
$167$	4.00729	0.310093	0.155047	+	0.987907i	$0.450447\pi$
$168$	1.74271	0.134453
$169$	−12.4421	−0.957085
$170$	0.230180	0.0176540
$171$	0.00279817	0.000213981 0
$172$	23.0997	1.76133
$173$	−3.52577	−0.268059	−0.134030	−	0.990977i	$-0.542792\pi$
$173$	−3.52577	−0.268059	−0.134030	+	0.990977i	$0.542792\pi$
$174$	−1.27170	−0.0964074
$175$	6.43273	0.486269
$176$	6.36004	0.479406
$177$	6.66092	0.500665
$178$	−1.13863	−0.0853437
$179$	−3.70572	−0.276979	−0.138489	−	0.990364i	$-0.544225\pi$
$179$	−3.70572	−0.276979	−0.138489	+	0.990364i	$0.544225\pi$
$180$	3.47295	0.258859
$181$	−17.3241	−1.28769	−0.643846	−	0.765155i	$-0.722662\pi$
$181$	−17.3241	−1.28769	−0.643846	+	0.765155i	$0.722662\pi$
$182$	0.326830	0.0242263
$183$	11.3075	0.835873
$184$	1.58514	0.116858
$185$	−8.72829	−0.641716
$186$	1.18219	0.0866827
$187$	1.63217	0.119356
$188$	−4.35341	−0.317505
$189$	3.32975	0.242204
$190$	0.000644082 0	4.67267e−5 0
$191$	5.38426	0.389591	0.194796	−	0.980844i	$-0.437596\pi$
$191$	5.38426	0.389591	0.194796	+	0.980844i	$0.437596\pi$
$192$	7.58852	0.547654
$193$	7.52794	0.541873	0.270936	−	0.962597i	$-0.412667\pi$
$193$	7.52794	0.541873	0.270936	+	0.962597i	$0.412667\pi$
$194$	0.505473	0.0362908
$195$	1.30832	0.0936904
$196$	−8.10395	−0.578853
$197$	12.5437	0.893704	0.446852	−	0.894608i	$-0.352545\pi$
$197$	12.5437	0.893704	0.446852	+	0.894608i	$0.352545\pi$
$198$	−0.214485	−0.0152428
$199$	6.80495	0.482390	0.241195	−	0.970477i	$-0.422461\pi$
$199$	6.80495	0.482390	0.241195	+	0.970477i	$0.422461\pi$
$200$	−1.01111	−0.0714960
$201$	7.22729	0.509774
$202$	0.0205927	0.00144889
$203$	32.2229	2.26160
$204$	1.98273	0.138819
$205$	12.1206	0.846542
$206$	0.535298	0.0372960
$207$	3.02868	0.210508
$208$	2.91053	0.201809
$209$	0.00456708	0.000315911 0
$210$	0.766443	0.0528896
$211$	−8.67872	−0.597468	−0.298734	−	0.954336i	$-0.596564\pi$
$211$	−8.67872	−0.597468	−0.298734	+	0.954336i	$0.596564\pi$
$212$	−21.1360	−1.45163
$213$	−3.50379	−0.240076
$214$	2.55703	0.174795
$215$	20.4069	1.39174
$216$	−0.523376	−0.0356112
$217$	−29.9549	−2.03347
$218$	2.03385	0.137750
$219$	−4.25786	−0.287720
$220$	5.66844	0.382166
$221$	0.746925	0.0502436
$222$	0.654827	0.0439491
$223$	−21.3462	−1.42945	−0.714724	−	0.699407i	$-0.753447\pi$
$223$	−21.3462	−1.42945	−0.714724	+	0.699407i	$0.753447\pi$
$224$	5.19049	0.346804
$225$	−1.93189	−0.128793
$226$	−0.690116	−0.0459058
$227$	−15.3280	−1.01735	−0.508676	−	0.860958i	$-0.669865\pi$
$227$	−15.3280	−1.01735	−0.508676	+	0.860958i	$0.669865\pi$
$228$	0.00554801	0.000367426 0
$229$	11.3514	0.750119	0.375059	−	0.927001i	$-0.377622\pi$
$229$	11.3514	0.750119	0.375059	+	0.927001i	$0.377622\pi$
$230$	0.697141	0.0459681
$231$	5.43472	0.357578
$232$	−5.06484	−0.332523
$233$	−13.9413	−0.913324	−0.456662	−	0.889640i	$-0.650955\pi$
$233$	−13.9413	−0.913324	−0.456662	+	0.889640i	$0.650955\pi$
$234$	−0.0981544	−0.00641655
$235$	−3.84593	−0.250881
$236$	13.2068	0.859690
$237$	−7.29929	−0.474140
$238$	0.437567	0.0283633
$239$	16.1994	1.04785	0.523927	−	0.851763i	$-0.324466\pi$
$239$	16.1994	1.04785	0.523927	+	0.851763i	$0.324466\pi$
$240$	6.82544	0.440580
$241$	18.5711	1.19627	0.598134	−	0.801396i	$-0.295909\pi$
$241$	18.5711	1.19627	0.598134	+	0.801396i	$0.295909\pi$
$242$	1.09545	0.0704181
$243$	−1.00000	−0.0641500
$244$	22.4197	1.43527
$245$	−7.15926	−0.457388
$246$	−0.909333	−0.0579769
$247$	0.00209002	0.000132985 0
$248$	4.70836	0.298981
$249$	17.2337	1.09214
$250$	−1.59558	−0.100914
$251$	28.6529	1.80856	0.904278	−	0.426945i	$-0.140410\pi$
$251$	28.6529	1.80856	0.904278	+	0.426945i	$0.140410\pi$
$252$	6.60201	0.415887
$253$	4.94331	0.310783
$254$	−0.561147	−0.0352095
$255$	1.75160	0.109690
$256$	14.6363	0.914769
$257$	−10.5167	−0.656012	−0.328006	−	0.944676i	$-0.606377\pi$
$257$	−10.5167	−0.656012	−0.328006	+	0.944676i	$0.606377\pi$
$258$	−1.53100	−0.0953158
$259$	−16.5923	−1.03099
$260$	2.59404	0.160875
$261$	−9.67725	−0.599007
$262$	0.321611	0.0198692
$263$	15.9896	0.985958	0.492979	−	0.870041i	$-0.335908\pi$
$263$	15.9896	0.985958	0.492979	+	0.870041i	$0.335908\pi$
$264$	−0.854237	−0.0525746
$265$	−18.6722	−1.14702
$266$	0.00122439	7.50719e−5 0
$267$	−8.66461	−0.530265
$268$	14.3298	0.875330
$269$	−18.7434	−1.14280	−0.571402	−	0.820670i	$-0.693600\pi$
$269$	−18.7434	−1.14280	−0.571402	+	0.820670i	$0.693600\pi$
$270$	−0.230180	−0.0140083
$271$	26.1000	1.58546	0.792730	−	0.609573i	$-0.208659\pi$
$271$	26.1000	1.58546	0.792730	+	0.609573i	$0.208659\pi$
$272$	3.89668	0.236271
$273$	2.48708	0.150525
$274$	−1.37418	−0.0830171
$275$	−3.15317	−0.190143
$276$	6.00505	0.361462
$277$	−7.71820	−0.463742	−0.231871	−	0.972747i	$-0.574485\pi$
$277$	−7.71820	−0.463742	−0.231871	+	0.972747i	$0.574485\pi$
$278$	0.279951	0.0167903
$279$	8.99614	0.538585
$280$	3.05254	0.182424
$281$	15.8556	0.945867	0.472933	−	0.881098i	$-0.343195\pi$
$281$	15.8556	0.945867	0.472933	+	0.881098i	$0.343195\pi$
$282$	0.288535	0.0171820
$283$	31.5897	1.87781	0.938906	−	0.344174i	$-0.111841\pi$
$283$	31.5897	1.87781	0.938906	+	0.344174i	$0.111841\pi$
$284$	−6.94708	−0.412233
$285$	0.00490127	0.000290326 0
$286$	−0.160204	−0.00947308
$287$	23.0411	1.36007
$288$	−1.55882	−0.0918543
$289$	1.00000	0.0588235
$290$	−2.22751	−0.130804
$291$	3.84649	0.225485
$292$	−8.44220	−0.494042
$293$	−20.1410	−1.17665	−0.588324	−	0.808625i	$-0.700212\pi$
$293$	−20.1410	−1.17665	−0.588324	+	0.808625i	$0.700212\pi$
$294$	0.537113	0.0313251
$295$	11.6673	0.679295
$296$	2.60800	0.151587
$297$	−1.63217	−0.0947079
$298$	−0.0326157	−0.00188938
$299$	2.26220	0.130826
$300$	−3.83043	−0.221150
$301$	38.7931	2.23600
$302$	−1.14717	−0.0660120
$303$	0.156704	0.00900240
$304$	0.0109036	0.000625363 0
$305$	19.8062	1.13410
$306$	−0.131411	−0.00751228
$307$	−2.65922	−0.151770	−0.0758848	−	0.997117i	$-0.524178\pi$
$307$	−2.65922	−0.151770	−0.0758848	+	0.997117i	$0.524178\pi$
$308$	10.7756	0.613996
$309$	4.07346	0.231731
$310$	2.07073	0.117610
$311$	23.5576	1.33583	0.667914	−	0.744238i	$-0.267187\pi$
$311$	23.5576	1.33583	0.667914	+	0.744238i	$0.267187\pi$
$312$	−0.390923	−0.0221316
$313$	−12.5272	−0.708078	−0.354039	−	0.935231i	$-0.615192\pi$
$313$	−12.5272	−0.708078	−0.354039	+	0.935231i	$0.615192\pi$
$314$	0.131411	0.00741597
$315$	5.83240	0.328619
$316$	−14.4725	−0.814143
$317$	−12.7062	−0.713652	−0.356826	−	0.934171i	$-0.616141\pi$
$317$	−12.7062	−0.713652	−0.356826	+	0.934171i	$0.616141\pi$
$318$	1.40085	0.0785558
$319$	−15.7949	−0.884344
$320$	13.2921	0.743049
$321$	19.4583	1.08605
$322$	1.32525	0.0738533
$323$	0.00279817	0.000155694 0
$324$	−1.98273	−0.110152
$325$	−1.44298	−0.0800421
$326$	0.167420	0.00927251
$327$	15.4770	0.855881
$328$	−3.62163	−0.199971
$329$	−7.31102	−0.403070
$330$	−0.375692	−0.0206812
$331$	12.1112	0.665690	0.332845	−	0.942982i	$-0.391991\pi$
$331$	12.1112	0.665690	0.332845	+	0.942982i	$0.391991\pi$
$332$	34.1698	1.87531
$333$	4.98303	0.273069
$334$	−0.526603	−0.0288144
$335$	12.6593	0.691653
$336$	12.9750	0.707844
$337$	21.5334	1.17300	0.586499	−	0.809950i	$-0.300506\pi$
$337$	21.5334	1.17300	0.586499	+	0.809950i	$0.300506\pi$
$338$	1.63503	0.0889341
$339$	−5.25157	−0.285226
$340$	3.47295	0.188347
$341$	14.6832	0.795140
$342$	−0.000367711 0	−1.98835e−5 0
$343$	9.69869	0.523680
$344$	−6.09756	−0.328758
$345$	5.30504	0.285613
$346$	0.463325	0.0249085
$347$	−4.33733	−0.232840	−0.116420	−	0.993200i	$-0.537142\pi$
$347$	−4.33733	−0.232840	−0.116420	+	0.993200i	$0.537142\pi$
$348$	−19.1874	−1.02855
$349$	−30.1358	−1.61313	−0.806565	−	0.591146i	$-0.798676\pi$
$349$	−30.1358	−1.61313	−0.806565	+	0.591146i	$0.798676\pi$
$350$	−0.845334	−0.0451850
$351$	−0.746925	−0.0398679
$352$	−2.54425	−0.135609
$353$	23.2240	1.23609	0.618045	−	0.786143i	$-0.287925\pi$
$353$	23.2240	1.23609	0.618045	+	0.786143i	$0.287925\pi$
$354$	−0.875320	−0.0465227
$355$	−6.13725	−0.325731
$356$	−17.1796	−0.910516
$357$	3.32975	0.176229
$358$	0.486974	0.0257374
$359$	−25.9092	−1.36744	−0.683718	−	0.729746i	$-0.739638\pi$
$359$	−25.9092	−1.36744	−0.683718	+	0.729746i	$0.739638\pi$
$360$	−0.916746	−0.0483167
$361$	−19.0000	−1.00000
$362$	2.27659	0.119655
$363$	8.33603	0.437528
$364$	4.93121	0.258465
$365$	−7.45808	−0.390374
$366$	−1.48593	−0.0776708
$367$	18.4880	0.965067	0.482533	−	0.875878i	$-0.339717\pi$
$367$	18.4880	0.965067	0.482533	+	0.875878i	$0.339717\pi$
$368$	11.8018	0.615211
$369$	−6.91975	−0.360228
$370$	1.14700	0.0596295
$371$	−35.4954	−1.84283
$372$	17.8369	0.924802
$373$	13.9727	0.723478	0.361739	−	0.932279i	$-0.382183\pi$
$373$	13.9727	0.723478	0.361739	+	0.932279i	$0.382183\pi$
$374$	−0.214485	−0.0110908
$375$	−12.1419	−0.627006
$376$	1.14916	0.0592633
$377$	−7.22819	−0.372271
$378$	−0.437567	−0.0225060
$379$	35.1255	1.80428	0.902138	−	0.431448i	$-0.141997\pi$
$379$	35.1255	1.80428	0.902138	+	0.431448i	$0.141997\pi$
$380$	0.00971790	0.000498518 0
$381$	−4.27016	−0.218767
$382$	−0.707553	−0.0362015
$383$	−38.4186	−1.96310	−0.981549	−	0.191213i	$-0.938758\pi$
$383$	−38.4186	−1.96310	−0.981549	+	0.191213i	$0.938758\pi$
$384$	−4.11486	−0.209985
$385$	9.51945	0.485156
$386$	−0.989256	−0.0503518
$387$	−11.6504	−0.592225
$388$	7.62656	0.387180
$389$	−4.40764	−0.223476	−0.111738	−	0.993738i	$-0.535642\pi$
$389$	−4.40764	−0.223476	−0.111738	+	0.993738i	$0.535642\pi$
$390$	−0.171927	−0.00870588
$391$	3.02868	0.153167
$392$	2.13918	0.108045
$393$	2.44736	0.123453
$394$	−1.64839	−0.0830446
$395$	−12.7854	−0.643305
$396$	−3.23615	−0.162623
$397$	6.15730	0.309026	0.154513	−	0.987991i	$-0.450619\pi$
$397$	6.15730	0.309026	0.154513	+	0.987991i	$0.450619\pi$
$398$	−0.894247	−0.0448245
$399$	0.00931721	0.000466444 0
$400$	−7.52798	−0.376399
$401$	−5.61886	−0.280593	−0.140296	−	0.990110i	$-0.544806\pi$
$401$	−5.61886	−0.280593	−0.140296	+	0.990110i	$0.544806\pi$
$402$	−0.949747	−0.0473691
$403$	6.71944	0.334719
$404$	0.310702	0.0154580
$405$	−1.75160	−0.0870378
$406$	−4.23445	−0.210152
$407$	8.13314	0.403145
$408$	−0.523376	−0.0259110
$409$	25.1618	1.24417	0.622085	−	0.782950i	$-0.286286\pi$
$409$	25.1618	1.24417	0.622085	+	0.782950i	$0.286286\pi$
$410$	−1.59279	−0.0786622
$411$	−10.4571	−0.515809
$412$	8.07657	0.397904
$413$	22.1792	1.09137
$414$	−0.398002	−0.0195608
$415$	30.1866	1.48180
$416$	−1.16432	−0.0570856
$417$	2.13034	0.104323
$418$	−0.000600165 0	−2.93550e−5 0
$419$	−23.7383	−1.15969	−0.579846	−	0.814726i	$-0.696887\pi$
$419$	−23.7383	−1.15969	−0.579846	+	0.814726i	$0.696887\pi$
$420$	11.5641	0.564270
$421$	33.7899	1.64682	0.823410	−	0.567447i	$-0.192069\pi$
$421$	33.7899	1.64682	0.823410	+	0.567447i	$0.192069\pi$
$422$	1.14048	0.0555178
$423$	2.19566	0.106757
$424$	5.57921	0.270951
$425$	−1.93189	−0.0937106
$426$	0.460438	0.0223083
$427$	37.6511	1.82207
$428$	38.5805	1.86486
$429$	−1.21911	−0.0588590
$430$	−2.68170	−0.129323
$431$	−30.9458	−1.49060	−0.745302	−	0.666727i	$-0.767695\pi$
$431$	−30.9458	−1.49060	−0.745302	+	0.666727i	$0.767695\pi$
$432$	−3.89668	−0.187479
$433$	24.4649	1.17571	0.587853	−	0.808968i	$-0.299973\pi$
$433$	24.4649	1.17571	0.587853	+	0.808968i	$0.299973\pi$
$434$	3.93642	0.188954
$435$	−16.9507	−0.812723
$436$	30.6867	1.46963
$437$	0.00847475	0.000405402 0
$438$	0.559531	0.0267354
$439$	−19.7202	−0.941194	−0.470597	−	0.882348i	$-0.655961\pi$
$439$	−19.7202	−0.941194	−0.470597	+	0.882348i	$0.655961\pi$
$440$	−1.49628	−0.0713324
$441$	4.08727	0.194632
$442$	−0.0981544	−0.00466873
$443$	−0.328670	−0.0156156	−0.00780779	−	0.999970i	$-0.502485\pi$
$443$	−0.328670	−0.0156156	−0.00780779	+	0.999970i	$0.502485\pi$
$444$	9.88002	0.468885
$445$	−15.1769	−0.719456
$446$	2.80513	0.132827
$447$	−0.248196	−0.0117393
$448$	25.2679	1.19380
$449$	−7.24576	−0.341948	−0.170974	−	0.985275i	$-0.554691\pi$
$449$	−7.24576	−0.341948	−0.170974	+	0.985275i	$0.554691\pi$
$450$	0.253873	0.0119677
$451$	−11.2942	−0.531822
$452$	−10.4125	−0.489761
$453$	−8.72959	−0.410152
$454$	2.01427	0.0945342
$455$	4.35637	0.204230
$456$	−0.00146449	−6.85812e−5 0
$457$	36.8443	1.72350	0.861752	−	0.507331i	$-0.169368\pi$
$457$	36.8443	1.72350	0.861752	+	0.507331i	$0.169368\pi$
$458$	−1.49170	−0.0697024
$459$	−1.00000	−0.0466760
$460$	10.5185	0.490426
$461$	29.0769	1.35425	0.677124	−	0.735869i	$-0.263226\pi$
$461$	29.0769	1.35425	0.677124	+	0.735869i	$0.263226\pi$
$462$	−0.714183	−0.0332268
$463$	21.4156	0.995268	0.497634	−	0.867387i	$-0.334202\pi$
$463$	21.4156	0.995268	0.497634	+	0.867387i	$0.334202\pi$
$464$	−37.7092	−1.75061
$465$	15.7576	0.730743
$466$	1.83204	0.0848677
$467$	18.4891	0.855573	0.427787	−	0.903880i	$-0.359293\pi$
$467$	18.4891	0.855573	0.427787	+	0.903880i	$0.359293\pi$
$468$	−1.48095	−0.0684570
$469$	24.0651	1.11122
$470$	0.505398	0.0233123
$471$	1.00000	0.0460776
$472$	−3.48616	−0.160464
$473$	−19.0155	−0.874332
$474$	0.959209	0.0440579
$475$	−0.00540576	−0.000248033 0
$476$	6.60201	0.302603
$477$	10.6601	0.488090
$478$	−2.12879	−0.0973685
$479$	−22.0171	−1.00599	−0.502994	−	0.864290i	$-0.667768\pi$
$479$	−22.0171	−1.00599	−0.502994	+	0.864290i	$0.667768\pi$
$480$	−2.73043	−0.124627
$481$	3.72195	0.169707
$482$	−2.44045	−0.111159
$483$	10.0848	0.458872
$484$	16.5281	0.751278
$485$	6.73752	0.305935
$486$	0.131411	0.00596094
$487$	−25.8567	−1.17168	−0.585840	−	0.810426i	$-0.699235\pi$
$487$	−25.8567	−1.17168	−0.585840	+	0.810426i	$0.699235\pi$
$488$	−5.91806	−0.267898
$489$	1.27401	0.0576128
$490$	0.940807	0.0425013
$491$	24.8296	1.12054	0.560271	−	0.828309i	$-0.310697\pi$
$491$	24.8296	1.12054	0.560271	+	0.828309i	$0.310697\pi$
$492$	−13.7200	−0.618545
$493$	−9.67725	−0.435842
$494$	−0.000274652 0	−1.23572e−5 0
$495$	−2.85891	−0.128498
$496$	35.0551	1.57402
$497$	−11.6668	−0.523326
$498$	−2.26471	−0.101484
$499$	−2.38244	−0.106653	−0.0533263	−	0.998577i	$-0.516982\pi$
$499$	−2.38244	−0.106653	−0.0533263	+	0.998577i	$0.516982\pi$
$500$	−24.0741	−1.07663
$501$	−4.00729	−0.179032
$502$	−3.76531	−0.168054
$503$	−27.3868	−1.22112	−0.610559	−	0.791971i	$-0.709055\pi$
$503$	−27.3868	−1.22112	−0.610559	+	0.791971i	$0.709055\pi$
$504$	−1.74271	−0.0776266
$505$	0.274483	0.0122143
$506$	−0.649606	−0.0288785
$507$	12.4421	0.552573
$508$	−8.46657	−0.375643
$509$	−0.950098	−0.0421123	−0.0210562	−	0.999778i	$-0.506703\pi$
$509$	−0.950098	−0.0421123	−0.0210562	+	0.999778i	$0.506703\pi$
$510$	−0.230180	−0.0101925
$511$	−14.1776	−0.627182
$512$	−10.1531	−0.448707
$513$	−0.00279817	−0.000123542 0
$514$	1.38201	0.0609578
$515$	7.13507	0.314409
$516$	−23.0997	−1.01691
$517$	3.58369	0.157611
$518$	2.18041	0.0958018
$519$	3.52577	0.154764
$520$	−0.684741	−0.0300279
$521$	−3.71319	−0.162678	−0.0813389	−	0.996687i	$-0.525920\pi$
$521$	−3.71319	−0.162678	−0.0813389	+	0.996687i	$0.525920\pi$
$522$	1.27170	0.0556608
$523$	−9.76736	−0.427097	−0.213548	−	0.976933i	$-0.568502\pi$
$523$	−9.76736	−0.427097	−0.213548	+	0.976933i	$0.568502\pi$
$524$	4.85246	0.211981
$525$	−6.43273	−0.280747
$526$	−2.10121	−0.0916170
$527$	8.99614	0.391878
$528$	−6.36004	−0.276785
$529$	−13.8271	−0.601179
$530$	2.45373	0.106583
$531$	−6.66092	−0.289059
$532$	0.0184735	0.000800929 0
$533$	−5.16853	−0.223874
$534$	1.13863	0.0492732
$535$	34.0831	1.47354
$536$	−3.78259	−0.163383
$537$	3.70572	0.159914
$538$	2.46309	0.106191
$539$	6.67110	0.287345
$540$	−3.47295	−0.149452
$541$	−23.7387	−1.02060	−0.510302	−	0.859995i	$-0.670466\pi$
$541$	−23.7387	−1.02060	−0.510302	+	0.859995i	$0.670466\pi$
$542$	−3.42983	−0.147324
$543$	17.3241	0.743450
$544$	−1.55882	−0.0668339
$545$	27.1095	1.16125
$546$	−0.326830	−0.0139870
$547$	−20.1379	−0.861036	−0.430518	−	0.902582i	$-0.641669\pi$
$547$	−20.1379	−0.861036	−0.430518	+	0.902582i	$0.641669\pi$
$548$	−20.7336	−0.885694
$549$	−11.3075	−0.482591
$550$	0.414363	0.0176685
$551$	−0.0270786	−0.00115359
$552$	−1.58514	−0.0674679
$553$	−24.3048	−1.03355
$554$	1.01426	0.0430917
$555$	8.72829	0.370495
$556$	4.22390	0.179133
$557$	34.6001	1.46605	0.733027	−	0.680199i	$-0.238107\pi$
$557$	34.6001	1.46605	0.733027	+	0.680199i	$0.238107\pi$
$558$	−1.18219	−0.0500463
$559$	−8.70201	−0.368056
$560$	22.7270	0.960392
$561$	−1.63217	−0.0689101
$562$	−2.08361	−0.0878916
$563$	5.74007	0.241915	0.120957	−	0.992658i	$-0.461404\pi$
$563$	5.74007	0.241915	0.120957	+	0.992658i	$0.461404\pi$
$564$	4.35341	0.183312
$565$	−9.19866	−0.386991
$566$	−4.15124	−0.174490
$567$	−3.32975	−0.139837
$568$	1.83380	0.0769446
$569$	20.0762	0.841640	0.420820	−	0.907144i	$-0.361742\pi$
$569$	20.0762	0.841640	0.420820	+	0.907144i	$0.361742\pi$
$570$	−0.000644082 0	−2.69776e−5 0
$571$	−26.4619	−1.10740	−0.553698	−	0.832718i	$-0.686784\pi$
$571$	−26.4619	−1.10740	−0.553698	+	0.832718i	$0.686784\pi$
$572$	−2.41716	−0.101067
$573$	−5.38426	−0.224931
$574$	−3.02785	−0.126380
$575$	−5.85108	−0.244007
$576$	−7.58852	−0.316188
$577$	−17.7374	−0.738419	−0.369210	−	0.929346i	$-0.620372\pi$
$577$	−17.7374	−0.738419	−0.369210	+	0.929346i	$0.620372\pi$
$578$	−0.131411	−0.00546599
$579$	−7.52794	−0.312850
$580$	−33.6087	−1.39552
$581$	57.3841	2.38069
$582$	−0.505473	−0.0209525
$583$	17.3990	0.720592
$584$	2.22846	0.0922144
$585$	−1.30832	−0.0540922
$586$	2.64675	0.109336
$587$	−31.9276	−1.31779	−0.658897	−	0.752234i	$-0.728977\pi$
$587$	−31.9276	−1.31779	−0.658897	+	0.752234i	$0.728977\pi$
$588$	8.10395	0.334201
$589$	0.0251727	0.00103722
$590$	−1.53321	−0.0631213
$591$	−12.5437	−0.515981
$592$	19.4173	0.798047
$593$	31.3187	1.28611	0.643053	−	0.765822i	$-0.277668\pi$
$593$	31.3187	1.28611	0.643053	+	0.765822i	$0.277668\pi$
$594$	0.214485	0.00880043
$595$	5.83240	0.239105
$596$	−0.492105	−0.0201574
$597$	−6.80495	−0.278508
$598$	−0.297278	−0.0121566
$599$	−30.1357	−1.23131	−0.615656	−	0.788015i	$-0.711109\pi$
$599$	−30.1357	−1.23131	−0.615656	+	0.788015i	$0.711109\pi$
$600$	1.01111	0.0412782
$601$	−9.81879	−0.400517	−0.200258	−	0.979743i	$-0.564178\pi$
$601$	−9.81879	−0.400517	−0.200258	+	0.979743i	$0.564178\pi$
$602$	−5.09785	−0.207773
$603$	−7.22729	−0.294318
$604$	−17.3084	−0.704270
$605$	14.6014	0.593631
$606$	−0.0205927	−0.000836519 0
$607$	5.54971	0.225256	0.112628	−	0.993637i	$-0.464073\pi$
$607$	5.54971	0.225256	0.112628	+	0.993637i	$0.464073\pi$
$608$	−0.00436184	−0.000176896 0
$609$	−32.2229	−1.30574
$610$	−2.60276	−0.105383
$611$	1.64000	0.0663472
$612$	−1.98273	−0.0801472
$613$	−22.7175	−0.917552	−0.458776	−	0.888552i	$-0.651712\pi$
$613$	−22.7175	−0.917552	−0.458776	+	0.888552i	$0.651712\pi$
$614$	0.349451	0.0141027
$615$	−12.1206	−0.488751
$616$	−2.84440	−0.114604
$617$	30.1135	1.21232	0.606161	−	0.795342i	$-0.292709\pi$
$617$	30.1135	1.21232	0.606161	+	0.795342i	$0.292709\pi$
$618$	−0.535298	−0.0215329
$619$	19.0748	0.766682	0.383341	−	0.923607i	$-0.374773\pi$
$619$	19.0748	0.766682	0.383341	+	0.923607i	$0.374773\pi$
$620$	31.2432	1.25476
$621$	−3.02868	−0.121537
$622$	−3.09573	−0.124128
$623$	−28.8510	−1.15589
$624$	−2.91053	−0.116515
$625$	−11.6083	−0.464333
$626$	1.64621	0.0657959
$627$	−0.00456708	−0.000182391 0
$628$	1.98273	0.0791196
$629$	4.98303	0.198687
$630$	−0.766443	−0.0305358
$631$	38.8593	1.54696	0.773482	−	0.633818i	$-0.218513\pi$
$631$	38.8593	1.54696	0.773482	+	0.633818i	$0.218513\pi$
$632$	3.82027	0.151962
$633$	8.67872	0.344948
$634$	1.66974	0.0663138
$635$	−7.47961	−0.296819
$636$	21.1360	0.838098
$637$	3.05288	0.120960
$638$	2.07563	0.0821749
$639$	3.50379	0.138608
$640$	−7.20759	−0.284905
$641$	−47.7473	−1.88591	−0.942953	−	0.332927i	$-0.891964\pi$
$641$	−47.7473	−1.88591	−0.942953	+	0.332927i	$0.891964\pi$
$642$	−2.55703	−0.100918
$643$	−3.61587	−0.142596	−0.0712980	−	0.997455i	$-0.522714\pi$
$643$	−3.61587	−0.142596	−0.0712980	+	0.997455i	$0.522714\pi$
$644$	19.9954	0.787927
$645$	−20.4069	−0.803522
$646$	−0.000367711 0	−1.44674e−5 0
$647$	22.5165	0.885216	0.442608	−	0.896715i	$-0.354053\pi$
$647$	22.5165	0.885216	0.442608	+	0.896715i	$0.354053\pi$
$648$	0.523376	0.0205601
$649$	−10.8717	−0.426753
$650$	0.189624	0.00743766
$651$	29.9549	1.17403
$652$	2.52602	0.0989267
$653$	10.9151	0.427140	0.213570	−	0.976928i	$-0.431491\pi$
$653$	10.9151	0.427140	0.213570	+	0.976928i	$0.431491\pi$
$654$	−2.03385	−0.0795300
$655$	4.28680	0.167499
$656$	−26.9641	−1.05277
$657$	4.25786	0.166115
$658$	0.960751	0.0374540
$659$	−21.7114	−0.845756	−0.422878	−	0.906187i	$-0.638980\pi$
$659$	−21.7114	−0.845756	−0.422878	+	0.906187i	$0.638980\pi$
$660$	−5.66844	−0.220644
$661$	33.2826	1.29455	0.647273	−	0.762259i	$-0.275910\pi$
$661$	33.2826	1.29455	0.647273	+	0.762259i	$0.275910\pi$
$662$	−1.59154	−0.0618571
$663$	−0.746925	−0.0290082
$664$	−9.01972	−0.350033
$665$	0.0163200	0.000632864 0
$666$	−0.654827	−0.0253740
$667$	−29.3093	−1.13486
$668$	−7.94537	−0.307416
$669$	21.3462	0.825292
$670$	−1.66358	−0.0642696
$671$	−18.4557	−0.712474
$672$	−5.19049	−0.200227
$673$	37.8165	1.45772	0.728859	−	0.684663i	$-0.240051\pi$
$673$	37.8165	1.45772	0.728859	+	0.684663i	$0.240051\pi$
$674$	−2.82973	−0.108997
$675$	1.93189	0.0743586
$676$	24.6693	0.948821
$677$	−25.4395	−0.977719	−0.488860	−	0.872362i	$-0.662587\pi$
$677$	−25.4395	−0.977719	−0.488860	+	0.872362i	$0.662587\pi$
$678$	0.690116	0.0265037
$679$	12.8079	0.491521
$680$	−0.916746	−0.0351556
$681$	15.3280	0.587368
$682$	−1.92954	−0.0738858
$683$	34.1113	1.30523	0.652617	−	0.757688i	$-0.273671\pi$
$683$	34.1113	1.30523	0.652617	+	0.757688i	$0.273671\pi$
$684$	−0.00554801	−0.000212134 0
$685$	−18.3166	−0.699842
$686$	−1.27452	−0.0486613
$687$	−11.3514	−0.433081
$688$	−45.3981	−1.73079
$689$	7.96226	0.303338
$690$	−0.697141	−0.0265397
$691$	12.4071	0.471988	0.235994	−	0.971754i	$-0.424165\pi$
$691$	12.4071	0.471988	0.235994	+	0.971754i	$0.424165\pi$
$692$	6.99065	0.265744
$693$	−5.43472	−0.206448
$694$	0.569974	0.0216359
$695$	3.73151	0.141544
$696$	5.06484	0.191982
$697$	−6.91975	−0.262104
$698$	3.96018	0.149895
$699$	13.9413	0.527308
$700$	−12.7544	−0.482070
$701$	−8.41738	−0.317920	−0.158960	−	0.987285i	$-0.550814\pi$
$701$	−8.41738	−0.317920	−0.158960	+	0.987285i	$0.550814\pi$
$702$	0.0981544	0.00370460
$703$	0.0139434	0.000525884 0
$704$	−12.3857	−0.466805
$705$	3.84593	0.144846
$706$	−3.05190	−0.114860
$707$	0.521785	0.0196238
$708$	−13.2068	−0.496342
$709$	22.8000	0.856272	0.428136	−	0.903714i	$-0.359170\pi$
$709$	22.8000	0.856272	0.428136	+	0.903714i	$0.359170\pi$
$710$	0.806504	0.0302675
$711$	7.29929	0.273745
$712$	4.53485	0.169951
$713$	27.2464	1.02039
$714$	−0.437567	−0.0163755
$715$	−2.13539	−0.0798590
$716$	7.34745	0.274587
$717$	−16.1994	−0.604979
$718$	3.40476	0.127065
$719$	23.2254	0.866161	0.433081	−	0.901355i	$-0.357427\pi$
$719$	23.2254	0.866161	0.433081	+	0.901355i	$0.357427\pi$
$720$	−6.82544	−0.254369
$721$	13.5636	0.505135
$722$	2.49681	0.0929218
$723$	−18.5711	−0.690666
$724$	34.3491	1.27657
$725$	18.6954	0.694331
$726$	−1.09545	−0.0406559
$727$	23.1611	0.858999	0.429499	−	0.903067i	$-0.358690\pi$
$727$	23.1611	0.858999	0.429499	+	0.903067i	$0.358690\pi$
$728$	−1.30168	−0.0482433
$729$	1.00000	0.0370370
$730$	0.980076	0.0362742
$731$	−11.6504	−0.430907
$732$	−22.4197	−0.828656
$733$	6.26413	0.231371	0.115685	−	0.993286i	$-0.463094\pi$
$733$	6.26413	0.231371	0.115685	+	0.993286i	$0.463094\pi$
$734$	−2.42953	−0.0896758
$735$	7.15926	0.264073
$736$	−4.72116	−0.174024
$737$	−11.7961	−0.434517
$738$	0.909333	0.0334730
$739$	4.84985	0.178405	0.0892024	−	0.996014i	$-0.471568\pi$
$739$	4.84985	0.178405	0.0892024	+	0.996014i	$0.471568\pi$
$740$	17.3058	0.636176
$741$	−0.00209002	−7.67789e−5 0
$742$	4.66449	0.171239
$743$	−31.6497	−1.16112	−0.580558	−	0.814219i	$-0.697165\pi$
$743$	−31.6497	−1.16112	−0.580558	+	0.814219i	$0.697165\pi$
$744$	−4.70836	−0.172617
$745$	−0.434740	−0.0159276
$746$	−1.83617	−0.0672268
$747$	−17.2337	−0.630549
$748$	−3.23615	−0.118325
$749$	64.7912	2.36742
$750$	1.59558	0.0582625
$751$	10.6121	0.387240	0.193620	−	0.981077i	$-0.437977\pi$
$751$	10.6121	0.387240	0.193620	+	0.981077i	$0.437977\pi$
$752$	8.55581	0.311998
$753$	−28.6529	−1.04417
$754$	0.949865	0.0345921
$755$	−15.2908	−0.556487
$756$	−6.60201	−0.240113
$757$	−37.3164	−1.35629	−0.678144	−	0.734929i	$-0.737216\pi$
$757$	−37.3164	−1.35629	−0.678144	+	0.734929i	$0.737216\pi$
$758$	−4.61589	−0.167657
$759$	−4.94331	−0.179431
$760$	−0.00256521	−9.30498e−5 0
$761$	9.16188	0.332118	0.166059	−	0.986116i	$-0.446896\pi$
$761$	9.16188	0.332118	0.166059	+	0.986116i	$0.446896\pi$
$762$	0.561147	0.0203282
$763$	51.5346	1.86568
$764$	−10.6755	−0.386227
$765$	−1.75160	−0.0633293
$766$	5.04863	0.182415
$767$	−4.97521	−0.179644
$768$	−14.6363	−0.528142
$769$	2.62408	0.0946268	0.0473134	−	0.998880i	$-0.484934\pi$
$769$	2.62408	0.0946268	0.0473134	+	0.998880i	$0.484934\pi$
$770$	−1.25096	−0.0450816
$771$	10.5167	0.378748
$772$	−14.9259	−0.537194
$773$	38.3053	1.37775	0.688873	−	0.724882i	$-0.258106\pi$
$773$	38.3053	1.37775	0.688873	+	0.724882i	$0.258106\pi$
$774$	1.53100	0.0550306
$775$	−17.3796	−0.624293
$776$	−2.01316	−0.0722683
$777$	16.5923	0.595245
$778$	0.579214	0.0207658
$779$	−0.0193626	−0.000693737 0
$780$	−2.59404	−0.0928814
$781$	5.71878	0.204634
$782$	−0.398002	−0.0142325
$783$	9.67725	0.345837
$784$	15.9268	0.568814
$785$	1.75160	0.0625173
$786$	−0.321611	−0.0114715
$787$	8.73058	0.311211	0.155606	−	0.987819i	$-0.450267\pi$
$787$	8.73058	0.311211	0.155606	+	0.987819i	$0.450267\pi$
$788$	−24.8709	−0.885988
$789$	−15.9896	−0.569243
$790$	1.68015	0.0597771
$791$	−17.4864	−0.621747
$792$	0.854237	0.0303540
$793$	−8.44584	−0.299921
$794$	−0.809138	−0.0287152
$795$	18.6722	0.662233
$796$	−13.4924	−0.478225
$797$	18.4939	0.655087	0.327544	−	0.944836i	$-0.393779\pi$
$797$	18.4939	0.655087	0.327544	+	0.944836i	$0.393779\pi$
$798$	−0.00122439	−4.33428e−5 0
$799$	2.19566	0.0776770
$800$	3.01147	0.106472
$801$	8.66461	0.306149
$802$	0.738382	0.0260732
$803$	6.94954	0.245244
$804$	−14.3298	−0.505372
$805$	17.6645	0.622591
$806$	−0.883011	−0.0311027
$807$	18.7434	0.659798
$808$	−0.0820150	−0.00288528
$809$	−32.6565	−1.14814	−0.574071	−	0.818805i	$-0.694637\pi$
$809$	−32.6565	−1.14814	−0.574071	+	0.818805i	$0.694637\pi$
$810$	0.230180	0.00808771
$811$	45.2782	1.58993	0.794967	−	0.606653i	$-0.207488\pi$
$811$	45.2782	1.58993	0.794967	+	0.606653i	$0.207488\pi$
$812$	−63.8893	−2.24208
$813$	−26.1000	−0.915366
$814$	−1.06879	−0.0374610
$815$	2.23156	0.0781682
$816$	−3.89668	−0.136411
$817$	−0.0325999	−0.00114053
$818$	−3.30654	−0.115611
$819$	−2.48708	−0.0869055
$820$	−24.0320	−0.839232
$821$	−46.9515	−1.63862	−0.819310	−	0.573351i	$-0.805643\pi$
$821$	−46.9515	−1.63862	−0.819310	+	0.573351i	$0.805643\pi$
$822$	1.37418	0.0479299
$823$	−6.00818	−0.209432	−0.104716	−	0.994502i	$-0.533393\pi$
$823$	−6.00818	−0.209432	−0.104716	+	0.994502i	$0.533393\pi$
$824$	−2.13195	−0.0742700
$825$	3.15317	0.109779
$826$	−2.91460	−0.101412
$827$	−45.1194	−1.56896	−0.784478	−	0.620156i	$-0.787069\pi$
$827$	−45.1194	−1.56896	−0.784478	+	0.620156i	$0.787069\pi$
$828$	−6.00505	−0.208690
$829$	−52.1050	−1.80968	−0.904841	−	0.425749i	$-0.860011\pi$
$829$	−52.1050	−1.80968	−0.904841	+	0.425749i	$0.860011\pi$
$830$	−3.96686	−0.137692
$831$	7.71820	0.267741
$832$	−5.66806	−0.196505
$833$	4.08727	0.141615
$834$	−0.279951	−0.00969391
$835$	−7.01917	−0.242908
$836$	−0.00905528	−0.000313183 0
$837$	−8.99614	−0.310952
$838$	3.11948	0.107761
$839$	−21.1090	−0.728763	−0.364382	−	0.931250i	$-0.618720\pi$
$839$	−21.1090	−0.728763	−0.364382	+	0.931250i	$0.618720\pi$
$840$	−3.05254	−0.105323
$841$	64.6493	2.22928
$842$	−4.44038	−0.153025
$843$	−15.8556	−0.546096
$844$	17.2076	0.592309
$845$	21.7936	0.749723
$846$	−0.288535	−0.00992004
$847$	27.7569	0.953740
$848$	41.5389	1.42645
$849$	−31.5897	−1.08415
$850$	0.253873	0.00870776
$851$	15.0920	0.517347
$852$	6.94708	0.238003
$853$	−30.7467	−1.05275	−0.526374	−	0.850253i	$-0.676449\pi$
$853$	−30.7467	−1.05275	−0.526374	+	0.850253i	$0.676449\pi$
$854$	−4.94778	−0.169310
$855$	−0.00490127	−0.000167620 0
$856$	−10.1840	−0.348081
$857$	48.0632	1.64181	0.820904	−	0.571067i	$-0.193470\pi$
$857$	48.0632	1.64181	0.820904	+	0.571067i	$0.193470\pi$
$858$	0.160204	0.00546929
$859$	14.1571	0.483033	0.241517	−	0.970397i	$-0.422355\pi$
$859$	14.1571	0.483033	0.241517	+	0.970397i	$0.422355\pi$
$860$	−40.4614	−1.37972
$861$	−23.0411	−0.785237
$862$	4.06662	0.138510
$863$	5.87423	0.199961	0.0999806	−	0.994989i	$-0.468122\pi$
$863$	5.87423	0.199961	0.0999806	+	0.994989i	$0.468122\pi$
$864$	1.55882	0.0530321
$865$	6.17574	0.209981
$866$	−3.21496	−0.109249
$867$	−1.00000	−0.0339618
$868$	59.3926	2.01592
$869$	11.9137	0.404143
$870$	2.22751	0.0755197
$871$	−5.39825	−0.182913
$872$	−8.10029	−0.274311
$873$	−3.84649	−0.130184
$874$	−0.00111368	−3.76707e−5 0
$875$	−40.4296	−1.36677
$876$	8.44220	0.285235
$877$	49.1066	1.65821	0.829106	−	0.559092i	$-0.188850\pi$
$877$	49.1066	1.65821	0.829106	+	0.559092i	$0.188850\pi$
$878$	2.59146	0.0874575
$879$	20.1410	0.679338
$880$	−11.1403	−0.375538
$881$	9.42582	0.317564	0.158782	−	0.987314i	$-0.449243\pi$
$881$	9.42582	0.317564	0.158782	+	0.987314i	$0.449243\pi$
$882$	−0.537113	−0.0180855
$883$	19.0835	0.642210	0.321105	−	0.947044i	$-0.395946\pi$
$883$	19.0835	0.642210	0.321105	+	0.947044i	$0.395946\pi$
$884$	−1.48095	−0.0498098
$885$	−11.6673	−0.392191
$886$	0.0431909	0.00145103
$887$	−2.83530	−0.0952000	−0.0476000	−	0.998866i	$-0.515157\pi$
$887$	−2.83530	−0.0952000	−0.0476000	+	0.998866i	$0.515157\pi$
$888$	−2.60800	−0.0875187
$889$	−14.2186	−0.476876
$890$	1.99442	0.0668531
$891$	1.63217	0.0546797
$892$	42.3238	1.41710
$893$	0.00614384	0.000205596 0
$894$	0.0326157	0.00109083
$895$	6.49095	0.216969
$896$	−13.7015	−0.457734
$897$	−2.26220	−0.0755325
$898$	0.952174	0.0317745
$899$	−87.0579	−2.90354
$900$	3.83043	0.127681
$901$	10.6601	0.355138
$902$	1.48418	0.0494179
$903$	−38.7931	−1.29095
$904$	2.74855	0.0914153
$905$	30.3450	1.00870
$906$	1.14717	0.0381120
$907$	−8.51423	−0.282710	−0.141355	−	0.989959i	$-0.545146\pi$
$907$	−8.51423	−0.282710	−0.141355	+	0.989959i	$0.545146\pi$
$908$	30.3912	1.00857
$909$	−0.156704	−0.00519754
$910$	−0.572476	−0.0189774
$911$	−38.2070	−1.26585	−0.632927	−	0.774211i	$-0.718147\pi$
$911$	−38.2070	−1.26585	−0.632927	+	0.774211i	$0.718147\pi$
$912$	−0.0109036	−0.000361053 0
$913$	−28.1283	−0.930912
$914$	−4.84176	−0.160151
$915$	−19.8062	−0.654773
$916$	−22.5067	−0.743642
$917$	8.14911	0.269107
$918$	0.131411	0.00433722
$919$	−24.2068	−0.798508	−0.399254	−	0.916840i	$-0.630731\pi$
$919$	−24.2068	−0.798508	−0.399254	+	0.916840i	$0.630731\pi$
$920$	−2.77653	−0.0915394
$921$	2.65922	0.0876242
$922$	−3.82104	−0.125839
$923$	2.61707	0.0861420
$924$	−10.7756	−0.354491
$925$	−9.62669	−0.316524
$926$	−2.81425	−0.0924821
$927$	−4.07346	−0.133790
$928$	15.0851	0.495193
$929$	−22.6334	−0.742578	−0.371289	−	0.928517i	$-0.621084\pi$
$929$	−22.6334	−0.742578	−0.371289	+	0.928517i	$0.621084\pi$
$930$	−2.07073	−0.0679020
$931$	0.0114369	0.000374828 0
$932$	27.6418	0.905438
$933$	−23.5576	−0.771241
$934$	−2.42968	−0.0795014
$935$	−2.85891	−0.0934962
$936$	0.390923	0.0127777
$937$	−36.3107	−1.18622	−0.593110	−	0.805121i	$-0.702100\pi$
$937$	−36.3107	−1.18622	−0.593110	+	0.805121i	$0.702100\pi$
$938$	−3.16243	−0.103257
$939$	12.5272	0.408809
$940$	7.62544	0.248714
$941$	2.99381	0.0975954	0.0487977	−	0.998809i	$-0.484461\pi$
$941$	2.99381	0.0975954	0.0487977	+	0.998809i	$0.484461\pi$
$942$	−0.131411	−0.00428161
$943$	−20.9577	−0.682476
$944$	−25.9555	−0.844779
$945$	−5.83240	−0.189728
$946$	2.49885	0.0812445
$947$	−20.0439	−0.651340	−0.325670	−	0.945483i	$-0.605590\pi$
$947$	−20.0439	−0.651340	−0.325670	+	0.945483i	$0.605590\pi$
$948$	14.4725	0.470046
$949$	3.18031	0.103237
$950$	0.000710378 0	2.30477e−5 0
$951$	12.7062	0.412027
$952$	−1.74271	−0.0564817
$953$	23.9461	0.775689	0.387845	−	0.921725i	$-0.373220\pi$
$953$	23.9461	0.775689	0.387845	+	0.921725i	$0.373220\pi$
$954$	−1.40085	−0.0453542
$955$	−9.43108	−0.305182
$956$	−32.1191	−1.03881
$957$	15.7949	0.510576
$958$	2.89330	0.0934782
$959$	−34.8195	−1.12438
$960$	−13.2921	−0.429000
$961$	49.9305	1.61066
$962$	−0.489107	−0.0157694
$963$	−19.4583	−0.627034
$964$	−36.8215	−1.18594
$965$	−13.1859	−0.424471
$966$	−1.32525	−0.0426392
$967$	−55.6840	−1.79068	−0.895338	−	0.445387i	$-0.853066\pi$
$967$	−55.6840	−1.79068	−0.895338	+	0.445387i	$0.853066\pi$
$968$	−4.36288	−0.140228
$969$	−0.00279817	−8.98901e−5 0
$970$	−0.885386	−0.0284280
$971$	−26.7963	−0.859936	−0.429968	−	0.902844i	$-0.641475\pi$
$971$	−26.7963	−0.859936	−0.429968	+	0.902844i	$0.641475\pi$
$972$	1.98273	0.0635961
$973$	7.09352	0.227408
$974$	3.39787	0.108875
$975$	1.44298	0.0462124
$976$	−44.0617	−1.41038
$977$	48.3584	1.54712	0.773561	−	0.633721i	$-0.218473\pi$
$977$	48.3584	1.54712	0.773561	+	0.633721i	$0.218473\pi$
$978$	−0.167420	−0.00535349
$979$	14.1421	0.451983
$980$	14.1949	0.453439
$981$	−15.4770	−0.494143
$982$	−3.26288	−0.104123
$983$	−11.6138	−0.370422	−0.185211	−	0.982699i	$-0.559297\pi$
$983$	−11.6138	−0.370422	−0.185211	+	0.982699i	$0.559297\pi$
$984$	3.62163	0.115453
$985$	−21.9716	−0.700074
$986$	1.27170	0.0404992
$987$	7.31102	0.232712
$988$	−0.00414395	−0.000131837 0
$989$	−35.2854	−1.12201
$990$	0.375692	0.0119403
$991$	12.8731	0.408928	0.204464	−	0.978874i	$-0.434455\pi$
$991$	12.8731	0.408928	0.204464	+	0.978874i	$0.434455\pi$
$992$	−14.0234	−0.445242
$993$	−12.1112	−0.384336
$994$	1.53315	0.0486284
$995$	−11.9196	−0.377875
$996$	−34.1698	−1.08271
$997$	33.0281	1.04601	0.523006	−	0.852329i	$-0.324811\pi$
$997$	33.0281	1.04601	0.523006	+	0.852329i	$0.324811\pi$
$998$	0.313080	0.00991036
$999$	−4.98303	−0.157656

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.29	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.29	✓	64	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-0.131411 q^{2} -1.00000 q^{3} -1.98273 q^{4} -1.75160 q^{5} +0.131411 q^{6} -3.32975 q^{7} +0.523376 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.131411 q^{2} -1.00000 q^{3} -1.98273 q^{4} -1.75160 q^{5} +0.131411 q^{6} -3.32975 q^{7} +0.523376 q^{8} +1.00000 q^{9} +0.230180 q^{10} +1.63217 q^{11} +1.98273 q^{12} +0.746925 q^{13} +0.437567 q^{14} +1.75160 q^{15} +3.89668 q^{16} +1.00000 q^{17} -0.131411 q^{18} +0.00279817 q^{19} +3.47295 q^{20} +3.32975 q^{21} -0.214485 q^{22} +3.02868 q^{23} -0.523376 q^{24} -1.93189 q^{25} -0.0981544 q^{26} -1.00000 q^{27} +6.60201 q^{28} -9.67725 q^{29} -0.230180 q^{30} +8.99614 q^{31} -1.55882 q^{32} -1.63217 q^{33} -0.131411 q^{34} +5.83240 q^{35} -1.98273 q^{36} +4.98303 q^{37} -0.000367711 q^{38} -0.746925 q^{39} -0.916746 q^{40} -6.91975 q^{41} -0.437567 q^{42} -11.6504 q^{43} -3.23615 q^{44} -1.75160 q^{45} -0.398002 q^{46} +2.19566 q^{47} -3.89668 q^{48} +4.08727 q^{49} +0.253873 q^{50} -1.00000 q^{51} -1.48095 q^{52} +10.6601 q^{53} +0.131411 q^{54} -2.85891 q^{55} -1.74271 q^{56} -0.00279817 q^{57} +1.27170 q^{58} -6.66092 q^{59} -3.47295 q^{60} -11.3075 q^{61} -1.18219 q^{62} -3.32975 q^{63} -7.58852 q^{64} -1.30832 q^{65} +0.214485 q^{66} -7.22729 q^{67} -1.98273 q^{68} -3.02868 q^{69} -0.766443 q^{70} +3.50379 q^{71} +0.523376 q^{72} +4.25786 q^{73} -0.654827 q^{74} +1.93189 q^{75} -0.00554801 q^{76} -5.43472 q^{77} +0.0981544 q^{78} +7.29929 q^{79} -6.82544 q^{80} +1.00000 q^{81} +0.909333 q^{82} -17.2337 q^{83} -6.60201 q^{84} -1.75160 q^{85} +1.53100 q^{86} +9.67725 q^{87} +0.854237 q^{88} +8.66461 q^{89} +0.230180 q^{90} -2.48708 q^{91} -6.00505 q^{92} -8.99614 q^{93} -0.288535 q^{94} -0.00490127 q^{95} +1.55882 q^{96} -3.84649 q^{97} -0.537113 q^{98} +1.63217 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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