LMFDB - Embedded newform 8007.2.a.j.1.59

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			1.59
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)

$f(q)$	$=$	$q+2.61228 q^{2} -1.00000 q^{3} +4.82400 q^{4} +0.172926 q^{5} -2.61228 q^{6} +2.37939 q^{7} +7.37708 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.61228 q^{2} -1.00000 q^{3} +4.82400 q^{4} +0.172926 q^{5} -2.61228 q^{6} +2.37939 q^{7} +7.37708 q^{8} +1.00000 q^{9} +0.451730 q^{10} -1.99950 q^{11} -4.82400 q^{12} +5.41833 q^{13} +6.21563 q^{14} -0.172926 q^{15} +9.62298 q^{16} +1.00000 q^{17} +2.61228 q^{18} +8.03513 q^{19} +0.834193 q^{20} -2.37939 q^{21} -5.22324 q^{22} -5.87622 q^{23} -7.37708 q^{24} -4.97010 q^{25} +14.1542 q^{26} -1.00000 q^{27} +11.4782 q^{28} -3.52223 q^{29} -0.451730 q^{30} +0.766246 q^{31} +10.3838 q^{32} +1.99950 q^{33} +2.61228 q^{34} +0.411457 q^{35} +4.82400 q^{36} +1.49160 q^{37} +20.9900 q^{38} -5.41833 q^{39} +1.27569 q^{40} +4.36981 q^{41} -6.21563 q^{42} +9.49910 q^{43} -9.64557 q^{44} +0.172926 q^{45} -15.3503 q^{46} -3.63701 q^{47} -9.62298 q^{48} -1.33851 q^{49} -12.9833 q^{50} -1.00000 q^{51} +26.1380 q^{52} +9.43332 q^{53} -2.61228 q^{54} -0.345764 q^{55} +17.5529 q^{56} -8.03513 q^{57} -9.20105 q^{58} +8.75152 q^{59} -0.834193 q^{60} -1.42373 q^{61} +2.00165 q^{62} +2.37939 q^{63} +7.87930 q^{64} +0.936967 q^{65} +5.22324 q^{66} -0.494389 q^{67} +4.82400 q^{68} +5.87622 q^{69} +1.07484 q^{70} -8.26294 q^{71} +7.37708 q^{72} -1.58112 q^{73} +3.89647 q^{74} +4.97010 q^{75} +38.7615 q^{76} -4.75758 q^{77} -14.1542 q^{78} +1.01375 q^{79} +1.66406 q^{80} +1.00000 q^{81} +11.4152 q^{82} +3.67017 q^{83} -11.4782 q^{84} +0.172926 q^{85} +24.8143 q^{86} +3.52223 q^{87} -14.7504 q^{88} -7.94528 q^{89} +0.451730 q^{90} +12.8923 q^{91} -28.3469 q^{92} -0.766246 q^{93} -9.50089 q^{94} +1.38948 q^{95} -10.3838 q^{96} +0.0539381 q^{97} -3.49656 q^{98} -1.99950 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.61228	1.84716	0.923580	−	0.383406i	$-0.125249\pi$
$2$	2.61228	1.84716	0.923580	+	0.383406i	$0.125249\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.82400	2.41200
$5$	0.172926	0.0773347	0.0386673	−	0.999252i	$-0.487689\pi$
$5$	0.172926	0.0773347	0.0386673	+	0.999252i	$0.487689\pi$
$6$	−2.61228	−1.06646
$7$	2.37939	0.899325	0.449662	−	0.893199i	$-0.351544\pi$
$7$	2.37939	0.899325	0.449662	+	0.893199i	$0.351544\pi$
$8$	7.37708	2.60819
$9$	1.00000	0.333333
$10$	0.451730	0.142850
$11$	−1.99950	−0.602871	−0.301435	−	0.953487i	$-0.597466\pi$
$11$	−1.99950	−0.602871	−0.301435	+	0.953487i	$0.597466\pi$
$12$	−4.82400	−1.39257
$13$	5.41833	1.50277	0.751387	−	0.659862i	$-0.229385\pi$
$13$	5.41833	1.50277	0.751387	+	0.659862i	$0.229385\pi$
$14$	6.21563	1.66120
$15$	−0.172926	−0.0446492
$16$	9.62298	2.40575
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.61228	0.615720
$19$	8.03513	1.84338	0.921692	−	0.387922i	$-0.126807\pi$
$19$	8.03513	1.84338	0.921692	+	0.387922i	$0.126807\pi$
$20$	0.834193	0.186531
$21$	−2.37939	−0.519225
$22$	−5.22324	−1.11360
$23$	−5.87622	−1.22528	−0.612639	−	0.790363i	$-0.709892\pi$
$23$	−5.87622	−1.22528	−0.612639	+	0.790363i	$0.709892\pi$
$24$	−7.37708	−1.50584
$25$	−4.97010	−0.994019
$26$	14.1542	2.77586
$27$	−1.00000	−0.192450
$28$	11.4782	2.16917
$29$	−3.52223	−0.654062	−0.327031	−	0.945014i	$-0.606048\pi$
$29$	−3.52223	−0.654062	−0.327031	+	0.945014i	$0.606048\pi$
$30$	−0.451730	−0.0824742
$31$	0.766246	0.137622	0.0688110	−	0.997630i	$-0.478079\pi$
$31$	0.766246	0.137622	0.0688110	+	0.997630i	$0.478079\pi$
$32$	10.3838	1.83561
$33$	1.99950	0.348067
$34$	2.61228	0.448002
$35$	0.411457	0.0695490
$36$	4.82400	0.804000
$37$	1.49160	0.245217	0.122609	−	0.992455i	$-0.460874\pi$
$37$	1.49160	0.245217	0.122609	+	0.992455i	$0.460874\pi$
$38$	20.9900	3.40503
$39$	−5.41833	−0.867626
$40$	1.27569	0.201704
$41$	4.36981	0.682450	0.341225	−	0.939982i	$-0.389158\pi$
$41$	4.36981	0.682450	0.341225	+	0.939982i	$0.389158\pi$
$42$	−6.21563	−0.959092
$43$	9.49910	1.44860	0.724299	−	0.689485i	$-0.242163\pi$
$43$	9.49910	1.44860	0.724299	+	0.689485i	$0.242163\pi$
$44$	−9.64557	−1.45412
$45$	0.172926	0.0257782
$46$	−15.3503	−2.26328
$47$	−3.63701	−0.530513	−0.265256	−	0.964178i	$-0.585457\pi$
$47$	−3.63701	−0.530513	−0.265256	+	0.964178i	$0.585457\pi$
$48$	−9.62298	−1.38896
$49$	−1.33851	−0.191215
$50$	−12.9833	−1.83611
$51$	−1.00000	−0.140028
$52$	26.1380	3.62469
$53$	9.43332	1.29577	0.647883	−	0.761740i	$-0.275654\pi$
$53$	9.43332	1.29577	0.647883	+	0.761740i	$0.275654\pi$
$54$	−2.61228	−0.355486
$55$	−0.345764	−0.0466228
$56$	17.5529	2.34561
$57$	−8.03513	−1.06428
$58$	−9.20105	−1.20816
$59$	8.75152	1.13935	0.569675	−	0.821870i	$-0.307069\pi$
$59$	8.75152	1.13935	0.569675	+	0.821870i	$0.307069\pi$
$60$	−0.834193	−0.107694
$61$	−1.42373	−0.182290	−0.0911452	−	0.995838i	$-0.529053\pi$
$61$	−1.42373	−0.182290	−0.0911452	+	0.995838i	$0.529053\pi$
$62$	2.00165	0.254210
$63$	2.37939	0.299775
$64$	7.87930	0.984913
$65$	0.936967	0.116216
$66$	5.22324	0.642936
$67$	−0.494389	−0.0603992	−0.0301996	−	0.999544i	$-0.509614\pi$
$67$	−0.494389	−0.0603992	−0.0301996	+	0.999544i	$0.509614\pi$
$68$	4.82400	0.584996
$69$	5.87622	0.707414
$70$	1.07484	0.128468
$71$	−8.26294	−0.980630	−0.490315	−	0.871545i	$-0.663118\pi$
$71$	−8.26294	−0.980630	−0.490315	+	0.871545i	$0.663118\pi$
$72$	7.37708	0.869397
$73$	−1.58112	−0.185056	−0.0925280	−	0.995710i	$-0.529495\pi$
$73$	−1.58112	−0.185056	−0.0925280	+	0.995710i	$0.529495\pi$
$74$	3.89647	0.452956
$75$	4.97010	0.573897
$76$	38.7615	4.44624
$77$	−4.75758	−0.542176
$78$	−14.1542	−1.60264
$79$	1.01375	0.114056	0.0570281	−	0.998373i	$-0.481838\pi$
$79$	1.01375	0.114056	0.0570281	+	0.998373i	$0.481838\pi$
$80$	1.66406	0.186048
$81$	1.00000	0.111111
$82$	11.4152	1.26059
$83$	3.67017	0.402854	0.201427	−	0.979504i	$-0.435442\pi$
$83$	3.67017	0.402854	0.201427	+	0.979504i	$0.435442\pi$
$84$	−11.4782	−1.25237
$85$	0.172926	0.0187564
$86$	24.8143	2.67579
$87$	3.52223	0.377623
$88$	−14.7504	−1.57240
$89$	−7.94528	−0.842198	−0.421099	−	0.907015i	$-0.638355\pi$
$89$	−7.94528	−0.842198	−0.421099	+	0.907015i	$0.638355\pi$
$90$	0.451730	0.0476165
$91$	12.8923	1.35148
$92$	−28.3469	−2.95537
$93$	−0.766246	−0.0794560
$94$	−9.50089	−0.979942
$95$	1.38948	0.142558
$96$	−10.3838	−1.05979
$97$	0.0539381	0.00547659	0.00273829	−	0.999996i	$-0.499128\pi$
$97$	0.0539381	0.00547659	0.00273829	+	0.999996i	$0.499128\pi$
$98$	−3.49656	−0.353205
$99$	−1.99950	−0.200957
$100$	−23.9757	−2.39757
$101$	−2.47424	−0.246196	−0.123098	−	0.992395i	$-0.539283\pi$
$101$	−2.47424	−0.246196	−0.123098	+	0.992395i	$0.539283\pi$
$102$	−2.61228	−0.258654
$103$	−2.01917	−0.198954	−0.0994772	−	0.995040i	$-0.531717\pi$
$103$	−2.01917	−0.198954	−0.0994772	+	0.995040i	$0.531717\pi$
$104$	39.9714	3.91952
$105$	−0.411457	−0.0401541
$106$	24.6425	2.39349
$107$	−1.93001	−0.186581	−0.0932903	−	0.995639i	$-0.529738\pi$
$107$	−1.93001	−0.186581	−0.0932903	+	0.995639i	$0.529738\pi$
$108$	−4.82400	−0.464190
$109$	1.28728	0.123299	0.0616495	−	0.998098i	$-0.480364\pi$
$109$	1.28728	0.123299	0.0616495	+	0.998098i	$0.480364\pi$
$110$	−0.903232	−0.0861198
$111$	−1.49160	−0.141576
$112$	22.8968	2.16355
$113$	−12.6731	−1.19218	−0.596092	−	0.802916i	$-0.703281\pi$
$113$	−12.6731	−1.19218	−0.596092	+	0.802916i	$0.703281\pi$
$114$	−20.9900	−1.96589
$115$	−1.01615	−0.0947564
$116$	−16.9913	−1.57760
$117$	5.41833	0.500924
$118$	22.8614	2.10456
$119$	2.37939	0.218118
$120$	−1.27569	−0.116454
$121$	−7.00202	−0.636547
$122$	−3.71919	−0.336720
$123$	−4.36981	−0.394013
$124$	3.69637	0.331944
$125$	−1.72408	−0.154207
$126$	6.21563	0.553732
$127$	−19.5201	−1.73213	−0.866063	−	0.499935i	$-0.833357\pi$
$127$	−19.5201	−1.73213	−0.866063	+	0.499935i	$0.833357\pi$
$128$	−0.184578	−0.0163145
$129$	−9.49910	−0.836349
$130$	2.44762	0.214670
$131$	−10.2427	−0.894913	−0.447457	−	0.894306i	$-0.647670\pi$
$131$	−10.2427	−0.894913	−0.447457	+	0.894306i	$0.647670\pi$
$132$	9.64557	0.839539
$133$	19.1187	1.65780
$134$	−1.29148	−0.111567
$135$	−0.172926	−0.0148831
$136$	7.37708	0.632579
$137$	1.06494	0.0909841	0.0454920	−	0.998965i	$-0.485514\pi$
$137$	1.06494	0.0909841	0.0454920	+	0.998965i	$0.485514\pi$
$138$	15.3503	1.30671
$139$	11.0035	0.933305	0.466652	−	0.884441i	$-0.345460\pi$
$139$	11.0035	0.933305	0.466652	+	0.884441i	$0.345460\pi$
$140$	1.98487	0.167752
$141$	3.63701	0.306292
$142$	−21.5851	−1.81138
$143$	−10.8339	−0.905978
$144$	9.62298	0.801915
$145$	−0.609084	−0.0505817
$146$	−4.13032	−0.341828
$147$	1.33851	0.110398
$148$	7.19547	0.591464
$149$	−1.49026	−0.122087	−0.0610436	−	0.998135i	$-0.519443\pi$
$149$	−1.49026	−0.122087	−0.0610436	+	0.998135i	$0.519443\pi$
$150$	12.9833	1.06008
$151$	10.6655	0.867947	0.433974	−	0.900926i	$-0.357111\pi$
$151$	10.6655	0.867947	0.433974	+	0.900926i	$0.357111\pi$
$152$	59.2758	4.80790
$153$	1.00000	0.0808452
$154$	−12.4281	−1.00149
$155$	0.132504	0.0106429
$156$	−26.1380	−2.09272
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	2.64821	0.210680
$159$	−9.43332	−0.748111
$160$	1.79562	0.141956
$161$	−13.9818	−1.10192
$162$	2.61228	0.205240
$163$	23.6219	1.85021	0.925105	−	0.379711i	$-0.123977\pi$
$163$	23.6219	1.85021	0.925105	+	0.379711i	$0.123977\pi$
$164$	21.0800	1.64607
$165$	0.345764	0.0269177
$166$	9.58752	0.744136
$167$	−6.94366	−0.537316	−0.268658	−	0.963236i	$-0.586580\pi$
$167$	−6.94366	−0.537316	−0.268658	+	0.963236i	$0.586580\pi$
$168$	−17.5529	−1.35424
$169$	16.3583	1.25833
$170$	0.451730	0.0346461
$171$	8.03513	0.614462
$172$	45.8237	3.49402
$173$	20.4622	1.55571	0.777855	−	0.628443i	$-0.216308\pi$
$173$	20.4622	1.55571	0.777855	+	0.628443i	$0.216308\pi$
$174$	9.20105	0.697530
$175$	−11.8258	−0.893946
$176$	−19.2411	−1.45035
$177$	−8.75152	−0.657804
$178$	−20.7553	−1.55567
$179$	20.0824	1.50103	0.750514	−	0.660855i	$-0.229806\pi$
$179$	20.0824	1.50103	0.750514	+	0.660855i	$0.229806\pi$
$180$	0.834193	0.0621771
$181$	22.6705	1.68509	0.842543	−	0.538629i	$-0.181058\pi$
$181$	22.6705	1.68509	0.842543	+	0.538629i	$0.181058\pi$
$182$	33.6783	2.49640
$183$	1.42373	0.105245
$184$	−43.3494	−3.19576
$185$	0.257936	0.0189638
$186$	−2.00165	−0.146768
$187$	−1.99950	−0.146218
$188$	−17.5450	−1.27960
$189$	−2.37939	−0.173075
$190$	3.62971	0.263327
$191$	0.600264	0.0434336	0.0217168	−	0.999764i	$-0.493087\pi$
$191$	0.600264	0.0434336	0.0217168	+	0.999764i	$0.493087\pi$
$192$	−7.87930	−0.568640
$193$	7.49613	0.539583	0.269792	−	0.962919i	$-0.413045\pi$
$193$	7.49613	0.539583	0.269792	+	0.962919i	$0.413045\pi$
$194$	0.140901	0.0101161
$195$	−0.936967	−0.0670976
$196$	−6.45696	−0.461212
$197$	−12.3778	−0.881880	−0.440940	−	0.897537i	$-0.645355\pi$
$197$	−12.3778	−0.881880	−0.440940	+	0.897537i	$0.645355\pi$
$198$	−5.22324	−0.371199
$199$	−24.8171	−1.75924	−0.879618	−	0.475681i	$-0.842202\pi$
$199$	−24.8171	−1.75924	−0.879618	+	0.475681i	$0.842202\pi$
$200$	−36.6648	−2.59259
$201$	0.494389	0.0348715
$202$	−6.46341	−0.454764
$203$	−8.38076	−0.588214
$204$	−4.82400	−0.337748
$205$	0.755652	0.0527771
$206$	−5.27463	−0.367501
$207$	−5.87622	−0.408426
$208$	52.1404	3.61529
$209$	−16.0662	−1.11132
$210$	−1.07484	−0.0741711
$211$	11.1616	0.768394	0.384197	−	0.923251i	$-0.374478\pi$
$211$	11.1616	0.768394	0.384197	+	0.923251i	$0.374478\pi$
$212$	45.5064	3.12539
$213$	8.26294	0.566167
$214$	−5.04171	−0.344644
$215$	1.64264	0.112027
$216$	−7.37708	−0.501947
$217$	1.82320	0.123767
$218$	3.36273	0.227753
$219$	1.58112	0.106842
$220$	−1.66797	−0.112454
$221$	5.41833	0.364476
$222$	−3.89647	−0.261514
$223$	−2.33157	−0.156134	−0.0780668	−	0.996948i	$-0.524875\pi$
$223$	−2.33157	−0.156134	−0.0780668	+	0.996948i	$0.524875\pi$
$224$	24.7070	1.65081
$225$	−4.97010	−0.331340
$226$	−33.1057	−2.20216
$227$	−10.6018	−0.703667	−0.351834	−	0.936063i	$-0.614442\pi$
$227$	−10.6018	−0.703667	−0.351834	+	0.936063i	$0.614442\pi$
$228$	−38.7615	−2.56704
$229$	2.08788	0.137971	0.0689856	−	0.997618i	$-0.478024\pi$
$229$	2.08788	0.137971	0.0689856	+	0.997618i	$0.478024\pi$
$230$	−2.65447	−0.175030
$231$	4.75758	0.313026
$232$	−25.9838	−1.70592
$233$	−18.6891	−1.22437	−0.612183	−	0.790716i	$-0.709708\pi$
$233$	−18.6891	−1.22437	−0.612183	+	0.790716i	$0.709708\pi$
$234$	14.1542	0.925287
$235$	−0.628933	−0.0410270
$236$	42.2173	2.74811
$237$	−1.01375	−0.0658504
$238$	6.21563	0.402899
$239$	−3.74073	−0.241967	−0.120984	−	0.992654i	$-0.538605\pi$
$239$	−3.74073	−0.241967	−0.120984	+	0.992654i	$0.538605\pi$
$240$	−1.66406	−0.107415
$241$	26.2221	1.68911	0.844557	−	0.535465i	$-0.179864\pi$
$241$	26.2221	1.68911	0.844557	+	0.535465i	$0.179864\pi$
$242$	−18.2912	−1.17580
$243$	−1.00000	−0.0641500
$244$	−6.86809	−0.439685
$245$	−0.231462	−0.0147876
$246$	−11.4152	−0.727805
$247$	43.5369	2.77019
$248$	5.65266	0.358944
$249$	−3.67017	−0.232588
$250$	−4.50379	−0.284845
$251$	17.9946	1.13581	0.567905	−	0.823094i	$-0.307754\pi$
$251$	17.9946	1.13581	0.567905	+	0.823094i	$0.307754\pi$
$252$	11.4782	0.723057
$253$	11.7495	0.738684
$254$	−50.9918	−3.19951
$255$	−0.172926	−0.0108290
$256$	−16.2408	−1.01505
$257$	30.6690	1.91308	0.956539	−	0.291604i	$-0.0941890\pi$
$257$	30.6690	1.91308	0.956539	+	0.291604i	$0.0941890\pi$
$258$	−24.8143	−1.54487
$259$	3.54909	0.220530
$260$	4.51993	0.280314
$261$	−3.52223	−0.218021
$262$	−26.7569	−1.65305
$263$	−8.55680	−0.527635	−0.263817	−	0.964573i	$-0.584982\pi$
$263$	−8.55680	−0.527635	−0.263817	+	0.964573i	$0.584982\pi$
$264$	14.7504	0.907826
$265$	1.63126	0.100208
$266$	49.9434	3.06222
$267$	7.94528	0.486243
$268$	−2.38493	−0.145683
$269$	−23.6373	−1.44119	−0.720597	−	0.693354i	$-0.756132\pi$
$269$	−23.6373	−1.44119	−0.720597	+	0.693354i	$0.756132\pi$
$270$	−0.451730	−0.0274914
$271$	−27.1790	−1.65101	−0.825503	−	0.564397i	$-0.809109\pi$
$271$	−27.1790	−1.65101	−0.825503	+	0.564397i	$0.809109\pi$
$272$	9.62298	0.583479
$273$	−12.8923	−0.780278
$274$	2.78192	0.168062
$275$	9.93769	0.599265
$276$	28.3469	1.70628
$277$	18.4820	1.11048	0.555238	−	0.831691i	$-0.312627\pi$
$277$	18.4820	1.11048	0.555238	+	0.831691i	$0.312627\pi$
$278$	28.7442	1.72396
$279$	0.766246	0.0458740
$280$	3.03535	0.181397
$281$	−18.1985	−1.08563	−0.542815	−	0.839852i	$-0.682642\pi$
$281$	−18.1985	−1.08563	−0.542815	+	0.839852i	$0.682642\pi$
$282$	9.50089	0.565770
$283$	−21.0110	−1.24897	−0.624487	−	0.781035i	$-0.714692\pi$
$283$	−21.0110	−1.24897	−0.624487	+	0.781035i	$0.714692\pi$
$284$	−39.8604	−2.36528
$285$	−1.38948	−0.0823056
$286$	−28.3012	−1.67349
$287$	10.3975	0.613744
$288$	10.3838	0.611869
$289$	1.00000	0.0588235
$290$	−1.59110	−0.0934325
$291$	−0.0539381	−0.00316191
$292$	−7.62732	−0.446355
$293$	−25.7699	−1.50549	−0.752746	−	0.658312i	$-0.771271\pi$
$293$	−25.7699	−1.50549	−0.752746	+	0.658312i	$0.771271\pi$
$294$	3.49656	0.203923
$295$	1.51336	0.0881113
$296$	11.0036	0.639573
$297$	1.99950	0.116022
$298$	−3.89299	−0.225515
$299$	−31.8393	−1.84131
$300$	23.9757	1.38424
$301$	22.6021	1.30276
$302$	27.8613	1.60324
$303$	2.47424	0.142141
$304$	77.3219	4.43471
$305$	−0.246200	−0.0140974
$306$	2.61228	0.149334
$307$	2.49142	0.142193	0.0710965	−	0.997469i	$-0.477350\pi$
$307$	2.49142	0.142193	0.0710965	+	0.997469i	$0.477350\pi$
$308$	−22.9506	−1.30773
$309$	2.01917	0.114866
$310$	0.346136	0.0196592
$311$	18.4720	1.04745	0.523727	−	0.851886i	$-0.324541\pi$
$311$	18.4720	1.04745	0.523727	+	0.851886i	$0.324541\pi$
$312$	−39.9714	−2.26294
$313$	18.5410	1.04800	0.524000	−	0.851718i	$-0.324439\pi$
$313$	18.5410	1.04800	0.524000	+	0.851718i	$0.324439\pi$
$314$	−2.61228	−0.147419
$315$	0.411457	0.0231830
$316$	4.89035	0.275104
$317$	20.1047	1.12919	0.564596	−	0.825367i	$-0.309032\pi$
$317$	20.1047	1.12919	0.564596	+	0.825367i	$0.309032\pi$
$318$	−24.6425	−1.38188
$319$	7.04269	0.394315
$320$	1.36253	0.0761679
$321$	1.93001	0.107722
$322$	−36.5244	−2.03543
$323$	8.03513	0.447086
$324$	4.82400	0.268000
$325$	−26.9296	−1.49379
$326$	61.7070	3.41763
$327$	−1.28728	−0.0711867
$328$	32.2364	1.77996
$329$	−8.65387	−0.477103
$330$	0.903232	0.0497213
$331$	−14.7100	−0.808536	−0.404268	−	0.914641i	$-0.632474\pi$
$331$	−14.7100	−0.808536	−0.404268	+	0.914641i	$0.632474\pi$
$332$	17.7049	0.971684
$333$	1.49160	0.0817391
$334$	−18.1388	−0.992510
$335$	−0.0854925	−0.00467095
$336$	−22.8968	−1.24912
$337$	19.9334	1.08584	0.542922	−	0.839783i	$-0.317318\pi$
$337$	19.9334	1.08584	0.542922	+	0.839783i	$0.317318\pi$
$338$	42.7323	2.32433
$339$	12.6731	0.688308
$340$	0.834193	0.0452405
$341$	−1.53211	−0.0829682
$342$	20.9900	1.13501
$343$	−19.8406	−1.07129
$344$	70.0756	3.77822
$345$	1.01615	0.0547076
$346$	53.4529	2.87365
$347$	1.68603	0.0905109	0.0452554	−	0.998975i	$-0.485590\pi$
$347$	1.68603	0.0905109	0.0452554	+	0.998975i	$0.485590\pi$
$348$	16.9913	0.910827
$349$	−17.6316	−0.943800	−0.471900	−	0.881652i	$-0.656432\pi$
$349$	−17.6316	−0.943800	−0.471900	+	0.881652i	$0.656432\pi$
$350$	−30.8923	−1.65126
$351$	−5.41833	−0.289209
$352$	−20.7623	−1.10663
$353$	5.30333	0.282268	0.141134	−	0.989991i	$-0.454925\pi$
$353$	5.30333	0.282268	0.141134	+	0.989991i	$0.454925\pi$
$354$	−22.8614	−1.21507
$355$	−1.42887	−0.0758367
$356$	−38.3280	−2.03138
$357$	−2.37939	−0.125931
$358$	52.4608	2.77264
$359$	−3.06408	−0.161716	−0.0808579	−	0.996726i	$-0.525766\pi$
$359$	−3.06408	−0.161716	−0.0808579	+	0.996726i	$0.525766\pi$
$360$	1.27569	0.0672345
$361$	45.5633	2.39807
$362$	59.2217	3.11262
$363$	7.00202	0.367511
$364$	62.1925	3.25977
$365$	−0.273416	−0.0143112
$366$	3.71919	0.194405
$367$	−20.5975	−1.07518	−0.537590	−	0.843206i	$-0.680665\pi$
$367$	−20.5975	−1.07518	−0.537590	+	0.843206i	$0.680665\pi$
$368$	−56.5468	−2.94771
$369$	4.36981	0.227483
$370$	0.673800	0.0350292
$371$	22.4455	1.16531
$372$	−3.69637	−0.191648
$373$	−8.56458	−0.443457	−0.221728	−	0.975108i	$-0.571170\pi$
$373$	−8.56458	−0.443457	−0.221728	+	0.975108i	$0.571170\pi$
$374$	−5.22324	−0.270087
$375$	1.72408	0.0890314
$376$	−26.8305	−1.38368
$377$	−19.0846	−0.982907
$378$	−6.21563	−0.319697
$379$	5.57982	0.286616	0.143308	−	0.989678i	$-0.454226\pi$
$379$	5.57982	0.286616	0.143308	+	0.989678i	$0.454226\pi$
$380$	6.70285	0.343849
$381$	19.5201	1.00004
$382$	1.56806	0.0802288
$383$	25.5816	1.30716	0.653580	−	0.756857i	$-0.273266\pi$
$383$	25.5816	1.30716	0.653580	+	0.756857i	$0.273266\pi$
$384$	0.184578	0.00941919
$385$	−0.822707	−0.0419290
$386$	19.5820	0.996697
$387$	9.49910	0.482866
$388$	0.260198	0.0132095
$389$	38.3273	1.94327	0.971636	−	0.236480i	$-0.0759937\pi$
$389$	38.3273	1.94327	0.971636	+	0.236480i	$0.0759937\pi$
$390$	−2.44762	−0.123940
$391$	−5.87622	−0.297173
$392$	−9.87427	−0.498726
$393$	10.2427	0.516678
$394$	−32.3342	−1.62897
$395$	0.175304	0.00882051
$396$	−9.64557	−0.484708
$397$	32.3100	1.62159	0.810796	−	0.585329i	$-0.199035\pi$
$397$	32.3100	1.62159	0.810796	+	0.585329i	$0.199035\pi$
$398$	−64.8291	−3.24959
$399$	−19.1187	−0.957132
$400$	−47.8271	−2.39136
$401$	1.91591	0.0956761	0.0478380	−	0.998855i	$-0.484767\pi$
$401$	1.91591	0.0956761	0.0478380	+	0.998855i	$0.484767\pi$
$402$	1.29148	0.0644133
$403$	4.15177	0.206815
$404$	−11.9357	−0.593825
$405$	0.172926	0.00859274
$406$	−21.8929	−1.08653
$407$	−2.98244	−0.147834
$408$	−7.37708	−0.365220
$409$	−0.791463	−0.0391353	−0.0195677	−	0.999809i	$-0.506229\pi$
$409$	−0.791463	−0.0391353	−0.0195677	+	0.999809i	$0.506229\pi$
$410$	1.97397	0.0974877
$411$	−1.06494	−0.0525297
$412$	−9.74046	−0.479878
$413$	20.8233	1.02465
$414$	−15.3503	−0.754428
$415$	0.634667	0.0311546
$416$	56.2626	2.75850
$417$	−11.0035	−0.538844
$418$	−41.9694	−2.05279
$419$	−30.5975	−1.49479	−0.747393	−	0.664382i	$-0.768695\pi$
$419$	−30.5975	−1.49479	−0.747393	+	0.664382i	$0.768695\pi$
$420$	−1.98487	−0.0968517
$421$	−12.0768	−0.588587	−0.294293	−	0.955715i	$-0.595084\pi$
$421$	−12.0768	−0.588587	−0.294293	+	0.955715i	$0.595084\pi$
$422$	29.1571	1.41935
$423$	−3.63701	−0.176838
$424$	69.5904	3.37961
$425$	−4.97010	−0.241085
$426$	21.5851	1.04580
$427$	−3.38762	−0.163938
$428$	−9.31035	−0.450033
$429$	10.8339	0.523066
$430$	4.29103	0.206932
$431$	−12.5513	−0.604577	−0.302288	−	0.953217i	$-0.597751\pi$
$431$	−12.5513	−0.604577	−0.302288	+	0.953217i	$0.597751\pi$
$432$	−9.62298	−0.462986
$433$	−9.57553	−0.460170	−0.230085	−	0.973170i	$-0.573901\pi$
$433$	−9.57553	−0.460170	−0.230085	+	0.973170i	$0.573901\pi$
$434$	4.76270	0.228617
$435$	0.609084	0.0292034
$436$	6.20984	0.297397
$437$	−47.2162	−2.25866
$438$	4.13032	0.197354
$439$	−25.2576	−1.20548	−0.602740	−	0.797937i	$-0.705924\pi$
$439$	−25.2576	−1.20548	−0.602740	+	0.797937i	$0.705924\pi$
$440$	−2.55073	−0.121601
$441$	−1.33851	−0.0637385
$442$	14.1542	0.673246
$443$	33.7724	1.60458	0.802288	−	0.596938i	$-0.203616\pi$
$443$	33.7724	1.60458	0.802288	+	0.596938i	$0.203616\pi$
$444$	−7.19547	−0.341482
$445$	−1.37394	−0.0651311
$446$	−6.09071	−0.288404
$447$	1.49026	0.0704871
$448$	18.7479	0.885756
$449$	−4.64296	−0.219115	−0.109557	−	0.993980i	$-0.534943\pi$
$449$	−4.64296	−0.219115	−0.109557	+	0.993980i	$0.534943\pi$
$450$	−12.9833	−0.612038
$451$	−8.73742	−0.411429
$452$	−61.1350	−2.87555
$453$	−10.6655	−0.501109
$454$	−27.6949	−1.29979
$455$	2.22941	0.104516
$456$	−59.2758	−2.77584
$457$	−24.3051	−1.13694	−0.568472	−	0.822703i	$-0.692465\pi$
$457$	−24.3051	−1.13694	−0.568472	+	0.822703i	$0.692465\pi$
$458$	5.45413	0.254855
$459$	−1.00000	−0.0466760
$460$	−4.90191	−0.228553
$461$	−12.3137	−0.573506	−0.286753	−	0.958004i	$-0.592576\pi$
$461$	−12.3137	−0.573506	−0.286753	+	0.958004i	$0.592576\pi$
$462$	12.4281	0.578208
$463$	−19.8848	−0.924126	−0.462063	−	0.886847i	$-0.652891\pi$
$463$	−19.8848	−0.924126	−0.462063	+	0.886847i	$0.652891\pi$
$464$	−33.8944	−1.57351
$465$	−0.132504	−0.00614471
$466$	−48.8212	−2.26160
$467$	−41.7561	−1.93224	−0.966120	−	0.258092i	$-0.916906\pi$
$467$	−41.7561	−1.93224	−0.966120	+	0.258092i	$0.916906\pi$
$468$	26.1380	1.20823
$469$	−1.17634	−0.0543185
$470$	−1.64295	−0.0757835
$471$	1.00000	0.0460776
$472$	64.5606	2.97164
$473$	−18.9934	−0.873318
$474$	−2.64821	−0.121636
$475$	−39.9354	−1.83236
$476$	11.4782	0.526101
$477$	9.43332	0.431922
$478$	−9.77182	−0.446953
$479$	−31.6625	−1.44670	−0.723348	−	0.690484i	$-0.757398\pi$
$479$	−31.6625	−1.44670	−0.723348	+	0.690484i	$0.757398\pi$
$480$	−1.79562	−0.0819583
$481$	8.08197	0.368506
$482$	68.4995	3.12006
$483$	13.9818	0.636195
$484$	−33.7777	−1.53535
$485$	0.00932728	0.000423530 0
$486$	−2.61228	−0.118495
$487$	−10.9491	−0.496149	−0.248075	−	0.968741i	$-0.579798\pi$
$487$	−10.9491	−0.496149	−0.248075	+	0.968741i	$0.579798\pi$
$488$	−10.5030	−0.475448
$489$	−23.6219	−1.06822
$490$	−0.604644	−0.0273150
$491$	18.2731	0.824654	0.412327	−	0.911036i	$-0.364716\pi$
$491$	18.2731	0.824654	0.412327	+	0.911036i	$0.364716\pi$
$492$	−21.0800	−0.950359
$493$	−3.52223	−0.158633
$494$	113.731	5.11698
$495$	−0.345764	−0.0155409
$496$	7.37357	0.331083
$497$	−19.6607	−0.881905
$498$	−9.58752	−0.429627
$499$	12.0378	0.538888	0.269444	−	0.963016i	$-0.413160\pi$
$499$	12.0378	0.538888	0.269444	+	0.963016i	$0.413160\pi$
$500$	−8.31699	−0.371947
$501$	6.94366	0.310220
$502$	47.0069	2.09802
$503$	−39.5957	−1.76549	−0.882743	−	0.469856i	$-0.844306\pi$
$503$	−39.5957	−1.76549	−0.882743	+	0.469856i	$0.844306\pi$
$504$	17.5529	0.781870
$505$	−0.427860	−0.0190395
$506$	30.6929	1.36447
$507$	−16.3583	−0.726495
$508$	−94.1648	−4.17789
$509$	−10.3361	−0.458138	−0.229069	−	0.973410i	$-0.573568\pi$
$509$	−10.3361	−0.458138	−0.229069	+	0.973410i	$0.573568\pi$
$510$	−0.451730	−0.0200029
$511$	−3.76210	−0.166425
$512$	−42.0563	−1.85864
$513$	−8.03513	−0.354760
$514$	80.1159	3.53376
$515$	−0.349166	−0.0153861
$516$	−45.8237	−2.01727
$517$	7.27219	0.319831
$518$	9.27122	0.407354
$519$	−20.4622	−0.898190
$520$	6.91208	0.303115
$521$	11.0631	0.484682	0.242341	−	0.970191i	$-0.422085\pi$
$521$	11.0631	0.484682	0.242341	+	0.970191i	$0.422085\pi$
$522$	−9.20105	−0.402719
$523$	−3.28430	−0.143612	−0.0718061	−	0.997419i	$-0.522876\pi$
$523$	−3.28430	−0.143612	−0.0718061	+	0.997419i	$0.522876\pi$
$524$	−49.4110	−2.15853
$525$	11.8258	0.516120
$526$	−22.3528	−0.974626
$527$	0.766246	0.0333782
$528$	19.2411	0.837362
$529$	11.5300	0.501305
$530$	4.26131	0.185100
$531$	8.75152	0.379784
$532$	92.2286	3.99862
$533$	23.6771	1.02557
$534$	20.7553	0.898169
$535$	−0.333747	−0.0144292
$536$	−3.64715	−0.157533
$537$	−20.0824	−0.866619
$538$	−61.7473	−2.66212
$539$	2.67634	0.115278
$540$	−0.834193	−0.0358980
$541$	−3.52748	−0.151658	−0.0758291	−	0.997121i	$-0.524160\pi$
$541$	−3.52748	−0.151658	−0.0758291	+	0.997121i	$0.524160\pi$
$542$	−70.9991	−3.04967
$543$	−22.6705	−0.972885
$544$	10.3838	0.445200
$545$	0.222603	0.00953529
$546$	−33.6783	−1.44130
$547$	−24.0633	−1.02887	−0.514437	−	0.857528i	$-0.671999\pi$
$547$	−24.0633	−1.02887	−0.514437	+	0.857528i	$0.671999\pi$
$548$	5.13728	0.219454
$549$	−1.42373	−0.0607635
$550$	25.9600	1.10694
$551$	−28.3016	−1.20569
$552$	43.3494	1.84507
$553$	2.41212	0.102574
$554$	48.2802	2.05123
$555$	−0.257936	−0.0109488
$556$	53.0809	2.25113
$557$	−37.2159	−1.57689	−0.788443	−	0.615108i	$-0.789113\pi$
$557$	−37.2159	−1.57689	−0.788443	+	0.615108i	$0.789113\pi$
$558$	2.00165	0.0847366
$559$	51.4692	2.17692
$560$	3.95945	0.167317
$561$	1.99950	0.0844188
$562$	−47.5395	−2.00533
$563$	16.7907	0.707643	0.353822	−	0.935313i	$-0.384882\pi$
$563$	16.7907	0.707643	0.353822	+	0.935313i	$0.384882\pi$
$564$	17.5450	0.738776
$565$	−2.19150	−0.0921972
$566$	−54.8866	−2.30705
$567$	2.37939	0.0999249
$568$	−60.9563	−2.55767
$569$	−26.9127	−1.12824	−0.564120	−	0.825693i	$-0.690785\pi$
$569$	−26.9127	−1.12824	−0.564120	+	0.825693i	$0.690785\pi$
$570$	−3.62971	−0.152032
$571$	3.48487	0.145837	0.0729186	−	0.997338i	$-0.476769\pi$
$571$	3.48487	0.145837	0.0729186	+	0.997338i	$0.476769\pi$
$572$	−52.2628	−2.18522
$573$	−0.600264	−0.0250764
$574$	27.1611	1.13368
$575$	29.2054	1.21795
$576$	7.87930	0.328304
$577$	−14.1465	−0.588925	−0.294462	−	0.955663i	$-0.595141\pi$
$577$	−14.1465	−0.588925	−0.294462	+	0.955663i	$0.595141\pi$
$578$	2.61228	0.108656
$579$	−7.49613	−0.311529
$580$	−2.93822	−0.122003
$581$	8.73277	0.362296
$582$	−0.140901	−0.00584055
$583$	−18.8619	−0.781180
$584$	−11.6640	−0.482661
$585$	0.936967	0.0387388
$586$	−67.3181	−2.78088
$587$	−8.92945	−0.368558	−0.184279	−	0.982874i	$-0.558995\pi$
$587$	−8.92945	−0.368558	−0.184279	+	0.982874i	$0.558995\pi$
$588$	6.45696	0.266281
$589$	6.15689	0.253690
$590$	3.95332	0.162756
$591$	12.3778	0.509154
$592$	14.3536	0.589930
$593$	−24.4530	−1.00417	−0.502083	−	0.864820i	$-0.667433\pi$
$593$	−24.4530	−1.00417	−0.502083	+	0.864820i	$0.667433\pi$
$594$	5.22324	0.214312
$595$	0.411457	0.0168681
$596$	−7.18904	−0.294474
$597$	24.8171	1.01570
$598$	−83.1731	−3.40120
$599$	−23.6790	−0.967496	−0.483748	−	0.875207i	$-0.660725\pi$
$599$	−23.6790	−0.967496	−0.483748	+	0.875207i	$0.660725\pi$
$600$	36.6648	1.49683
$601$	36.4902	1.48847	0.744234	−	0.667919i	$-0.232815\pi$
$601$	36.4902	1.48847	0.744234	+	0.667919i	$0.232815\pi$
$602$	59.0429	2.40641
$603$	−0.494389	−0.0201331
$604$	51.4504	2.09349
$605$	−1.21083	−0.0492272
$606$	6.46341	0.262558
$607$	14.3433	0.582176	0.291088	−	0.956696i	$-0.405983\pi$
$607$	14.3433	0.582176	0.291088	+	0.956696i	$0.405983\pi$
$608$	83.4348	3.38373
$609$	8.38076	0.339606
$610$	−0.643143	−0.0260401
$611$	−19.7065	−0.797240
$612$	4.82400	0.194999
$613$	−45.4184	−1.83443	−0.917217	−	0.398388i	$-0.869570\pi$
$613$	−45.4184	−1.83443	−0.917217	+	0.398388i	$0.869570\pi$
$614$	6.50829	0.262653
$615$	−0.755652	−0.0304708
$616$	−35.0970	−1.41410
$617$	17.2325	0.693756	0.346878	−	0.937910i	$-0.387242\pi$
$617$	17.2325	0.693756	0.346878	+	0.937910i	$0.387242\pi$
$618$	5.27463	0.212177
$619$	−1.64731	−0.0662112	−0.0331056	−	0.999452i	$-0.510540\pi$
$619$	−1.64731	−0.0662112	−0.0331056	+	0.999452i	$0.510540\pi$
$620$	0.639197	0.0256708
$621$	5.87622	0.235805
$622$	48.2541	1.93481
$623$	−18.9049	−0.757409
$624$	−52.1404	−2.08729
$625$	24.5523	0.982094
$626$	48.4343	1.93582
$627$	16.0662	0.641622
$628$	−4.82400	−0.192499
$629$	1.49160	0.0594739
$630$	1.07484	0.0428227
$631$	46.3130	1.84369	0.921846	−	0.387556i	$-0.126680\pi$
$631$	46.3130	1.84369	0.921846	+	0.387556i	$0.126680\pi$
$632$	7.47854	0.297481
$633$	−11.1616	−0.443632
$634$	52.5191	2.08580
$635$	−3.37552	−0.133953
$636$	−45.5064	−1.80444
$637$	−7.25247	−0.287353
$638$	18.3975	0.728363
$639$	−8.26294	−0.326877
$640$	−0.0319182	−0.00126168
$641$	−38.2779	−1.51189	−0.755944	−	0.654637i	$-0.772822\pi$
$641$	−38.2779	−1.51189	−0.755944	+	0.654637i	$0.772822\pi$
$642$	5.04171	0.198981
$643$	−15.7431	−0.620846	−0.310423	−	0.950599i	$-0.600471\pi$
$643$	−15.7431	−0.620846	−0.310423	+	0.950599i	$0.600471\pi$
$644$	−67.4483	−2.65784
$645$	−1.64264	−0.0646788
$646$	20.9900	0.825840
$647$	−22.3333	−0.878012	−0.439006	−	0.898484i	$-0.644669\pi$
$647$	−22.3333	−0.878012	−0.439006	+	0.898484i	$0.644669\pi$
$648$	7.37708	0.289799
$649$	−17.4986	−0.686881
$650$	−70.3476	−2.75926
$651$	−1.82320	−0.0714568
$652$	113.952	4.46271
$653$	35.9362	1.40629	0.703146	−	0.711045i	$-0.251778\pi$
$653$	35.9362	1.40629	0.703146	+	0.711045i	$0.251778\pi$
$654$	−3.36273	−0.131493
$655$	−1.77123	−0.0692078
$656$	42.0506	1.64180
$657$	−1.58112	−0.0616853
$658$	−22.6063	−0.881286
$659$	−27.3132	−1.06397	−0.531985	−	0.846754i	$-0.678554\pi$
$659$	−27.3132	−1.06397	−0.531985	+	0.846754i	$0.678554\pi$
$660$	1.66797	0.0649255
$661$	−16.1068	−0.626482	−0.313241	−	0.949674i	$-0.601415\pi$
$661$	−16.1068	−0.626482	−0.313241	+	0.949674i	$0.601415\pi$
$662$	−38.4267	−1.49350
$663$	−5.41833	−0.210430
$664$	27.0752	1.05072
$665$	3.30611	0.128205
$666$	3.89647	0.150985
$667$	20.6974	0.801408
$668$	−33.4962	−1.29601
$669$	2.33157	0.0901437
$670$	−0.223330	−0.00862800
$671$	2.84675	0.109898
$672$	−24.7070	−0.953093
$673$	−35.8531	−1.38203	−0.691017	−	0.722839i	$-0.742837\pi$
$673$	−35.8531	−1.38203	−0.691017	+	0.722839i	$0.742837\pi$
$674$	52.0717	2.00573
$675$	4.97010	0.191299
$676$	78.9122	3.03509
$677$	−32.9166	−1.26509	−0.632543	−	0.774525i	$-0.717989\pi$
$677$	−32.9166	−1.26509	−0.632543	+	0.774525i	$0.717989\pi$
$678$	33.1057	1.27142
$679$	0.128340	0.00492523
$680$	1.27569	0.0489203
$681$	10.6018	0.406263
$682$	−4.00229	−0.153256
$683$	44.3764	1.69802	0.849008	−	0.528381i	$-0.177201\pi$
$683$	44.3764	1.69802	0.849008	+	0.528381i	$0.177201\pi$
$684$	38.7615	1.48208
$685$	0.184156	0.00703622
$686$	−51.8291	−1.97884
$687$	−2.08788	−0.0796577
$688$	91.4096	3.48496
$689$	51.1128	1.94724
$690$	2.65447	0.101054
$691$	−49.4076	−1.87955	−0.939777	−	0.341788i	$-0.888968\pi$
$691$	−49.4076	−1.87955	−0.939777	+	0.341788i	$0.888968\pi$
$692$	98.7096	3.75237
$693$	−4.75758	−0.180725
$694$	4.40438	0.167188
$695$	1.90279	0.0721768
$696$	25.9838	0.984913
$697$	4.36981	0.165518
$698$	−46.0588	−1.74335
$699$	18.6891	0.706888
$700$	−57.0476	−2.15620
$701$	−1.37376	−0.0518863	−0.0259431	−	0.999663i	$-0.508259\pi$
$701$	−1.37376	−0.0518863	−0.0259431	+	0.999663i	$0.508259\pi$
$702$	−14.1542	−0.534215
$703$	11.9852	0.452030
$704$	−15.7546	−0.593775
$705$	0.628933	0.0236870
$706$	13.8538	0.521394
$707$	−5.88718	−0.221410
$708$	−42.2173	−1.58662
$709$	−20.9885	−0.788239	−0.394120	−	0.919059i	$-0.628950\pi$
$709$	−20.9885	−0.788239	−0.394120	+	0.919059i	$0.628950\pi$
$710$	−3.73261	−0.140083
$711$	1.01375	0.0380188
$712$	−58.6129	−2.19661
$713$	−4.50264	−0.168625
$714$	−6.21563	−0.232614
$715$	−1.87346	−0.0700635
$716$	96.8774	3.62048
$717$	3.74073	0.139700
$718$	−8.00422	−0.298715
$719$	25.8782	0.965093	0.482546	−	0.875870i	$-0.339712\pi$
$719$	25.8782	0.965093	0.482546	+	0.875870i	$0.339712\pi$
$720$	1.66406	0.0620158
$721$	−4.80438	−0.178925
$722$	119.024	4.42961
$723$	−26.2221	−0.975211
$724$	109.363	4.06443
$725$	17.5058	0.650150
$726$	18.2912	0.678851
$727$	−22.4344	−0.832047	−0.416024	−	0.909354i	$-0.636577\pi$
$727$	−22.4344	−0.832047	−0.416024	+	0.909354i	$0.636577\pi$
$728$	95.1075	3.52492
$729$	1.00000	0.0370370
$730$	−0.714238	−0.0264351
$731$	9.49910	0.351337
$732$	6.86809	0.253852
$733$	−15.5752	−0.575281	−0.287641	−	0.957738i	$-0.592871\pi$
$733$	−15.5752	−0.575281	−0.287641	+	0.957738i	$0.592871\pi$
$734$	−53.8064	−1.98603
$735$	0.231462	0.00853761
$736$	−61.0173	−2.24913
$737$	0.988528	0.0364129
$738$	11.4152	0.420198
$739$	−8.61992	−0.317089	−0.158544	−	0.987352i	$-0.550680\pi$
$739$	−8.61992	−0.317089	−0.158544	+	0.987352i	$0.550680\pi$
$740$	1.24428	0.0457407
$741$	−43.5369	−1.59937
$742$	58.6340	2.15252
$743$	−0.803501	−0.0294776	−0.0147388	−	0.999891i	$-0.504692\pi$
$743$	−0.803501	−0.0294776	−0.0147388	+	0.999891i	$0.504692\pi$
$744$	−5.65266	−0.207237
$745$	−0.257705	−0.00944158
$746$	−22.3731	−0.819136
$747$	3.67017	0.134285
$748$	−9.64557	−0.352677
$749$	−4.59223	−0.167797
$750$	4.50379	0.164455
$751$	−2.09477	−0.0764393	−0.0382196	−	0.999269i	$-0.512169\pi$
$751$	−2.09477	−0.0764393	−0.0382196	+	0.999269i	$0.512169\pi$
$752$	−34.9989	−1.27628
$753$	−17.9946	−0.655760
$754$	−49.8543	−1.81559
$755$	1.84434	0.0671224
$756$	−11.4782	−0.417457
$757$	−14.4806	−0.526307	−0.263154	−	0.964754i	$-0.584763\pi$
$757$	−14.4806	−0.526307	−0.263154	+	0.964754i	$0.584763\pi$
$758$	14.5760	0.529426
$759$	−11.7495	−0.426479
$760$	10.2503	0.371817
$761$	0.531888	0.0192809	0.00964046	−	0.999954i	$-0.496931\pi$
$761$	0.531888	0.0192809	0.00964046	+	0.999954i	$0.496931\pi$
$762$	50.9918	1.84724
$763$	3.06294	0.110886
$764$	2.89567	0.104762
$765$	0.172926	0.00625214
$766$	66.8264	2.41454
$767$	47.4186	1.71219
$768$	16.2408	0.586038
$769$	41.9558	1.51296	0.756482	−	0.654015i	$-0.226917\pi$
$769$	41.9558	1.51296	0.756482	+	0.654015i	$0.226917\pi$
$770$	−2.14914	−0.0774496
$771$	−30.6690	−1.10452
$772$	36.1613	1.30148
$773$	−40.0754	−1.44141	−0.720706	−	0.693241i	$-0.756182\pi$
$773$	−40.0754	−1.44141	−0.720706	+	0.693241i	$0.756182\pi$
$774$	24.8143	0.891931
$775$	−3.80832	−0.136799
$776$	0.397906	0.0142840
$777$	−3.54909	−0.127323
$778$	100.122	3.58954
$779$	35.1120	1.25802
$780$	−4.51993	−0.161839
$781$	16.5217	0.591193
$782$	−15.3503	−0.548927
$783$	3.52223	0.125874
$784$	−12.8804	−0.460016
$785$	−0.172926	−0.00617198
$786$	26.7569	0.954387
$787$	−11.9104	−0.424561	−0.212281	−	0.977209i	$-0.568089\pi$
$787$	−11.9104	−0.424561	−0.212281	+	0.977209i	$0.568089\pi$
$788$	−59.7104	−2.12709
$789$	8.55680	0.304630
$790$	0.457943	0.0162929
$791$	−30.1542	−1.07216
$792$	−14.7504	−0.524134
$793$	−7.71425	−0.273941
$794$	84.4027	2.99534
$795$	−1.63126	−0.0578549
$796$	−119.718	−4.24328
$797$	−9.64606	−0.341681	−0.170841	−	0.985299i	$-0.554648\pi$
$797$	−9.64606	−0.341681	−0.170841	+	0.985299i	$0.554648\pi$
$798$	−49.9434	−1.76798
$799$	−3.63701	−0.128668
$800$	−51.6083	−1.82463
$801$	−7.94528	−0.280733
$802$	5.00490	0.176729
$803$	3.16144	0.111565
$804$	2.38493	0.0841101
$805$	−2.41781	−0.0852168
$806$	10.8456	0.382019
$807$	23.6373	0.832074
$808$	−18.2527	−0.642127
$809$	20.8633	0.733514	0.366757	−	0.930317i	$-0.380468\pi$
$809$	20.8633	0.733514	0.366757	+	0.930317i	$0.380468\pi$
$810$	0.451730	0.0158722
$811$	17.9114	0.628954	0.314477	−	0.949265i	$-0.398171\pi$
$811$	17.9114	0.628954	0.314477	+	0.949265i	$0.398171\pi$
$812$	−40.4288	−1.41877
$813$	27.1790	0.953209
$814$	−7.79098	−0.273074
$815$	4.08483	0.143085
$816$	−9.62298	−0.336872
$817$	76.3265	2.67032
$818$	−2.06752	−0.0722892
$819$	12.8923	0.450494
$820$	3.64527	0.127298
$821$	−28.4294	−0.992192	−0.496096	−	0.868268i	$-0.665234\pi$
$821$	−28.4294	−0.992192	−0.496096	+	0.868268i	$0.665234\pi$
$822$	−2.78192	−0.0970307
$823$	23.1743	0.807804	0.403902	−	0.914802i	$-0.367654\pi$
$823$	23.1743	0.807804	0.403902	+	0.914802i	$0.367654\pi$
$824$	−14.8955	−0.518911
$825$	−9.93769	−0.345986
$826$	54.3962	1.89268
$827$	−3.08818	−0.107387	−0.0536933	−	0.998557i	$-0.517099\pi$
$827$	−3.08818	−0.107387	−0.0536933	+	0.998557i	$0.517099\pi$
$828$	−28.3469	−0.985123
$829$	47.0748	1.63498	0.817488	−	0.575945i	$-0.195366\pi$
$829$	47.0748	1.63498	0.817488	+	0.575945i	$0.195366\pi$
$830$	1.65793	0.0575475
$831$	−18.4820	−0.641134
$832$	42.6926	1.48010
$833$	−1.33851	−0.0463765
$834$	−28.7442	−0.995331
$835$	−1.20074	−0.0415532
$836$	−77.5034	−2.68051
$837$	−0.766246	−0.0264853
$838$	−79.9293	−2.76111
$839$	−26.5874	−0.917900	−0.458950	−	0.888462i	$-0.651774\pi$
$839$	−26.5874	−0.917900	−0.458950	+	0.888462i	$0.651774\pi$
$840$	−3.03535	−0.104730
$841$	−16.5939	−0.572203
$842$	−31.5479	−1.08721
$843$	18.1985	0.626789
$844$	53.8434	1.85337
$845$	2.82876	0.0973123
$846$	−9.50089	−0.326647
$847$	−16.6605	−0.572462
$848$	90.7767	3.11728
$849$	21.0110	0.721095
$850$	−12.9833	−0.445323
$851$	−8.76497	−0.300459
$852$	39.8604	1.36560
$853$	−2.87378	−0.0983965	−0.0491982	−	0.998789i	$-0.515667\pi$
$853$	−2.87378	−0.0983965	−0.0491982	+	0.998789i	$0.515667\pi$
$854$	−8.84940	−0.302820
$855$	1.38948	0.0475192
$856$	−14.2378	−0.486638
$857$	2.37684	0.0811912	0.0405956	−	0.999176i	$-0.487074\pi$
$857$	2.37684	0.0811912	0.0405956	+	0.999176i	$0.487074\pi$
$858$	28.3012	0.966187
$859$	−28.7599	−0.981277	−0.490638	−	0.871363i	$-0.663236\pi$
$859$	−28.7599	−0.981277	−0.490638	+	0.871363i	$0.663236\pi$
$860$	7.92408	0.270209
$861$	−10.3975	−0.354345
$862$	−32.7876	−1.11675
$863$	3.98043	0.135496	0.0677478	−	0.997702i	$-0.478419\pi$
$863$	3.98043	0.135496	0.0677478	+	0.997702i	$0.478419\pi$
$864$	−10.3838	−0.353263
$865$	3.53843	0.120310
$866$	−25.0139	−0.850009
$867$	−1.00000	−0.0339618
$868$	8.79511	0.298525
$869$	−2.02700	−0.0687612
$870$	1.59110	0.0539433
$871$	−2.67876	−0.0907663
$872$	9.49636	0.321587
$873$	0.0539381	0.00182553
$874$	−123.342	−4.17210
$875$	−4.10227	−0.138682
$876$	7.62732	0.257703
$877$	−35.5660	−1.20098	−0.600488	−	0.799633i	$-0.705027\pi$
$877$	−35.5660	−1.20098	−0.600488	+	0.799633i	$0.705027\pi$
$878$	−65.9799	−2.22672
$879$	25.7699	0.869196
$880$	−3.32728	−0.112163
$881$	47.4215	1.59767	0.798836	−	0.601549i	$-0.205449\pi$
$881$	47.4215	1.59767	0.798836	+	0.601549i	$0.205449\pi$
$882$	−3.49656	−0.117735
$883$	−5.03941	−0.169590	−0.0847948	−	0.996398i	$-0.527023\pi$
$883$	−5.03941	−0.169590	−0.0847948	+	0.996398i	$0.527023\pi$
$884$	26.1380	0.879116
$885$	−1.51336	−0.0508711
$886$	88.2229	2.96391
$887$	−28.3377	−0.951486	−0.475743	−	0.879584i	$-0.657821\pi$
$887$	−28.3377	−0.951486	−0.475743	+	0.879584i	$0.657821\pi$
$888$	−11.0036	−0.369258
$889$	−46.4458	−1.55774
$890$	−3.58912	−0.120308
$891$	−1.99950	−0.0669856
$892$	−11.2475	−0.376594
$893$	−29.2239	−0.977939
$894$	3.89299	0.130201
$895$	3.47276	0.116082
$896$	−0.439182	−0.0146720
$897$	31.8393	1.06308
$898$	−12.1287	−0.404740
$899$	−2.69890	−0.0900133
$900$	−23.9757	−0.799192
$901$	9.43332	0.314270
$902$	−22.8246	−0.759975
$903$	−22.6021	−0.752149
$904$	−93.4904	−3.10944
$905$	3.92031	0.130316
$906$	−27.8613	−0.925629
$907$	7.01434	0.232907	0.116454	−	0.993196i	$-0.462847\pi$
$907$	7.01434	0.232907	0.116454	+	0.993196i	$0.462847\pi$
$908$	−51.1432	−1.69725
$909$	−2.47424	−0.0820654
$910$	5.82384	0.193058
$911$	−25.0739	−0.830735	−0.415368	−	0.909654i	$-0.636347\pi$
$911$	−25.0739	−0.830735	−0.415368	+	0.909654i	$0.636347\pi$
$912$	−77.3219	−2.56038
$913$	−7.33850	−0.242869
$914$	−63.4916	−2.10012
$915$	0.246200	0.00813912
$916$	10.0719	0.332787
$917$	−24.3715	−0.804817
$918$	−2.61228	−0.0862180
$919$	9.33013	0.307773	0.153886	−	0.988089i	$-0.450821\pi$
$919$	9.33013	0.307773	0.153886	+	0.988089i	$0.450821\pi$
$920$	−7.49621	−0.247143
$921$	−2.49142	−0.0820952
$922$	−32.1668	−1.05936
$923$	−44.7713	−1.47366
$924$	22.9506	0.755018
$925$	−7.41339	−0.243751
$926$	−51.9447	−1.70701
$927$	−2.01917	−0.0663181
$928$	−36.5740	−1.20060
$929$	−22.5543	−0.739984	−0.369992	−	0.929035i	$-0.620640\pi$
$929$	−22.5543	−0.739984	−0.369992	+	0.929035i	$0.620640\pi$
$930$	−0.346136	−0.0113503
$931$	−10.7551	−0.352484
$932$	−90.1563	−2.95317
$933$	−18.4720	−0.604748
$934$	−109.078	−3.56916
$935$	−0.345764	−0.0113077
$936$	39.9714	1.30651
$937$	26.0789	0.851960	0.425980	−	0.904733i	$-0.359929\pi$
$937$	26.0789	0.851960	0.425980	+	0.904733i	$0.359929\pi$
$938$	−3.07294	−0.100335
$939$	−18.5410	−0.605063
$940$	−3.03397	−0.0989572
$941$	−8.76145	−0.285615	−0.142808	−	0.989750i	$-0.545613\pi$
$941$	−8.76145	−0.285615	−0.142808	+	0.989750i	$0.545613\pi$
$942$	2.61228	0.0851126
$943$	−25.6780	−0.836191
$944$	84.2157	2.74099
$945$	−0.411457	−0.0133847
$946$	−49.6161	−1.61316
$947$	56.3719	1.83184	0.915920	−	0.401362i	$-0.131463\pi$
$947$	56.3719	1.83184	0.915920	+	0.401362i	$0.131463\pi$
$948$	−4.89035	−0.158831
$949$	−8.56701	−0.278097
$950$	−104.322	−3.38466
$951$	−20.1047	−0.651939
$952$	17.5529	0.568894
$953$	52.9700	1.71587	0.857934	−	0.513760i	$-0.171748\pi$
$953$	52.9700	1.71587	0.857934	+	0.513760i	$0.171748\pi$
$954$	24.6425	0.797830
$955$	0.103801	0.00335892
$956$	−18.0453	−0.583626
$957$	−7.04269	−0.227658
$958$	−82.7112	−2.67228
$959$	2.53391	0.0818242
$960$	−1.36253	−0.0439756
$961$	−30.4129	−0.981060
$962$	21.1123	0.680689
$963$	−1.93001	−0.0621936
$964$	126.495	4.07414
$965$	1.29627	0.0417285
$966$	36.5244	1.17515
$967$	10.7544	0.345838	0.172919	−	0.984936i	$-0.444680\pi$
$967$	10.7544	0.345838	0.172919	+	0.984936i	$0.444680\pi$
$968$	−51.6544	−1.66024
$969$	−8.03513	−0.258125
$970$	0.0243655	0.000782328 0
$971$	5.41349	0.173727	0.0868636	−	0.996220i	$-0.472316\pi$
$971$	5.41349	0.173727	0.0868636	+	0.996220i	$0.472316\pi$
$972$	−4.82400	−0.154730
$973$	26.1816	0.839344
$974$	−28.6020	−0.916467
$975$	26.9296	0.862437
$976$	−13.7006	−0.438544
$977$	2.30049	0.0735993	0.0367996	−	0.999323i	$-0.488284\pi$
$977$	2.30049	0.0735993	0.0367996	+	0.999323i	$0.488284\pi$
$978$	−61.7070	−1.97317
$979$	15.8865	0.507736
$980$	−1.11657	−0.0356676
$981$	1.28728	0.0410997
$982$	47.7345	1.52327
$983$	36.6294	1.16830	0.584148	−	0.811647i	$-0.301429\pi$
$983$	36.6294	1.16830	0.584148	+	0.811647i	$0.301429\pi$
$984$	−32.2364	−1.02766
$985$	−2.14043	−0.0681999
$986$	−9.20105	−0.293021
$987$	8.65387	0.275456
$988$	210.022	6.68170
$989$	−55.8188	−1.77494
$990$	−0.903232	−0.0287066
$991$	12.6680	0.402413	0.201207	−	0.979549i	$-0.435514\pi$
$991$	12.6680	0.402413	0.201207	+	0.979549i	$0.435514\pi$
$992$	7.95651	0.252620
$993$	14.7100	0.466808
$994$	−51.3593	−1.62902
$995$	−4.29151	−0.136050
$996$	−17.7049	−0.561002
$997$	46.8246	1.48295	0.741475	−	0.670981i	$-0.234127\pi$
$997$	46.8246	1.48295	0.741475	+	0.670981i	$0.234127\pi$
$998$	31.4462	0.995413
$999$	−1.49160	−0.0471921

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.59	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.59	✓	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)

\(f(q)\)	\(=\)	\(q+2.61228 q^{2} -1.00000 q^{3} +4.82400 q^{4} +0.172926 q^{5} -2.61228 q^{6} +2.37939 q^{7} +7.37708 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.61228 q^{2} -1.00000 q^{3} +4.82400 q^{4} +0.172926 q^{5} -2.61228 q^{6} +2.37939 q^{7} +7.37708 q^{8} +1.00000 q^{9} +0.451730 q^{10} -1.99950 q^{11} -4.82400 q^{12} +5.41833 q^{13} +6.21563 q^{14} -0.172926 q^{15} +9.62298 q^{16} +1.00000 q^{17} +2.61228 q^{18} +8.03513 q^{19} +0.834193 q^{20} -2.37939 q^{21} -5.22324 q^{22} -5.87622 q^{23} -7.37708 q^{24} -4.97010 q^{25} +14.1542 q^{26} -1.00000 q^{27} +11.4782 q^{28} -3.52223 q^{29} -0.451730 q^{30} +0.766246 q^{31} +10.3838 q^{32} +1.99950 q^{33} +2.61228 q^{34} +0.411457 q^{35} +4.82400 q^{36} +1.49160 q^{37} +20.9900 q^{38} -5.41833 q^{39} +1.27569 q^{40} +4.36981 q^{41} -6.21563 q^{42} +9.49910 q^{43} -9.64557 q^{44} +0.172926 q^{45} -15.3503 q^{46} -3.63701 q^{47} -9.62298 q^{48} -1.33851 q^{49} -12.9833 q^{50} -1.00000 q^{51} +26.1380 q^{52} +9.43332 q^{53} -2.61228 q^{54} -0.345764 q^{55} +17.5529 q^{56} -8.03513 q^{57} -9.20105 q^{58} +8.75152 q^{59} -0.834193 q^{60} -1.42373 q^{61} +2.00165 q^{62} +2.37939 q^{63} +7.87930 q^{64} +0.936967 q^{65} +5.22324 q^{66} -0.494389 q^{67} +4.82400 q^{68} +5.87622 q^{69} +1.07484 q^{70} -8.26294 q^{71} +7.37708 q^{72} -1.58112 q^{73} +3.89647 q^{74} +4.97010 q^{75} +38.7615 q^{76} -4.75758 q^{77} -14.1542 q^{78} +1.01375 q^{79} +1.66406 q^{80} +1.00000 q^{81} +11.4152 q^{82} +3.67017 q^{83} -11.4782 q^{84} +0.172926 q^{85} +24.8143 q^{86} +3.52223 q^{87} -14.7504 q^{88} -7.94528 q^{89} +0.451730 q^{90} +12.8923 q^{91} -28.3469 q^{92} -0.766246 q^{93} -9.50089 q^{94} +1.38948 q^{95} -10.3838 q^{96} +0.0539381 q^{97} -3.49656 q^{98} -1.99950 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 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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