LMFDB - Embedded newform 8007.2.a.j.1.13

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			1.13
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)

$f(q)$	$=$	$q-1.78864 q^{2} -1.00000 q^{3} +1.19923 q^{4} -3.68881 q^{5} +1.78864 q^{6} +4.99843 q^{7} +1.43229 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.78864 q^{2} -1.00000 q^{3} +1.19923 q^{4} -3.68881 q^{5} +1.78864 q^{6} +4.99843 q^{7} +1.43229 q^{8} +1.00000 q^{9} +6.59796 q^{10} +6.42178 q^{11} -1.19923 q^{12} +0.498319 q^{13} -8.94039 q^{14} +3.68881 q^{15} -4.96031 q^{16} +1.00000 q^{17} -1.78864 q^{18} -6.09004 q^{19} -4.42373 q^{20} -4.99843 q^{21} -11.4862 q^{22} -0.523686 q^{23} -1.43229 q^{24} +8.60735 q^{25} -0.891313 q^{26} -1.00000 q^{27} +5.99427 q^{28} -5.30029 q^{29} -6.59796 q^{30} +11.1068 q^{31} +6.00762 q^{32} -6.42178 q^{33} -1.78864 q^{34} -18.4383 q^{35} +1.19923 q^{36} +8.07574 q^{37} +10.8929 q^{38} -0.498319 q^{39} -5.28345 q^{40} +10.3622 q^{41} +8.94039 q^{42} +9.75318 q^{43} +7.70118 q^{44} -3.68881 q^{45} +0.936685 q^{46} -0.340550 q^{47} +4.96031 q^{48} +17.9843 q^{49} -15.3954 q^{50} -1.00000 q^{51} +0.597599 q^{52} -6.33403 q^{53} +1.78864 q^{54} -23.6887 q^{55} +7.15921 q^{56} +6.09004 q^{57} +9.48030 q^{58} +2.65352 q^{59} +4.42373 q^{60} +0.558687 q^{61} -19.8660 q^{62} +4.99843 q^{63} -0.824845 q^{64} -1.83821 q^{65} +11.4862 q^{66} -2.80896 q^{67} +1.19923 q^{68} +0.523686 q^{69} +32.9794 q^{70} -7.18263 q^{71} +1.43229 q^{72} +8.94140 q^{73} -14.4446 q^{74} -8.60735 q^{75} -7.30336 q^{76} +32.0988 q^{77} +0.891313 q^{78} +16.9055 q^{79} +18.2977 q^{80} +1.00000 q^{81} -18.5343 q^{82} +5.45638 q^{83} -5.99427 q^{84} -3.68881 q^{85} -17.4449 q^{86} +5.30029 q^{87} +9.19785 q^{88} -1.05029 q^{89} +6.59796 q^{90} +2.49082 q^{91} -0.628019 q^{92} -11.1068 q^{93} +0.609121 q^{94} +22.4650 q^{95} -6.00762 q^{96} -4.64699 q^{97} -32.1675 q^{98} +6.42178 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.78864	−1.26476	−0.632379	−	0.774659i	$-0.717922\pi$
$2$	−1.78864	−1.26476	−0.632379	+	0.774659i	$0.717922\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.19923	0.599614
$5$	−3.68881	−1.64969	−0.824844	−	0.565361i	$-0.808737\pi$
$5$	−3.68881	−1.64969	−0.824844	+	0.565361i	$0.808737\pi$
$6$	1.78864	0.730209
$7$	4.99843	1.88923	0.944615	−	0.328180i	$-0.106435\pi$
$7$	4.99843	1.88923	0.944615	+	0.328180i	$0.106435\pi$
$8$	1.43229	0.506391
$9$	1.00000	0.333333
$10$	6.59796	2.08646
$11$	6.42178	1.93624	0.968119	−	0.250489i	$-0.0805914\pi$
$11$	6.42178	1.93624	0.968119	+	0.250489i	$0.0805914\pi$
$12$	−1.19923	−0.346188
$13$	0.498319	0.138209	0.0691045	−	0.997609i	$-0.477986\pi$
$13$	0.498319	0.138209	0.0691045	+	0.997609i	$0.477986\pi$
$14$	−8.94039	−2.38942
$15$	3.68881	0.952448
$16$	−4.96031	−1.24008
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.78864	−0.421586
$19$	−6.09004	−1.39715	−0.698576	−	0.715536i	$-0.746183\pi$
$19$	−6.09004	−1.39715	−0.698576	+	0.715536i	$0.746183\pi$
$20$	−4.42373	−0.989177
$21$	−4.99843	−1.09075
$22$	−11.4862	−2.44887
$23$	−0.523686	−0.109196	−0.0545980	−	0.998508i	$-0.517388\pi$
$23$	−0.523686	−0.109196	−0.0545980	+	0.998508i	$0.517388\pi$
$24$	−1.43229	−0.292365
$25$	8.60735	1.72147
$26$	−0.891313	−0.174801
$27$	−1.00000	−0.192450
$28$	5.99427	1.13281
$29$	−5.30029	−0.984239	−0.492119	−	0.870528i	$-0.663778\pi$
$29$	−5.30029	−0.984239	−0.492119	+	0.870528i	$0.663778\pi$
$30$	−6.59796	−1.20462
$31$	11.1068	1.99484	0.997419	−	0.0717957i	$-0.0228729\pi$
$31$	11.1068	1.99484	0.997419	+	0.0717957i	$0.0228729\pi$
$32$	6.00762	1.06201
$33$	−6.42178	−1.11789
$34$	−1.78864	−0.306749
$35$	−18.4383	−3.11664
$36$	1.19923	0.199871
$37$	8.07574	1.32764	0.663822	−	0.747891i	$-0.268933\pi$
$37$	8.07574	1.32764	0.663822	+	0.747891i	$0.268933\pi$
$38$	10.8929	1.76706
$39$	−0.498319	−0.0797949
$40$	−5.28345	−0.835387
$41$	10.3622	1.61831	0.809154	−	0.587596i	$-0.199926\pi$
$41$	10.3622	1.61831	0.809154	+	0.587596i	$0.199926\pi$
$42$	8.94039	1.37953
$43$	9.75318	1.48735	0.743673	−	0.668543i	$-0.233082\pi$
$43$	9.75318	1.48735	0.743673	+	0.668543i	$0.233082\pi$
$44$	7.70118	1.16100
$45$	−3.68881	−0.549896
$46$	0.936685	0.138107
$47$	−0.340550	−0.0496743	−0.0248371	−	0.999692i	$-0.507907\pi$
$47$	−0.340550	−0.0496743	−0.0248371	+	0.999692i	$0.507907\pi$
$48$	4.96031	0.715959
$49$	17.9843	2.56919
$50$	−15.3954	−2.17724
$51$	−1.00000	−0.140028
$52$	0.597599	0.0828721
$53$	−6.33403	−0.870046	−0.435023	−	0.900419i	$-0.643260\pi$
$53$	−6.33403	−0.870046	−0.435023	+	0.900419i	$0.643260\pi$
$54$	1.78864	0.243403
$55$	−23.6887	−3.19419
$56$	7.15921	0.956689
$57$	6.09004	0.806646
$58$	9.48030	1.24482
$59$	2.65352	0.345459	0.172730	−	0.984969i	$-0.444741\pi$
$59$	2.65352	0.345459	0.172730	+	0.984969i	$0.444741\pi$
$60$	4.42373	0.571101
$61$	0.558687	0.0715326	0.0357663	−	0.999360i	$-0.488613\pi$
$61$	0.558687	0.0715326	0.0357663	+	0.999360i	$0.488613\pi$
$62$	−19.8660	−2.52299
$63$	4.99843	0.629743
$64$	−0.824845	−0.103106
$65$	−1.83821	−0.228002
$66$	11.4862	1.41386
$67$	−2.80896	−0.343170	−0.171585	−	0.985169i	$-0.554889\pi$
$67$	−2.80896	−0.343170	−0.171585	+	0.985169i	$0.554889\pi$
$68$	1.19923	0.145428
$69$	0.523686	0.0630444
$70$	32.9794	3.94180
$71$	−7.18263	−0.852421	−0.426211	−	0.904624i	$-0.640152\pi$
$71$	−7.18263	−0.852421	−0.426211	+	0.904624i	$0.640152\pi$
$72$	1.43229	0.168797
$73$	8.94140	1.04651	0.523256	−	0.852176i	$-0.324717\pi$
$73$	8.94140	1.04651	0.523256	+	0.852176i	$0.324717\pi$
$74$	−14.4446	−1.67915
$75$	−8.60735	−0.993891
$76$	−7.30336	−0.837752
$77$	32.0988	3.65800
$78$	0.891313	0.100921
$79$	16.9055	1.90202	0.951010	−	0.309159i	$-0.100047\pi$
$79$	16.9055	1.90202	0.951010	+	0.309159i	$0.100047\pi$
$80$	18.2977	2.04574
$81$	1.00000	0.111111
$82$	−18.5343	−2.04677
$83$	5.45638	0.598916	0.299458	−	0.954110i	$-0.403194\pi$
$83$	5.45638	0.598916	0.299458	+	0.954110i	$0.403194\pi$
$84$	−5.99427	−0.654028
$85$	−3.68881	−0.400108
$86$	−17.4449	−1.88113
$87$	5.30029	0.568251
$88$	9.19785	0.980494
$89$	−1.05029	−0.111330	−0.0556650	−	0.998450i	$-0.517728\pi$
$89$	−1.05029	−0.111330	−0.0556650	+	0.998450i	$0.517728\pi$
$90$	6.59796	0.695486
$91$	2.49082	0.261108
$92$	−0.628019	−0.0654755
$93$	−11.1068	−1.15172
$94$	0.609121	0.0628260
$95$	22.4650	2.30486
$96$	−6.00762	−0.613150
$97$	−4.64699	−0.471830	−0.235915	−	0.971774i	$-0.575809\pi$
$97$	−4.64699	−0.471830	−0.235915	+	0.971774i	$0.575809\pi$
$98$	−32.1675	−3.24941
$99$	6.42178	0.645413
$100$	10.3222	1.03222
$101$	−9.92040	−0.987117	−0.493558	−	0.869713i	$-0.664304\pi$
$101$	−9.92040	−0.987117	−0.493558	+	0.869713i	$0.664304\pi$
$102$	1.78864	0.177102
$103$	−6.29664	−0.620427	−0.310213	−	0.950667i	$-0.600400\pi$
$103$	−6.29664	−0.620427	−0.310213	+	0.950667i	$0.600400\pi$
$104$	0.713738	0.0699878
$105$	18.4383	1.79939
$106$	11.3293	1.10040
$107$	−6.10636	−0.590324	−0.295162	−	0.955447i	$-0.595374\pi$
$107$	−6.10636	−0.590324	−0.295162	+	0.955447i	$0.595374\pi$
$108$	−1.19923	−0.115396
$109$	−8.69436	−0.832768	−0.416384	−	0.909189i	$-0.636703\pi$
$109$	−8.69436	−0.832768	−0.416384	+	0.909189i	$0.636703\pi$
$110$	42.3706	4.03988
$111$	−8.07574	−0.766515
$112$	−24.7938	−2.34279
$113$	17.0902	1.60771	0.803853	−	0.594828i	$-0.202780\pi$
$113$	17.0902	1.60771	0.803853	+	0.594828i	$0.202780\pi$
$114$	−10.8929	−1.02021
$115$	1.93178	0.180139
$116$	−6.35626	−0.590164
$117$	0.498319	0.0460696
$118$	−4.74620	−0.436923
$119$	4.99843	0.458206
$120$	5.28345	0.482311
$121$	30.2392	2.74902
$122$	−0.999290	−0.0904715
$123$	−10.3622	−0.934331
$124$	13.3196	1.19613
$125$	−13.3068	−1.19020
$126$	−8.94039	−0.796473
$127$	−0.669840	−0.0594387	−0.0297193	−	0.999558i	$-0.509461\pi$
$127$	−0.669840	−0.0594387	−0.0297193	+	0.999558i	$0.509461\pi$
$128$	−10.5399	−0.931603
$129$	−9.75318	−0.858720
$130$	3.28789	0.288367
$131$	7.07731	0.618347	0.309174	−	0.951006i	$-0.399948\pi$
$131$	7.07731	0.618347	0.309174	+	0.951006i	$0.399948\pi$
$132$	−7.70118	−0.670302
$133$	−30.4407	−2.63954
$134$	5.02422	0.434027
$135$	3.68881	0.317483
$136$	1.43229	0.122818
$137$	12.8025	1.09379	0.546896	−	0.837201i	$-0.315809\pi$
$137$	12.8025	1.09379	0.546896	+	0.837201i	$0.315809\pi$
$138$	−0.936685	−0.0797359
$139$	6.91581	0.586592	0.293296	−	0.956022i	$-0.405248\pi$
$139$	6.91581	0.586592	0.293296	+	0.956022i	$0.405248\pi$
$140$	−22.1117	−1.86878
$141$	0.340550	0.0286795
$142$	12.8471	1.07811
$143$	3.20010	0.267605
$144$	−4.96031	−0.413359
$145$	19.5518	1.62369
$146$	−15.9929	−1.32358
$147$	−17.9843	−1.48332
$148$	9.68466	0.796074
$149$	16.5982	1.35977	0.679887	−	0.733317i	$-0.262029\pi$
$149$	16.5982	1.35977	0.679887	+	0.733317i	$0.262029\pi$
$150$	15.3954	1.25703
$151$	−9.60086	−0.781307	−0.390653	−	0.920538i	$-0.627751\pi$
$151$	−9.60086	−0.781307	−0.390653	+	0.920538i	$0.627751\pi$
$152$	−8.72271	−0.707505
$153$	1.00000	0.0808452
$154$	−57.4132	−4.62649
$155$	−40.9709	−3.29086
$156$	−0.597599	−0.0478462
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−30.2379	−2.40560
$159$	6.33403	0.502321
$160$	−22.1610	−1.75198
$161$	−2.61761	−0.206296
$162$	−1.78864	−0.140529
$163$	11.3561	0.889481	0.444740	−	0.895660i	$-0.353296\pi$
$163$	11.3561	0.889481	0.444740	+	0.895660i	$0.353296\pi$
$164$	12.4267	0.970361
$165$	23.6887	1.84417
$166$	−9.75949	−0.757484
$167$	−8.19440	−0.634102	−0.317051	−	0.948409i	$-0.602693\pi$
$167$	−8.19440	−0.634102	−0.317051	+	0.948409i	$0.602693\pi$
$168$	−7.15921	−0.552345
$169$	−12.7517	−0.980898
$170$	6.59796	0.506040
$171$	−6.09004	−0.465717
$172$	11.6963	0.891834
$173$	−3.38489	−0.257349	−0.128674	−	0.991687i	$-0.541072\pi$
$173$	−3.38489	−0.257349	−0.128674	+	0.991687i	$0.541072\pi$
$174$	−9.48030	−0.718700
$175$	43.0232	3.25225
$176$	−31.8540	−2.40109
$177$	−2.65352	−0.199451
$178$	1.87858	0.140806
$179$	−18.5579	−1.38708	−0.693540	−	0.720418i	$-0.743950\pi$
$179$	−18.5579	−1.38708	−0.693540	+	0.720418i	$0.743950\pi$
$180$	−4.42373	−0.329726
$181$	10.4065	0.773509	0.386754	−	0.922183i	$-0.373596\pi$
$181$	10.4065	0.773509	0.386754	+	0.922183i	$0.373596\pi$
$182$	−4.45517	−0.330239
$183$	−0.558687	−0.0412994
$184$	−0.750070	−0.0552959
$185$	−29.7899	−2.19020
$186$	19.8660	1.45665
$187$	6.42178	0.469607
$188$	−0.408397	−0.0297854
$189$	−4.99843	−0.363583
$190$	−40.1818	−2.91510
$191$	−1.94279	−0.140576	−0.0702878	−	0.997527i	$-0.522392\pi$
$191$	−1.94279	−0.140576	−0.0702878	+	0.997527i	$0.522392\pi$
$192$	0.824845	0.0595280
$193$	−16.9622	−1.22097	−0.610485	−	0.792028i	$-0.709025\pi$
$193$	−16.9622	−1.22097	−0.610485	+	0.792028i	$0.709025\pi$
$194$	8.31178	0.596751
$195$	1.83821	0.131637
$196$	21.5673	1.54052
$197$	−25.5899	−1.82320	−0.911602	−	0.411075i	$-0.865153\pi$
$197$	−25.5899	−1.82320	−0.911602	+	0.411075i	$0.865153\pi$
$198$	−11.4862	−0.816292
$199$	17.1968	1.21905	0.609525	−	0.792767i	$-0.291360\pi$
$199$	17.1968	1.21905	0.609525	+	0.792767i	$0.291360\pi$
$200$	12.3282	0.871737
$201$	2.80896	0.198129
$202$	17.7440	1.24846
$203$	−26.4931	−1.85945
$204$	−1.19923	−0.0839628
$205$	−38.2243	−2.66970
$206$	11.2624	0.784690
$207$	−0.523686	−0.0363987
$208$	−2.47182	−0.171390
$209$	−39.1089	−2.70522
$210$	−32.9794	−2.27580
$211$	−4.38406	−0.301811	−0.150905	−	0.988548i	$-0.548219\pi$
$211$	−4.38406	−0.301811	−0.150905	+	0.988548i	$0.548219\pi$
$212$	−7.59595	−0.521692
$213$	7.18263	0.492146
$214$	10.9221	0.746618
$215$	−35.9777	−2.45366
$216$	−1.43229	−0.0974550
$217$	55.5166	3.76871
$218$	15.5511	1.05325
$219$	−8.94140	−0.604204
$220$	−28.4082	−1.91528
$221$	0.498319	0.0335206
$222$	14.4446	0.969457
$223$	10.5981	0.709703	0.354852	−	0.934923i	$-0.384531\pi$
$223$	10.5981	0.709703	0.354852	+	0.934923i	$0.384531\pi$
$224$	30.0287	2.00638
$225$	8.60735	0.573823
$226$	−30.5681	−2.03336
$227$	15.6722	1.04020	0.520100	−	0.854106i	$-0.325895\pi$
$227$	15.6722	1.04020	0.520100	+	0.854106i	$0.325895\pi$
$228$	7.30336	0.483677
$229$	−26.1823	−1.73018	−0.865088	−	0.501620i	$-0.832737\pi$
$229$	−26.1823	−1.73018	−0.865088	+	0.501620i	$0.832737\pi$
$230$	−3.45526	−0.227833
$231$	−32.0988	−2.11195
$232$	−7.59155	−0.498410
$233$	8.14008	0.533275	0.266637	−	0.963797i	$-0.414087\pi$
$233$	8.14008	0.533275	0.266637	+	0.963797i	$0.414087\pi$
$234$	−0.891313	−0.0582670
$235$	1.25622	0.0819471
$236$	3.18218	0.207142
$237$	−16.9055	−1.09813
$238$	−8.94039	−0.579520
$239$	−13.8131	−0.893496	−0.446748	−	0.894660i	$-0.647418\pi$
$239$	−13.8131	−0.893496	−0.446748	+	0.894660i	$0.647418\pi$
$240$	−18.2977	−1.18111
$241$	27.6965	1.78409	0.892045	−	0.451946i	$-0.149270\pi$
$241$	27.6965	1.78409	0.892045	+	0.451946i	$0.149270\pi$
$242$	−54.0871	−3.47685
$243$	−1.00000	−0.0641500
$244$	0.669994	0.0428920
$245$	−66.3409	−4.23836
$246$	18.5343	1.18170
$247$	−3.03479	−0.193099
$248$	15.9081	1.01017
$249$	−5.45638	−0.345784
$250$	23.8011	1.50531
$251$	−4.06052	−0.256298	−0.128149	−	0.991755i	$-0.540904\pi$
$251$	−4.06052	−0.256298	−0.128149	+	0.991755i	$0.540904\pi$
$252$	5.99427	0.377603
$253$	−3.36299	−0.211430
$254$	1.19810	0.0751756
$255$	3.68881	0.231002
$256$	20.5017	1.28136
$257$	−29.5186	−1.84132	−0.920660	−	0.390366i	$-0.872349\pi$
$257$	−29.5186	−1.84132	−0.920660	+	0.390366i	$0.872349\pi$
$258$	17.4449	1.08607
$259$	40.3660	2.50822
$260$	−2.20443	−0.136713
$261$	−5.30029	−0.328080
$262$	−12.6587	−0.782060
$263$	−6.79580	−0.419047	−0.209523	−	0.977804i	$-0.567191\pi$
$263$	−6.79580	−0.419047	−0.209523	+	0.977804i	$0.567191\pi$
$264$	−9.19785	−0.566089
$265$	23.3651	1.43530
$266$	54.4474	3.33838
$267$	1.05029	0.0642764
$268$	−3.36859	−0.205769
$269$	−23.1537	−1.41171	−0.705853	−	0.708358i	$-0.749436\pi$
$269$	−23.1537	−1.41171	−0.705853	+	0.708358i	$0.749436\pi$
$270$	−6.59796	−0.401539
$271$	−6.38779	−0.388030	−0.194015	−	0.980999i	$-0.562151\pi$
$271$	−6.38779	−0.388030	−0.194015	+	0.980999i	$0.562151\pi$
$272$	−4.96031	−0.300763
$273$	−2.49082	−0.150751
$274$	−22.8991	−1.38338
$275$	55.2745	3.33318
$276$	0.628019	0.0378023
$277$	−7.67985	−0.461437	−0.230719	−	0.973021i	$-0.574108\pi$
$277$	−7.67985	−0.461437	−0.230719	+	0.973021i	$0.574108\pi$
$278$	−12.3699	−0.741897
$279$	11.1068	0.664946
$280$	−26.4090	−1.57824
$281$	−8.61923	−0.514180	−0.257090	−	0.966387i	$-0.582764\pi$
$281$	−8.61923	−0.514180	−0.257090	+	0.966387i	$0.582764\pi$
$282$	−0.609121	−0.0362726
$283$	−1.38010	−0.0820383	−0.0410192	−	0.999158i	$-0.513060\pi$
$283$	−1.38010	−0.0820383	−0.0410192	+	0.999158i	$0.513060\pi$
$284$	−8.61362	−0.511124
$285$	−22.4650	−1.33071
$286$	−5.72382	−0.338456
$287$	51.7949	3.05736
$288$	6.00762	0.354002
$289$	1.00000	0.0588235
$290$	−34.9711	−2.05357
$291$	4.64699	0.272411
$292$	10.7228	0.627503
$293$	−24.4425	−1.42795	−0.713974	−	0.700172i	$-0.753106\pi$
$293$	−24.4425	−1.42795	−0.713974	+	0.700172i	$0.753106\pi$
$294$	32.1675	1.87605
$295$	−9.78836	−0.569900
$296$	11.5668	0.672307
$297$	−6.42178	−0.372629
$298$	−29.6881	−1.71979
$299$	−0.260963	−0.0150919
$300$	−10.3222	−0.595951
$301$	48.7506	2.80994
$302$	17.1725	0.988164
$303$	9.92040	0.569912
$304$	30.2085	1.73258
$305$	−2.06089	−0.118006
$306$	−1.78864	−0.102250
$307$	−23.1189	−1.31946	−0.659732	−	0.751501i	$-0.729330\pi$
$307$	−23.1189	−1.31946	−0.659732	+	0.751501i	$0.729330\pi$
$308$	38.4938	2.19339
$309$	6.29664	0.358204
$310$	73.2821	4.16214
$311$	21.6190	1.22590	0.612951	−	0.790121i	$-0.289982\pi$
$311$	21.6190	1.22590	0.612951	+	0.790121i	$0.289982\pi$
$312$	−0.713738	−0.0404074
$313$	20.4821	1.15771	0.578857	−	0.815429i	$-0.303499\pi$
$313$	20.4821	1.15771	0.578857	+	0.815429i	$0.303499\pi$
$314$	1.78864	0.100939
$315$	−18.4383	−1.03888
$316$	20.2736	1.14048
$317$	4.01241	0.225359	0.112680	−	0.993631i	$-0.464057\pi$
$317$	4.01241	0.225359	0.112680	+	0.993631i	$0.464057\pi$
$318$	−11.3293	−0.635315
$319$	−34.0373	−1.90572
$320$	3.04270	0.170092
$321$	6.10636	0.340824
$322$	4.68196	0.260915
$323$	−6.09004	−0.338859
$324$	1.19923	0.0666238
$325$	4.28921	0.237922
$326$	−20.3120	−1.12498
$327$	8.69436	0.480799
$328$	14.8417	0.819497
$329$	−1.70222	−0.0938462
$330$	−42.3706	−2.33243
$331$	11.6058	0.637911	0.318956	−	0.947770i	$-0.396668\pi$
$331$	11.6058	0.637911	0.318956	+	0.947770i	$0.396668\pi$
$332$	6.54345	0.359118
$333$	8.07574	0.442548
$334$	14.6568	0.801985
$335$	10.3617	0.566123
$336$	24.7938	1.35261
$337$	−10.0710	−0.548601	−0.274301	−	0.961644i	$-0.588446\pi$
$337$	−10.0710	−0.548601	−0.274301	+	0.961644i	$0.588446\pi$
$338$	22.8081	1.24060
$339$	−17.0902	−0.928210
$340$	−4.42373	−0.239911
$341$	71.3254	3.86248
$342$	10.8929	0.589020
$343$	54.9045	2.96456
$344$	13.9694	0.753179
$345$	−1.93178	−0.104003
$346$	6.05435	0.325484
$347$	13.7175	0.736393	0.368197	−	0.929748i	$-0.379975\pi$
$347$	13.7175	0.736393	0.368197	+	0.929748i	$0.379975\pi$
$348$	6.35626	0.340731
$349$	−19.1623	−1.02573	−0.512866	−	0.858468i	$-0.671416\pi$
$349$	−19.1623	−1.02573	−0.512866	+	0.858468i	$0.671416\pi$
$350$	−76.9531	−4.11331
$351$	−0.498319	−0.0265983
$352$	38.5796	2.05630
$353$	6.53268	0.347700	0.173850	−	0.984772i	$-0.444379\pi$
$353$	6.53268	0.347700	0.173850	+	0.984772i	$0.444379\pi$
$354$	4.74620	0.252258
$355$	26.4954	1.40623
$356$	−1.25953	−0.0667551
$357$	−4.99843	−0.264545
$358$	33.1933	1.75432
$359$	7.77596	0.410399	0.205200	−	0.978720i	$-0.434216\pi$
$359$	7.77596	0.410399	0.205200	+	0.978720i	$0.434216\pi$
$360$	−5.28345	−0.278462
$361$	18.0886	0.952033
$362$	−18.6135	−0.978302
$363$	−30.2392	−1.58715
$364$	2.98706	0.156564
$365$	−32.9831	−1.72642
$366$	0.999290	0.0522337
$367$	−2.99896	−0.156545	−0.0782723	−	0.996932i	$-0.524940\pi$
$367$	−2.99896	−0.156545	−0.0782723	+	0.996932i	$0.524940\pi$
$368$	2.59764	0.135411
$369$	10.3622	0.539436
$370$	53.2834	2.77007
$371$	−31.6602	−1.64372
$372$	−13.3196	−0.690588
$373$	−23.0479	−1.19337	−0.596687	−	0.802474i	$-0.703516\pi$
$373$	−23.0479	−1.19337	−0.596687	+	0.802474i	$0.703516\pi$
$374$	−11.4862	−0.593939
$375$	13.3068	0.687162
$376$	−0.487766	−0.0251546
$377$	−2.64124	−0.136031
$378$	8.94039	0.459844
$379$	31.2737	1.60642	0.803212	−	0.595694i	$-0.203123\pi$
$379$	31.2737	1.60642	0.803212	+	0.595694i	$0.203123\pi$
$380$	26.9407	1.38203
$381$	0.669840	0.0343169
$382$	3.47496	0.177794
$383$	2.40636	0.122959	0.0614796	−	0.998108i	$-0.480418\pi$
$383$	2.40636	0.122959	0.0614796	+	0.998108i	$0.480418\pi$
$384$	10.5399	0.537861
$385$	−118.407	−6.03456
$386$	30.3393	1.54423
$387$	9.75318	0.495782
$388$	−5.57280	−0.282916
$389$	6.22776	0.315760	0.157880	−	0.987458i	$-0.449534\pi$
$389$	6.22776	0.315760	0.157880	+	0.987458i	$0.449534\pi$
$390$	−3.28789	−0.166489
$391$	−0.523686	−0.0264839
$392$	25.7588	1.30102
$393$	−7.07731	−0.357003
$394$	45.7710	2.30591
$395$	−62.3614	−3.13774
$396$	7.70118	0.386999
$397$	−4.81061	−0.241437	−0.120719	−	0.992687i	$-0.538520\pi$
$397$	−4.81061	−0.241437	−0.120719	+	0.992687i	$0.538520\pi$
$398$	−30.7589	−1.54180
$399$	30.4407	1.52394
$400$	−42.6951	−2.13475
$401$	32.2728	1.61163	0.805813	−	0.592171i	$-0.201729\pi$
$401$	32.2728	1.61163	0.805813	+	0.592171i	$0.201729\pi$
$402$	−5.02422	−0.250585
$403$	5.53473	0.275704
$404$	−11.8968	−0.591890
$405$	−3.68881	−0.183299
$406$	47.3867	2.35176
$407$	51.8606	2.57064
$408$	−1.43229	−0.0709089
$409$	−26.5320	−1.31192	−0.655962	−	0.754794i	$-0.727737\pi$
$409$	−26.5320	−1.31192	−0.655962	+	0.754794i	$0.727737\pi$
$410$	68.3695	3.37653
$411$	−12.8025	−0.631501
$412$	−7.55112	−0.372017
$413$	13.2635	0.652652
$414$	0.936685	0.0460355
$415$	−20.1276	−0.988024
$416$	2.99371	0.146779
$417$	−6.91581	−0.338669
$418$	69.9517	3.42145
$419$	−29.2525	−1.42908	−0.714539	−	0.699596i	$-0.753363\pi$
$419$	−29.2525	−1.42908	−0.714539	+	0.699596i	$0.753363\pi$
$420$	22.1117	1.07894
$421$	25.1079	1.22368	0.611841	−	0.790981i	$-0.290429\pi$
$421$	25.1079	1.22368	0.611841	+	0.790981i	$0.290429\pi$
$422$	7.84149	0.381718
$423$	−0.340550	−0.0165581
$424$	−9.07217	−0.440584
$425$	8.60735	0.417518
$426$	−12.8471	−0.622446
$427$	2.79256	0.135142
$428$	−7.32293	−0.353967
$429$	−3.20010	−0.154502
$430$	64.3511	3.10328
$431$	6.49029	0.312626	0.156313	−	0.987708i	$-0.450039\pi$
$431$	6.49029	0.312626	0.156313	+	0.987708i	$0.450039\pi$
$432$	4.96031	0.238653
$433$	−34.7770	−1.67128	−0.835638	−	0.549281i	$-0.814902\pi$
$433$	−34.7770	−1.67128	−0.835638	+	0.549281i	$0.814902\pi$
$434$	−99.2991	−4.76651
$435$	−19.5518	−0.937436
$436$	−10.4265	−0.499340
$437$	3.18927	0.152563
$438$	15.9929	0.764172
$439$	−33.4638	−1.59714	−0.798570	−	0.601902i	$-0.794410\pi$
$439$	−33.4638	−1.59714	−0.798570	+	0.601902i	$0.794410\pi$
$440$	−33.9292	−1.61751
$441$	17.9843	0.856397
$442$	−0.891313	−0.0423954
$443$	12.4743	0.592671	0.296335	−	0.955084i	$-0.404235\pi$
$443$	12.4743	0.592671	0.296335	+	0.955084i	$0.404235\pi$
$444$	−9.68466	−0.459614
$445$	3.87431	0.183660
$446$	−18.9562	−0.897604
$447$	−16.5982	−0.785066
$448$	−4.12293	−0.194790
$449$	27.9597	1.31950	0.659751	−	0.751485i	$-0.270662\pi$
$449$	27.9597	1.31950	0.659751	+	0.751485i	$0.270662\pi$
$450$	−15.3954	−0.725748
$451$	66.5439	3.13343
$452$	20.4950	0.964004
$453$	9.60086	0.451088
$454$	−28.0319	−1.31560
$455$	−9.18815	−0.430747
$456$	8.72271	0.408478
$457$	−9.07744	−0.424625	−0.212312	−	0.977202i	$-0.568099\pi$
$457$	−9.07744	−0.424625	−0.212312	+	0.977202i	$0.568099\pi$
$458$	46.8307	2.18825
$459$	−1.00000	−0.0466760
$460$	2.31665	0.108014
$461$	−14.1094	−0.657140	−0.328570	−	0.944480i	$-0.606567\pi$
$461$	−14.1094	−0.657140	−0.328570	+	0.944480i	$0.606567\pi$
$462$	57.4132	2.67110
$463$	0.164941	0.00766544	0.00383272	−	0.999993i	$-0.498780\pi$
$463$	0.164941	0.00766544	0.00383272	+	0.999993i	$0.498780\pi$
$464$	26.2911	1.22053
$465$	40.9709	1.89998
$466$	−14.5597	−0.674464
$467$	31.5513	1.46002	0.730010	−	0.683436i	$-0.239515\pi$
$467$	31.5513	1.46002	0.730010	+	0.683436i	$0.239515\pi$
$468$	0.597599	0.0276240
$469$	−14.0404	−0.648326
$470$	−2.24693	−0.103643
$471$	1.00000	0.0460776
$472$	3.80062	0.174938
$473$	62.6328	2.87986
$474$	30.2379	1.38887
$475$	−52.4191	−2.40515
$476$	5.99427	0.274747
$477$	−6.33403	−0.290015
$478$	24.7067	1.13006
$479$	11.0714	0.505863	0.252931	−	0.967484i	$-0.418605\pi$
$479$	11.0714	0.505863	0.252931	+	0.967484i	$0.418605\pi$
$480$	22.1610	1.01151
$481$	4.02430	0.183492
$482$	−49.5391	−2.25644
$483$	2.61761	0.119105
$484$	36.2638	1.64835
$485$	17.1419	0.778372
$486$	1.78864	0.0811343
$487$	25.9356	1.17525	0.587626	−	0.809133i	$-0.300063\pi$
$487$	25.9356	1.17525	0.587626	+	0.809133i	$0.300063\pi$
$488$	0.800202	0.0362235
$489$	−11.3561	−0.513542
$490$	118.660	5.36050
$491$	−36.4550	−1.64519	−0.822595	−	0.568628i	$-0.807474\pi$
$491$	−36.4550	−1.64519	−0.822595	+	0.568628i	$0.807474\pi$
$492$	−12.4267	−0.560238
$493$	−5.30029	−0.238713
$494$	5.42814	0.244223
$495$	−23.6887	−1.06473
$496$	−55.0931	−2.47375
$497$	−35.9019	−1.61042
$498$	9.75949	0.437333
$499$	27.4277	1.22783	0.613917	−	0.789370i	$-0.289593\pi$
$499$	27.4277	1.22783	0.613917	+	0.789370i	$0.289593\pi$
$500$	−15.9579	−0.713661
$501$	8.19440	0.366099
$502$	7.26281	0.324155
$503$	−14.1495	−0.630897	−0.315448	−	0.948943i	$-0.602155\pi$
$503$	−14.1495	−0.630897	−0.315448	+	0.948943i	$0.602155\pi$
$504$	7.15921	0.318896
$505$	36.5945	1.62843
$506$	6.01518	0.267407
$507$	12.7517	0.566322
$508$	−0.803292	−0.0356403
$509$	−30.0441	−1.33168	−0.665842	−	0.746093i	$-0.731927\pi$
$509$	−30.0441	−1.33168	−0.665842	+	0.746093i	$0.731927\pi$
$510$	−6.59796	−0.292162
$511$	44.6930	1.97710
$512$	−15.5904	−0.689007
$513$	6.09004	0.268882
$514$	52.7981	2.32883
$515$	23.2271	1.02351
$516$	−11.6963	−0.514901
$517$	−2.18694	−0.0961813
$518$	−72.2003	−3.17230
$519$	3.38489	0.148580
$520$	−2.63285	−0.115458
$521$	−35.4315	−1.55228	−0.776141	−	0.630559i	$-0.782826\pi$
$521$	−35.4315	−1.55228	−0.776141	+	0.630559i	$0.782826\pi$
$522$	9.48030	0.414942
$523$	−10.3511	−0.452623	−0.226312	−	0.974055i	$-0.572667\pi$
$523$	−10.3511	−0.452623	−0.226312	+	0.974055i	$0.572667\pi$
$524$	8.48731	0.370770
$525$	−43.0232	−1.87769
$526$	12.1552	0.529993
$527$	11.1068	0.483819
$528$	31.8540	1.38627
$529$	−22.7258	−0.988076
$530$	−41.7917	−1.81531
$531$	2.65352	0.115153
$532$	−36.5053	−1.58271
$533$	5.16370	0.223665
$534$	−1.87858	−0.0812941
$535$	22.5252	0.973851
$536$	−4.02325	−0.173778
$537$	18.5579	0.800831
$538$	41.4136	1.78547
$539$	115.491	4.97457
$540$	4.42373	0.190367
$541$	41.4031	1.78006	0.890029	−	0.455903i	$-0.150684\pi$
$541$	41.4031	1.78006	0.890029	+	0.455903i	$0.150684\pi$
$542$	11.4254	0.490765
$543$	−10.4065	−0.446586
$544$	6.00762	0.257575
$545$	32.0719	1.37381
$546$	4.45517	0.190664
$547$	0.323912	0.0138495	0.00692474	−	0.999976i	$-0.497796\pi$
$547$	0.323912	0.0138495	0.00692474	+	0.999976i	$0.497796\pi$
$548$	15.3531	0.655854
$549$	0.558687	0.0238442
$550$	−98.8661	−4.21566
$551$	32.2790	1.37513
$552$	0.750070	0.0319251
$553$	84.5012	3.59336
$554$	13.7365	0.583607
$555$	29.7899	1.26451
$556$	8.29364	0.351729
$557$	41.1175	1.74220	0.871102	−	0.491102i	$-0.163406\pi$
$557$	41.1175	1.74220	0.871102	+	0.491102i	$0.163406\pi$
$558$	−19.8660	−0.840997
$559$	4.86020	0.205564
$560$	91.4596	3.86487
$561$	−6.42178	−0.271128
$562$	15.4167	0.650314
$563$	−12.9058	−0.543916	−0.271958	−	0.962309i	$-0.587671\pi$
$563$	−12.9058	−0.543916	−0.271958	+	0.962309i	$0.587671\pi$
$564$	0.408397	0.0171966
$565$	−63.0424	−2.65221
$566$	2.46850	0.103759
$567$	4.99843	0.209914
$568$	−10.2876	−0.431659
$569$	−28.6992	−1.20313	−0.601566	−	0.798823i	$-0.705456\pi$
$569$	−28.6992	−1.20313	−0.601566	+	0.798823i	$0.705456\pi$
$570$	40.1818	1.68303
$571$	37.3400	1.56263	0.781316	−	0.624136i	$-0.214549\pi$
$571$	37.3400	1.56263	0.781316	+	0.624136i	$0.214549\pi$
$572$	3.83765	0.160460
$573$	1.94279	0.0811614
$574$	−92.6424	−3.86682
$575$	−4.50754	−0.187978
$576$	−0.824845	−0.0343685
$577$	−7.67580	−0.319548	−0.159774	−	0.987154i	$-0.551077\pi$
$577$	−7.67580	−0.319548	−0.159774	+	0.987154i	$0.551077\pi$
$578$	−1.78864	−0.0743976
$579$	16.9622	0.704927
$580$	23.4471	0.973586
$581$	27.2734	1.13149
$582$	−8.31178	−0.344534
$583$	−40.6757	−1.68462
$584$	12.8067	0.529944
$585$	−1.83821	−0.0760005
$586$	43.7189	1.80601
$587$	16.5758	0.684156	0.342078	−	0.939672i	$-0.388869\pi$
$587$	16.5758	0.684156	0.342078	+	0.939672i	$0.388869\pi$
$588$	−21.5673	−0.889422
$589$	−67.6408	−2.78709
$590$	17.5078	0.720786
$591$	25.5899	1.05263
$592$	−40.0582	−1.64638
$593$	12.4162	0.509873	0.254936	−	0.966958i	$-0.417945\pi$
$593$	12.4162	0.509873	0.254936	+	0.966958i	$0.417945\pi$
$594$	11.4862	0.471286
$595$	−18.4383	−0.755896
$596$	19.9050	0.815340
$597$	−17.1968	−0.703819
$598$	0.466768	0.0190876
$599$	17.3062	0.707113	0.353556	−	0.935413i	$-0.384972\pi$
$599$	17.3062	0.707113	0.353556	+	0.935413i	$0.384972\pi$
$600$	−12.3282	−0.503297
$601$	−35.7423	−1.45796	−0.728979	−	0.684536i	$-0.760005\pi$
$601$	−35.7423	−1.45796	−0.728979	+	0.684536i	$0.760005\pi$
$602$	−87.1973	−3.55389
$603$	−2.80896	−0.114390
$604$	−11.5136	−0.468483
$605$	−111.547	−4.53503
$606$	−17.7440	−0.720801
$607$	2.96323	0.120274	0.0601369	−	0.998190i	$-0.480846\pi$
$607$	2.96323	0.120274	0.0601369	+	0.998190i	$0.480846\pi$
$608$	−36.5867	−1.48378
$609$	26.4931	1.07356
$610$	3.68619	0.149250
$611$	−0.169703	−0.00686543
$612$	1.19923	0.0484760
$613$	−8.10755	−0.327461	−0.163730	−	0.986505i	$-0.552353\pi$
$613$	−8.10755	−0.327461	−0.163730	+	0.986505i	$0.552353\pi$
$614$	41.3513	1.66880
$615$	38.2243	1.54135
$616$	45.9748	1.85238
$617$	−15.1282	−0.609039	−0.304520	−	0.952506i	$-0.598496\pi$
$617$	−15.1282	−0.609039	−0.304520	+	0.952506i	$0.598496\pi$
$618$	−11.2624	−0.453041
$619$	22.7058	0.912625	0.456312	−	0.889820i	$-0.349170\pi$
$619$	22.7058	0.912625	0.456312	+	0.889820i	$0.349170\pi$
$620$	−49.1335	−1.97325
$621$	0.523686	0.0210148
$622$	−38.6686	−1.55047
$623$	−5.24978	−0.210328
$624$	2.47182	0.0989519
$625$	6.04968	0.241987
$626$	−36.6350	−1.46423
$627$	39.1089	1.56186
$628$	−1.19923	−0.0478544
$629$	8.07574	0.322001
$630$	32.9794	1.31393
$631$	−27.7112	−1.10316	−0.551582	−	0.834120i	$-0.685976\pi$
$631$	−27.7112	−1.10316	−0.551582	+	0.834120i	$0.685976\pi$
$632$	24.2136	0.963166
$633$	4.38406	0.174251
$634$	−7.17675	−0.285025
$635$	2.47092	0.0980553
$636$	7.59595	0.301199
$637$	8.96194	0.355085
$638$	60.8804	2.41028
$639$	−7.18263	−0.284140
$640$	38.8797	1.53685
$641$	−27.7653	−1.09666	−0.548332	−	0.836261i	$-0.684737\pi$
$641$	−27.7653	−1.09666	−0.548332	+	0.836261i	$0.684737\pi$
$642$	−10.9221	−0.431060
$643$	34.3396	1.35422	0.677111	−	0.735881i	$-0.263232\pi$
$643$	34.3396	1.35422	0.677111	+	0.735881i	$0.263232\pi$
$644$	−3.13911	−0.123698
$645$	35.9777	1.41662
$646$	10.8929	0.428575
$647$	−5.68618	−0.223547	−0.111773	−	0.993734i	$-0.535653\pi$
$647$	−5.68618	−0.223547	−0.111773	+	0.993734i	$0.535653\pi$
$648$	1.43229	0.0562657
$649$	17.0403	0.668892
$650$	−7.67184	−0.300914
$651$	−55.5166	−2.17587
$652$	13.6186	0.533345
$653$	19.2310	0.752569	0.376284	−	0.926504i	$-0.377202\pi$
$653$	19.2310	0.752569	0.376284	+	0.926504i	$0.377202\pi$
$654$	−15.5511	−0.608095
$655$	−26.1069	−1.02008
$656$	−51.3999	−2.00683
$657$	8.94140	0.348837
$658$	3.04465	0.118693
$659$	−16.6730	−0.649488	−0.324744	−	0.945802i	$-0.605278\pi$
$659$	−16.6730	−0.649488	−0.324744	+	0.945802i	$0.605278\pi$
$660$	28.4082	1.10579
$661$	26.0439	1.01299	0.506496	−	0.862242i	$-0.330941\pi$
$661$	26.0439	1.01299	0.506496	+	0.862242i	$0.330941\pi$
$662$	−20.7586	−0.806804
$663$	−0.498319	−0.0193531
$664$	7.81512	0.303285
$665$	112.290	4.35442
$666$	−14.4446	−0.559716
$667$	2.77569	0.107475
$668$	−9.82696	−0.380216
$669$	−10.5981	−0.409747
$670$	−18.5334	−0.716009
$671$	3.58777	0.138504
$672$	−30.0287	−1.15838
$673$	−33.6384	−1.29666	−0.648332	−	0.761358i	$-0.724533\pi$
$673$	−33.6384	−1.29666	−0.648332	+	0.761358i	$0.724533\pi$
$674$	18.0133	0.693848
$675$	−8.60735	−0.331297
$676$	−15.2922	−0.588161
$677$	2.88919	0.111040	0.0555202	−	0.998458i	$-0.482318\pi$
$677$	2.88919	0.111040	0.0555202	+	0.998458i	$0.482318\pi$
$678$	30.5681	1.17396
$679$	−23.2276	−0.891395
$680$	−5.28345	−0.202611
$681$	−15.6722	−0.600559
$682$	−127.575	−4.88511
$683$	4.92486	0.188445	0.0942223	−	0.995551i	$-0.469964\pi$
$683$	4.92486	0.188445	0.0942223	+	0.995551i	$0.469964\pi$
$684$	−7.30336	−0.279251
$685$	−47.2261	−1.80442
$686$	−98.2042	−3.74946
$687$	26.1823	0.998917
$688$	−48.3788	−1.84442
$689$	−3.15637	−0.120248
$690$	3.45526	0.131539
$691$	33.1752	1.26204	0.631022	−	0.775765i	$-0.282636\pi$
$691$	33.1752	1.26204	0.631022	+	0.775765i	$0.282636\pi$
$692$	−4.05926	−0.154310
$693$	32.0988	1.21933
$694$	−24.5356	−0.931360
$695$	−25.5111	−0.967693
$696$	7.59155	0.287757
$697$	10.3622	0.392497
$698$	34.2744	1.29730
$699$	−8.14008	−0.307886
$700$	51.5947	1.95010
$701$	2.79468	0.105554	0.0527769	−	0.998606i	$-0.483193\pi$
$701$	2.79468	0.105554	0.0527769	+	0.998606i	$0.483193\pi$
$702$	0.891313	0.0336405
$703$	−49.1816	−1.85492
$704$	−5.29697	−0.199637
$705$	−1.25622	−0.0473122
$706$	−11.6846	−0.439756
$707$	−49.5865	−1.86489
$708$	−3.18218	−0.119594
$709$	−31.9364	−1.19940	−0.599699	−	0.800226i	$-0.704713\pi$
$709$	−31.9364	−1.19940	−0.599699	+	0.800226i	$0.704713\pi$
$710$	−47.3907	−1.77854
$711$	16.9055	0.634007
$712$	−1.50431	−0.0563765
$713$	−5.81647	−0.217828
$714$	8.94039	0.334586
$715$	−11.8046	−0.441465
$716$	−22.2551	−0.831713
$717$	13.8131	0.515860
$718$	−13.9084	−0.519056
$719$	−10.7154	−0.399618	−0.199809	−	0.979835i	$-0.564032\pi$
$719$	−10.7154	−0.399618	−0.199809	+	0.979835i	$0.564032\pi$
$720$	18.2977	0.681913
$721$	−31.4734	−1.17213
$722$	−32.3540	−1.20409
$723$	−27.6965	−1.03005
$724$	12.4798	0.463807
$725$	−45.6214	−1.69434
$726$	54.0871	2.00736
$727$	−35.2447	−1.30715	−0.653577	−	0.756860i	$-0.726732\pi$
$727$	−35.2447	−1.30715	−0.653577	+	0.756860i	$0.726732\pi$
$728$	3.56757	0.132223
$729$	1.00000	0.0370370
$730$	58.9949	2.18350
$731$	9.75318	0.360734
$732$	−0.669994	−0.0247637
$733$	−6.36318	−0.235029	−0.117515	−	0.993071i	$-0.537493\pi$
$733$	−6.36318	−0.235029	−0.117515	+	0.993071i	$0.537493\pi$
$734$	5.36406	0.197991
$735$	66.3409	2.44702
$736$	−3.14610	−0.115967
$737$	−18.0385	−0.664458
$738$	−18.5343	−0.682257
$739$	31.9258	1.17441	0.587204	−	0.809439i	$-0.300229\pi$
$739$	31.9258	1.17441	0.587204	+	0.809439i	$0.300229\pi$
$740$	−35.7249	−1.31327
$741$	3.03479	0.111486
$742$	56.6287	2.07891
$743$	7.72069	0.283244	0.141622	−	0.989921i	$-0.454768\pi$
$743$	7.72069	0.283244	0.141622	+	0.989921i	$0.454768\pi$
$744$	−15.9081	−0.583221
$745$	−61.2275	−2.24320
$746$	41.2243	1.50933
$747$	5.45638	0.199639
$748$	7.70118	0.281583
$749$	−30.5222	−1.11526
$750$	−23.8011	−0.869094
$751$	19.9841	0.729231	0.364616	−	0.931158i	$-0.381200\pi$
$751$	19.9841	0.729231	0.364616	+	0.931158i	$0.381200\pi$
$752$	1.68923	0.0615999
$753$	4.06052	0.147974
$754$	4.72422	0.172046
$755$	35.4158	1.28891
$756$	−5.99427	−0.218009
$757$	−25.1730	−0.914929	−0.457464	−	0.889228i	$-0.651242\pi$
$757$	−25.1730	−0.914929	−0.457464	+	0.889228i	$0.651242\pi$
$758$	−55.9374	−2.03174
$759$	3.36299	0.122069
$760$	32.1764	1.16716
$761$	−12.6032	−0.456866	−0.228433	−	0.973560i	$-0.573360\pi$
$761$	−12.6032	−0.456866	−0.228433	+	0.973560i	$0.573360\pi$
$762$	−1.19810	−0.0434027
$763$	−43.4582	−1.57329
$764$	−2.32985	−0.0842912
$765$	−3.68881	−0.133369
$766$	−4.30410	−0.155514
$767$	1.32230	0.0477456
$768$	−20.5017	−0.739793
$769$	−41.4989	−1.49649	−0.748244	−	0.663423i	$-0.769103\pi$
$769$	−41.4989	−1.49649	−0.748244	+	0.663423i	$0.769103\pi$
$770$	211.787	7.63226
$771$	29.5186	1.06309
$772$	−20.3416	−0.732111
$773$	50.8582	1.82924	0.914622	−	0.404311i	$-0.132489\pi$
$773$	50.8582	1.82924	0.914622	+	0.404311i	$0.132489\pi$
$774$	−17.4449	−0.627045
$775$	95.6000	3.43405
$776$	−6.65583	−0.238930
$777$	−40.3660	−1.44812
$778$	−11.1392	−0.399360
$779$	−63.1064	−2.26102
$780$	2.20443	0.0789313
$781$	−46.1253	−1.65049
$782$	0.936685	0.0334958
$783$	5.30029	0.189417
$784$	−89.2078	−3.18599
$785$	3.68881	0.131659
$786$	12.6587	0.451523
$787$	3.12825	0.111510	0.0557550	−	0.998444i	$-0.482243\pi$
$787$	3.12825	0.111510	0.0557550	+	0.998444i	$0.482243\pi$
$788$	−30.6881	−1.09322
$789$	6.79580	0.241937
$790$	111.542	3.96848
$791$	85.4240	3.03733
$792$	9.19785	0.326831
$793$	0.278405	0.00988644
$794$	8.60444	0.305360
$795$	−23.3651	−0.828673
$796$	20.6229	0.730960
$797$	22.1524	0.784679	0.392339	−	0.919820i	$-0.371666\pi$
$797$	22.1524	0.784679	0.392339	+	0.919820i	$0.371666\pi$
$798$	−54.4474	−1.92742
$799$	−0.340550	−0.0120478
$800$	51.7097	1.82821
$801$	−1.05029	−0.0371100
$802$	−57.7243	−2.03832
$803$	57.4197	2.02630
$804$	3.36859	0.118801
$805$	9.65587	0.340325
$806$	−9.89963	−0.348700
$807$	23.1537	0.815049
$808$	−14.2089	−0.499867
$809$	−6.13956	−0.215855	−0.107928	−	0.994159i	$-0.534422\pi$
$809$	−6.13956	−0.215855	−0.107928	+	0.994159i	$0.534422\pi$
$810$	6.59796	0.231829
$811$	23.8867	0.838776	0.419388	−	0.907807i	$-0.362245\pi$
$811$	23.8867	0.838776	0.419388	+	0.907807i	$0.362245\pi$
$812$	−31.7713	−1.11496
$813$	6.38779	0.224029
$814$	−92.7599	−3.25123
$815$	−41.8906	−1.46737
$816$	4.96031	0.173646
$817$	−59.3973	−2.07805
$818$	47.4562	1.65927
$819$	2.49082	0.0870361
$820$	−45.8397	−1.60079
$821$	3.73180	0.130241	0.0651203	−	0.997877i	$-0.479257\pi$
$821$	3.73180	0.130241	0.0651203	+	0.997877i	$0.479257\pi$
$822$	22.8991	0.798697
$823$	−8.79021	−0.306407	−0.153204	−	0.988195i	$-0.548959\pi$
$823$	−8.79021	−0.306407	−0.153204	+	0.988195i	$0.548959\pi$
$824$	−9.01862	−0.314179
$825$	−55.2745	−1.92441
$826$	−23.7235	−0.825448
$827$	33.8786	1.17807	0.589037	−	0.808106i	$-0.299507\pi$
$827$	33.8786	1.17807	0.589037	+	0.808106i	$0.299507\pi$
$828$	−0.628019	−0.0218252
$829$	−6.89122	−0.239342	−0.119671	−	0.992814i	$-0.538184\pi$
$829$	−6.89122	−0.239342	−0.119671	+	0.992814i	$0.538184\pi$
$830$	36.0010	1.24961
$831$	7.67985	0.266411
$832$	−0.411036	−0.0142501
$833$	17.9843	0.623120
$834$	12.3699	0.428334
$835$	30.2276	1.04607
$836$	−46.9005	−1.62209
$837$	−11.1068	−0.383907
$838$	52.3221	1.80744
$839$	−19.5207	−0.673930	−0.336965	−	0.941517i	$-0.609400\pi$
$839$	−19.5207	−0.673930	−0.336965	+	0.941517i	$0.609400\pi$
$840$	26.4090	0.911196
$841$	−0.906939	−0.0312738
$842$	−44.9089	−1.54766
$843$	8.61923	0.296862
$844$	−5.25749	−0.180970
$845$	47.0386	1.61818
$846$	0.609121	0.0209420
$847$	151.149	5.19353
$848$	31.4187	1.07892
$849$	1.38010	0.0473648
$850$	−15.3954	−0.528059
$851$	−4.22915	−0.144973
$852$	8.61362	0.295098
$853$	−41.7096	−1.42811	−0.714054	−	0.700090i	$-0.753143\pi$
$853$	−41.7096	−1.42811	−0.714054	+	0.700090i	$0.753143\pi$
$854$	−4.99488	−0.170921
$855$	22.4650	0.768288
$856$	−8.74608	−0.298935
$857$	−30.3859	−1.03796	−0.518981	−	0.854786i	$-0.673688\pi$
$857$	−30.3859	−1.03796	−0.518981	+	0.854786i	$0.673688\pi$
$858$	5.72382	0.195408
$859$	−12.0865	−0.412385	−0.206192	−	0.978511i	$-0.566107\pi$
$859$	−12.0865	−0.412385	−0.206192	+	0.978511i	$0.566107\pi$
$860$	−43.1455	−1.47125
$861$	−51.7949	−1.76517
$862$	−11.6088	−0.395397
$863$	43.9719	1.49682	0.748410	−	0.663236i	$-0.230817\pi$
$863$	43.9719	1.49682	0.748410	+	0.663236i	$0.230817\pi$
$864$	−6.00762	−0.204383
$865$	12.4862	0.424545
$866$	62.2035	2.11376
$867$	−1.00000	−0.0339618
$868$	66.5771	2.25977
$869$	108.564	3.68277
$870$	34.9711	1.18563
$871$	−1.39976	−0.0474291
$872$	−12.4528	−0.421706
$873$	−4.64699	−0.157277
$874$	−5.70445	−0.192956
$875$	−66.5133	−2.24856
$876$	−10.7228	−0.362289
$877$	15.6894	0.529795	0.264897	−	0.964277i	$-0.414662\pi$
$877$	15.6894	0.529795	0.264897	+	0.964277i	$0.414662\pi$
$878$	59.8546	2.02000
$879$	24.4425	0.824426
$880$	117.503	3.96104
$881$	−16.2523	−0.547555	−0.273777	−	0.961793i	$-0.588273\pi$
$881$	−16.2523	−0.547555	−0.273777	+	0.961793i	$0.588273\pi$
$882$	−32.1675	−1.08314
$883$	4.96920	0.167227	0.0836135	−	0.996498i	$-0.473354\pi$
$883$	4.96920	0.167227	0.0836135	+	0.996498i	$0.473354\pi$
$884$	0.597599	0.0200994
$885$	9.78836	0.329032
$886$	−22.3120	−0.749586
$887$	−1.73078	−0.0581138	−0.0290569	−	0.999578i	$-0.509250\pi$
$887$	−1.73078	−0.0581138	−0.0290569	+	0.999578i	$0.509250\pi$
$888$	−11.5668	−0.388157
$889$	−3.34815	−0.112293
$890$	−6.92973	−0.232285
$891$	6.42178	0.215138
$892$	12.7096	0.425548
$893$	2.07396	0.0694025
$894$	29.6881	0.992918
$895$	68.4565	2.28825
$896$	−52.6829	−1.76001
$897$	0.260963	0.00871329
$898$	−50.0099	−1.66885
$899$	−58.8692	−1.96340
$900$	10.3222	0.344073
$901$	−6.33403	−0.211017
$902$	−119.023	−3.96304
$903$	−48.7506	−1.62232
$904$	24.4781	0.814128
$905$	−38.3876	−1.27605
$906$	−17.1725	−0.570517
$907$	−30.3560	−1.00796	−0.503978	−	0.863717i	$-0.668131\pi$
$907$	−30.3560	−1.00796	−0.503978	+	0.863717i	$0.668131\pi$
$908$	18.7945	0.623718
$909$	−9.92040	−0.329039
$910$	16.4343	0.544791
$911$	17.0157	0.563755	0.281877	−	0.959450i	$-0.409043\pi$
$911$	17.0157	0.563755	0.281877	+	0.959450i	$0.409043\pi$
$912$	−30.2085	−1.00030
$913$	35.0397	1.15964
$914$	16.2363	0.537048
$915$	2.06089	0.0681310
$916$	−31.3986	−1.03744
$917$	35.3754	1.16820
$918$	1.78864	0.0590339
$919$	−31.5392	−1.04038	−0.520190	−	0.854050i	$-0.674139\pi$
$919$	−31.5392	−1.04038	−0.520190	+	0.854050i	$0.674139\pi$
$920$	2.76687	0.0912210
$921$	23.1189	0.761793
$922$	25.2366	0.831124
$923$	−3.57924	−0.117812
$924$	−38.4938	−1.26635
$925$	69.5107	2.28550
$926$	−0.295019	−0.00969493
$927$	−6.29664	−0.206809
$928$	−31.8421	−1.04527
$929$	−1.41769	−0.0465131	−0.0232565	−	0.999730i	$-0.507403\pi$
$929$	−1.41769	−0.0465131	−0.0232565	+	0.999730i	$0.507403\pi$
$930$	−73.2821	−2.40302
$931$	−109.525	−3.58955
$932$	9.76183	0.319759
$933$	−21.6190	−0.707775
$934$	−56.4339	−1.84657
$935$	−23.6887	−0.774705
$936$	0.713738	0.0233293
$937$	−24.0410	−0.785385	−0.392693	−	0.919670i	$-0.628456\pi$
$937$	−24.0410	−0.785385	−0.392693	+	0.919670i	$0.628456\pi$
$938$	25.1132	0.819976
$939$	−20.4821	−0.668407
$940$	1.50650	0.0491366
$941$	−3.88309	−0.126585	−0.0632925	−	0.997995i	$-0.520160\pi$
$941$	−3.88309	−0.126585	−0.0632925	+	0.997995i	$0.520160\pi$
$942$	−1.78864	−0.0582770
$943$	−5.42655	−0.176713
$944$	−13.1623	−0.428396
$945$	18.4383	0.599798
$946$	−112.027	−3.64232
$947$	41.3097	1.34239	0.671193	−	0.741283i	$-0.265782\pi$
$947$	41.3097	1.34239	0.671193	+	0.741283i	$0.265782\pi$
$948$	−20.2736	−0.658456
$949$	4.45567	0.144637
$950$	93.7589	3.04194
$951$	−4.01241	−0.130111
$952$	7.15921	0.232031
$953$	52.6727	1.70624	0.853118	−	0.521719i	$-0.174709\pi$
$953$	52.6727	1.70624	0.853118	+	0.521719i	$0.174709\pi$
$954$	11.3293	0.366799
$955$	7.16660	0.231906
$956$	−16.5651	−0.535753
$957$	34.0373	1.10027
$958$	−19.8026	−0.639795
$959$	63.9925	2.06643
$960$	−3.04270	−0.0982027
$961$	92.3608	2.97938
$962$	−7.19801	−0.232073
$963$	−6.10636	−0.196775
$964$	33.2145	1.06977
$965$	62.5706	2.01422
$966$	−4.68196	−0.150639
$967$	9.06672	0.291566	0.145783	−	0.989317i	$-0.453430\pi$
$967$	9.06672	0.291566	0.145783	+	0.989317i	$0.453430\pi$
$968$	43.3114	1.39208
$969$	6.09004	0.195640
$970$	−30.6606	−0.984453
$971$	−22.9332	−0.735960	−0.367980	−	0.929834i	$-0.619950\pi$
$971$	−22.9332	−0.735960	−0.367980	+	0.929834i	$0.619950\pi$
$972$	−1.19923	−0.0384653
$973$	34.5682	1.10821
$974$	−46.3893	−1.48641
$975$	−4.28921	−0.137365
$976$	−2.77126	−0.0887059
$977$	57.0979	1.82672	0.913361	−	0.407150i	$-0.133477\pi$
$977$	57.0979	1.82672	0.913361	+	0.407150i	$0.133477\pi$
$978$	20.3120	0.649507
$979$	−6.74470	−0.215561
$980$	−79.5579	−2.54138
$981$	−8.69436	−0.277589
$982$	65.2048	2.08077
$983$	−21.0500	−0.671390	−0.335695	−	0.941971i	$-0.608971\pi$
$983$	−21.0500	−0.671390	−0.335695	+	0.941971i	$0.608971\pi$
$984$	−14.8417	−0.473137
$985$	94.3963	3.00772
$986$	9.48030	0.301914
$987$	1.70222	0.0541821
$988$	−3.63940	−0.115785
$989$	−5.10760	−0.162412
$990$	42.3706	1.34663
$991$	−37.0232	−1.17608	−0.588040	−	0.808832i	$-0.700100\pi$
$991$	−37.0232	−1.17608	−0.588040	+	0.808832i	$0.700100\pi$
$992$	66.7254	2.11853
$993$	−11.6058	−0.368298
$994$	64.2155	2.03679
$995$	−63.4359	−2.01105
$996$	−6.54345	−0.207337
$997$	56.2009	1.77990	0.889950	−	0.456058i	$-0.150739\pi$
$997$	56.2009	1.77990	0.889950	+	0.456058i	$0.150739\pi$
$998$	−49.0583	−1.55291
$999$	−8.07574	−0.255505

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.13	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-1.78864 q^{2} -1.00000 q^{3} +1.19923 q^{4} -3.68881 q^{5} +1.78864 q^{6} +4.99843 q^{7} +1.43229 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.78864 q^{2} -1.00000 q^{3} +1.19923 q^{4} -3.68881 q^{5} +1.78864 q^{6} +4.99843 q^{7} +1.43229 q^{8} +1.00000 q^{9} +6.59796 q^{10} +6.42178 q^{11} -1.19923 q^{12} +0.498319 q^{13} -8.94039 q^{14} +3.68881 q^{15} -4.96031 q^{16} +1.00000 q^{17} -1.78864 q^{18} -6.09004 q^{19} -4.42373 q^{20} -4.99843 q^{21} -11.4862 q^{22} -0.523686 q^{23} -1.43229 q^{24} +8.60735 q^{25} -0.891313 q^{26} -1.00000 q^{27} +5.99427 q^{28} -5.30029 q^{29} -6.59796 q^{30} +11.1068 q^{31} +6.00762 q^{32} -6.42178 q^{33} -1.78864 q^{34} -18.4383 q^{35} +1.19923 q^{36} +8.07574 q^{37} +10.8929 q^{38} -0.498319 q^{39} -5.28345 q^{40} +10.3622 q^{41} +8.94039 q^{42} +9.75318 q^{43} +7.70118 q^{44} -3.68881 q^{45} +0.936685 q^{46} -0.340550 q^{47} +4.96031 q^{48} +17.9843 q^{49} -15.3954 q^{50} -1.00000 q^{51} +0.597599 q^{52} -6.33403 q^{53} +1.78864 q^{54} -23.6887 q^{55} +7.15921 q^{56} +6.09004 q^{57} +9.48030 q^{58} +2.65352 q^{59} +4.42373 q^{60} +0.558687 q^{61} -19.8660 q^{62} +4.99843 q^{63} -0.824845 q^{64} -1.83821 q^{65} +11.4862 q^{66} -2.80896 q^{67} +1.19923 q^{68} +0.523686 q^{69} +32.9794 q^{70} -7.18263 q^{71} +1.43229 q^{72} +8.94140 q^{73} -14.4446 q^{74} -8.60735 q^{75} -7.30336 q^{76} +32.0988 q^{77} +0.891313 q^{78} +16.9055 q^{79} +18.2977 q^{80} +1.00000 q^{81} -18.5343 q^{82} +5.45638 q^{83} -5.99427 q^{84} -3.68881 q^{85} -17.4449 q^{86} +5.30029 q^{87} +9.19785 q^{88} -1.05029 q^{89} +6.59796 q^{90} +2.49082 q^{91} -0.628019 q^{92} -11.1068 q^{93} +0.609121 q^{94} +22.4650 q^{95} -6.00762 q^{96} -4.64699 q^{97} -32.1675 q^{98} +6.42178 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 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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