LMFDB - Embedded newform 8007.2.a.j.1.53

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			1.53
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)

$f(q)$	$=$	$q+2.10563 q^{2} -1.00000 q^{3} +2.43368 q^{4} +0.950902 q^{5} -2.10563 q^{6} -0.758079 q^{7} +0.913167 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.10563 q^{2} -1.00000 q^{3} +2.43368 q^{4} +0.950902 q^{5} -2.10563 q^{6} -0.758079 q^{7} +0.913167 q^{8} +1.00000 q^{9} +2.00225 q^{10} +3.29657 q^{11} -2.43368 q^{12} +1.58535 q^{13} -1.59623 q^{14} -0.950902 q^{15} -2.94456 q^{16} +1.00000 q^{17} +2.10563 q^{18} +6.02906 q^{19} +2.31419 q^{20} +0.758079 q^{21} +6.94136 q^{22} +0.826198 q^{23} -0.913167 q^{24} -4.09579 q^{25} +3.33816 q^{26} -1.00000 q^{27} -1.84492 q^{28} +4.45560 q^{29} -2.00225 q^{30} +5.73876 q^{31} -8.02650 q^{32} -3.29657 q^{33} +2.10563 q^{34} -0.720858 q^{35} +2.43368 q^{36} +1.81184 q^{37} +12.6950 q^{38} -1.58535 q^{39} +0.868332 q^{40} -2.07448 q^{41} +1.59623 q^{42} -12.7658 q^{43} +8.02280 q^{44} +0.950902 q^{45} +1.73967 q^{46} +11.1930 q^{47} +2.94456 q^{48} -6.42532 q^{49} -8.62421 q^{50} -1.00000 q^{51} +3.85824 q^{52} +10.4904 q^{53} -2.10563 q^{54} +3.13471 q^{55} -0.692253 q^{56} -6.02906 q^{57} +9.38185 q^{58} -3.01470 q^{59} -2.31419 q^{60} +10.1798 q^{61} +12.0837 q^{62} -0.758079 q^{63} -11.0117 q^{64} +1.50751 q^{65} -6.94136 q^{66} -16.1861 q^{67} +2.43368 q^{68} -0.826198 q^{69} -1.51786 q^{70} -13.1762 q^{71} +0.913167 q^{72} -7.58330 q^{73} +3.81507 q^{74} +4.09579 q^{75} +14.6728 q^{76} -2.49906 q^{77} -3.33816 q^{78} -0.909801 q^{79} -2.79999 q^{80} +1.00000 q^{81} -4.36809 q^{82} +17.1339 q^{83} +1.84492 q^{84} +0.950902 q^{85} -26.8800 q^{86} -4.45560 q^{87} +3.01032 q^{88} +5.22243 q^{89} +2.00225 q^{90} -1.20182 q^{91} +2.01070 q^{92} -5.73876 q^{93} +23.5682 q^{94} +5.73304 q^{95} +8.02650 q^{96} +15.5144 q^{97} -13.5293 q^{98} +3.29657 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.10563	1.48891	0.744453	−	0.667675i	$-0.232710\pi$
$2$	2.10563	1.48891	0.744453	+	0.667675i	$0.232710\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.43368	1.21684
$5$	0.950902	0.425256	0.212628	−	0.977133i	$-0.431798\pi$
$5$	0.950902	0.425256	0.212628	+	0.977133i	$0.431798\pi$
$6$	−2.10563	−0.859620
$7$	−0.758079	−0.286527	−0.143263	−	0.989685i	$-0.545760\pi$
$7$	−0.758079	−0.286527	−0.143263	+	0.989685i	$0.545760\pi$
$8$	0.913167	0.322853
$9$	1.00000	0.333333
$10$	2.00225	0.633166
$11$	3.29657	0.993954	0.496977	−	0.867764i	$-0.334443\pi$
$11$	3.29657	0.993954	0.496977	+	0.867764i	$0.334443\pi$
$12$	−2.43368	−0.702543
$13$	1.58535	0.439697	0.219849	−	0.975534i	$-0.429444\pi$
$13$	1.58535	0.439697	0.219849	+	0.975534i	$0.429444\pi$
$14$	−1.59623	−0.426611
$15$	−0.950902	−0.245522
$16$	−2.94456	−0.736141
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.10563	0.496302
$19$	6.02906	1.38316	0.691581	−	0.722299i	$-0.256915\pi$
$19$	6.02906	1.38316	0.691581	+	0.722299i	$0.256915\pi$
$20$	2.31419	0.517468
$21$	0.758079	0.165426
$22$	6.94136	1.47990
$23$	0.826198	0.172274	0.0861370	−	0.996283i	$-0.472548\pi$
$23$	0.826198	0.172274	0.0861370	+	0.996283i	$0.472548\pi$
$24$	−0.913167	−0.186400
$25$	−4.09579	−0.819157
$26$	3.33816	0.654668
$27$	−1.00000	−0.192450
$28$	−1.84492	−0.348657
$29$	4.45560	0.827385	0.413692	−	0.910417i	$-0.364239\pi$
$29$	4.45560	0.827385	0.413692	+	0.910417i	$0.364239\pi$
$30$	−2.00225	−0.365559
$31$	5.73876	1.03071	0.515356	−	0.856976i	$-0.327660\pi$
$31$	5.73876	1.03071	0.515356	+	0.856976i	$0.327660\pi$
$32$	−8.02650	−1.41890
$33$	−3.29657	−0.573859
$34$	2.10563	0.361113
$35$	−0.720858	−0.121847
$36$	2.43368	0.405613
$37$	1.81184	0.297865	0.148932	−	0.988847i	$-0.452416\pi$
$37$	1.81184	0.297865	0.148932	+	0.988847i	$0.452416\pi$
$38$	12.6950	2.05940
$39$	−1.58535	−0.253859
$40$	0.868332	0.137295
$41$	−2.07448	−0.323980	−0.161990	−	0.986792i	$-0.551791\pi$
$41$	−2.07448	−0.323980	−0.161990	+	0.986792i	$0.551791\pi$
$42$	1.59623	0.246304
$43$	−12.7658	−1.94676	−0.973381	−	0.229194i	$-0.926391\pi$
$43$	−12.7658	−1.94676	−0.973381	+	0.229194i	$0.926391\pi$
$44$	8.02280	1.20948
$45$	0.950902	0.141752
$46$	1.73967	0.256500
$47$	11.1930	1.63266	0.816331	−	0.577585i	$-0.196005\pi$
$47$	11.1930	1.63266	0.816331	+	0.577585i	$0.196005\pi$
$48$	2.94456	0.425011
$49$	−6.42532	−0.917902
$50$	−8.62421	−1.21965
$51$	−1.00000	−0.140028
$52$	3.85824	0.535041
$53$	10.4904	1.44097	0.720486	−	0.693470i	$-0.243919\pi$
$53$	10.4904	1.44097	0.720486	+	0.693470i	$0.243919\pi$
$54$	−2.10563	−0.286540
$55$	3.13471	0.422685
$56$	−0.692253	−0.0925062
$57$	−6.02906	−0.798569
$58$	9.38185	1.23190
$59$	−3.01470	−0.392481	−0.196240	−	0.980556i	$-0.562873\pi$
$59$	−3.01470	−0.392481	−0.196240	+	0.980556i	$0.562873\pi$
$60$	−2.31419	−0.298761
$61$	10.1798	1.30339	0.651694	−	0.758482i	$-0.274058\pi$
$61$	10.1798	1.30339	0.651694	+	0.758482i	$0.274058\pi$
$62$	12.0837	1.53463
$63$	−0.758079	−0.0955089
$64$	−11.0117	−1.37646
$65$	1.50751	0.186984
$66$	−6.94136	−0.854422
$67$	−16.1861	−1.97744	−0.988721	−	0.149771i	$-0.952146\pi$
$67$	−16.1861	−1.97744	−0.988721	+	0.149771i	$0.952146\pi$
$68$	2.43368	0.295127
$69$	−0.826198	−0.0994625
$70$	−1.51786	−0.181419
$71$	−13.1762	−1.56373	−0.781863	−	0.623450i	$-0.785730\pi$
$71$	−13.1762	−1.56373	−0.781863	+	0.623450i	$0.785730\pi$
$72$	0.913167	0.107618
$73$	−7.58330	−0.887558	−0.443779	−	0.896136i	$-0.646363\pi$
$73$	−7.58330	−0.887558	−0.443779	+	0.896136i	$0.646363\pi$
$74$	3.81507	0.443492
$75$	4.09579	0.472941
$76$	14.6728	1.68309
$77$	−2.49906	−0.284794
$78$	−3.33816	−0.377973
$79$	−0.909801	−0.102361	−0.0511803	−	0.998689i	$-0.516298\pi$
$79$	−0.909801	−0.102361	−0.0511803	+	0.998689i	$0.516298\pi$
$80$	−2.79999	−0.313049
$81$	1.00000	0.111111
$82$	−4.36809	−0.482375
$83$	17.1339	1.88069	0.940343	−	0.340229i	$-0.110504\pi$
$83$	17.1339	1.88069	0.940343	+	0.340229i	$0.110504\pi$
$84$	1.84492	0.201297
$85$	0.950902	0.103140
$86$	−26.8800	−2.89854
$87$	−4.45560	−0.477691
$88$	3.01032	0.320901
$89$	5.22243	0.553576	0.276788	−	0.960931i	$-0.410730\pi$
$89$	5.22243	0.553576	0.276788	+	0.960931i	$0.410730\pi$
$90$	2.00225	0.211055
$91$	−1.20182	−0.125985
$92$	2.01070	0.209630
$93$	−5.73876	−0.595081
$94$	23.5682	2.43088
$95$	5.73304	0.588198
$96$	8.02650	0.819201
$97$	15.5144	1.57525	0.787625	−	0.616155i	$-0.211311\pi$
$97$	15.5144	1.57525	0.787625	+	0.616155i	$0.211311\pi$
$98$	−13.5293	−1.36667
$99$	3.29657	0.331318
$100$	−9.96783	−0.996783
$101$	−2.63246	−0.261939	−0.130970	−	0.991386i	$-0.541809\pi$
$101$	−2.63246	−0.261939	−0.130970	+	0.991386i	$0.541809\pi$
$102$	−2.10563	−0.208488
$103$	19.5565	1.92696	0.963479	−	0.267784i	$-0.0862913\pi$
$103$	19.5565	1.92696	0.963479	+	0.267784i	$0.0862913\pi$
$104$	1.44769	0.141958
$105$	0.720858	0.0703486
$106$	22.0890	2.14547
$107$	6.24954	0.604166	0.302083	−	0.953282i	$-0.402318\pi$
$107$	6.24954	0.604166	0.302083	+	0.953282i	$0.402318\pi$
$108$	−2.43368	−0.234181
$109$	15.3584	1.47107	0.735534	−	0.677488i	$-0.236932\pi$
$109$	15.3584	1.47107	0.735534	+	0.677488i	$0.236932\pi$
$110$	6.60055	0.629338
$111$	−1.81184	−0.171972
$112$	2.23221	0.210924
$113$	−6.00576	−0.564974	−0.282487	−	0.959271i	$-0.591159\pi$
$113$	−6.00576	−0.564974	−0.282487	+	0.959271i	$0.591159\pi$
$114$	−12.6950	−1.18899
$115$	0.785633	0.0732606
$116$	10.8435	1.00679
$117$	1.58535	0.146566
$118$	−6.34785	−0.584367
$119$	−0.758079	−0.0694930
$120$	−0.868332	−0.0792675
$121$	−0.132617	−0.0120561
$122$	21.4349	1.94062
$123$	2.07448	0.187050
$124$	13.9663	1.25421
$125$	−8.64920	−0.773608
$126$	−1.59623	−0.142204
$127$	6.97953	0.619333	0.309667	−	0.950845i	$-0.399783\pi$
$127$	6.97953	0.619333	0.309667	+	0.950845i	$0.399783\pi$
$128$	−7.13359	−0.630526
$129$	12.7658	1.12396
$130$	3.17427	0.278401
$131$	6.07887	0.531113	0.265557	−	0.964095i	$-0.414444\pi$
$131$	6.07887	0.531113	0.265557	+	0.964095i	$0.414444\pi$
$132$	−8.02280	−0.698295
$133$	−4.57050	−0.396313
$134$	−34.0819	−2.94422
$135$	−0.950902	−0.0818406
$136$	0.913167	0.0783035
$137$	22.1461	1.89207	0.946035	−	0.324064i	$-0.105049\pi$
$137$	22.1461	1.89207	0.946035	+	0.324064i	$0.105049\pi$
$138$	−1.73967	−0.148090
$139$	14.6697	1.24427	0.622134	−	0.782911i	$-0.286266\pi$
$139$	14.6697	1.24427	0.622134	+	0.782911i	$0.286266\pi$
$140$	−1.75434	−0.148269
$141$	−11.1930	−0.942617
$142$	−27.7442	−2.32824
$143$	5.22622	0.437039
$144$	−2.94456	−0.245380
$145$	4.23684	0.351850
$146$	−15.9676	−1.32149
$147$	6.42532	0.529951
$148$	4.40944	0.362454
$149$	5.91908	0.484910	0.242455	−	0.970163i	$-0.422047\pi$
$149$	5.91908	0.484910	0.242455	+	0.970163i	$0.422047\pi$
$150$	8.62421	0.704164
$151$	18.4451	1.50104	0.750518	−	0.660849i	$-0.229804\pi$
$151$	18.4451	1.50104	0.750518	+	0.660849i	$0.229804\pi$
$152$	5.50554	0.446558
$153$	1.00000	0.0808452
$154$	−5.26210	−0.424032
$155$	5.45699	0.438316
$156$	−3.85824	−0.308906
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−1.91570	−0.152405
$159$	−10.4904	−0.831945
$160$	−7.63241	−0.603395
$161$	−0.626323	−0.0493611
$162$	2.10563	0.165434
$163$	−18.7722	−1.47035	−0.735175	−	0.677877i	$-0.762900\pi$
$163$	−18.7722	−1.47035	−0.735175	+	0.677877i	$0.762900\pi$
$164$	−5.04862	−0.394231
$165$	−3.13471	−0.244037
$166$	36.0776	2.80016
$167$	14.3946	1.11389	0.556943	−	0.830551i	$-0.311974\pi$
$167$	14.3946	1.11389	0.556943	+	0.830551i	$0.311974\pi$
$168$	0.692253	0.0534085
$169$	−10.4867	−0.806666
$170$	2.00225	0.153565
$171$	6.02906	0.461054
$172$	−31.0678	−2.36890
$173$	−13.0297	−0.990630	−0.495315	−	0.868714i	$-0.664947\pi$
$173$	−13.0297	−0.990630	−0.495315	+	0.868714i	$0.664947\pi$
$174$	−9.38185	−0.711236
$175$	3.10493	0.234711
$176$	−9.70697	−0.731690
$177$	3.01470	0.226599
$178$	10.9965	0.824223
$179$	−16.3153	−1.21946	−0.609731	−	0.792608i	$-0.708723\pi$
$179$	−16.3153	−1.21946	−0.609731	+	0.792608i	$0.708723\pi$
$180$	2.31419	0.172489
$181$	−9.88249	−0.734559	−0.367280	−	0.930111i	$-0.619711\pi$
$181$	−9.88249	−0.734559	−0.367280	+	0.930111i	$0.619711\pi$
$182$	−2.53059	−0.187580
$183$	−10.1798	−0.752512
$184$	0.754457	0.0556193
$185$	1.72288	0.126669
$186$	−12.0837	−0.886020
$187$	3.29657	0.241069
$188$	27.2401	1.98669
$189$	0.758079	0.0551421
$190$	12.0717	0.875771
$191$	24.3526	1.76209	0.881047	−	0.473028i	$-0.156839\pi$
$191$	24.3526	1.76209	0.881047	+	0.473028i	$0.156839\pi$
$192$	11.0117	0.794702
$193$	23.0406	1.65850	0.829248	−	0.558881i	$-0.188769\pi$
$193$	23.0406	1.65850	0.829248	+	0.558881i	$0.188769\pi$
$194$	32.6676	2.34540
$195$	−1.50751	−0.107955
$196$	−15.6372	−1.11694
$197$	−2.07667	−0.147957	−0.0739784	−	0.997260i	$-0.523570\pi$
$197$	−2.07667	−0.147957	−0.0739784	+	0.997260i	$0.523570\pi$
$198$	6.94136	0.493301
$199$	−21.6234	−1.53285	−0.766423	−	0.642336i	$-0.777965\pi$
$199$	−21.6234	−1.53285	−0.766423	+	0.642336i	$0.777965\pi$
$200$	−3.74014	−0.264468
$201$	16.1861	1.14168
$202$	−5.54299	−0.390003
$203$	−3.37770	−0.237068
$204$	−2.43368	−0.170392
$205$	−1.97263	−0.137774
$206$	41.1787	2.86906
$207$	0.826198	0.0574247
$208$	−4.66817	−0.323679
$209$	19.8752	1.37480
$210$	1.51786	0.104742
$211$	−5.42519	−0.373485	−0.186743	−	0.982409i	$-0.559793\pi$
$211$	−5.42519	−0.373485	−0.186743	+	0.982409i	$0.559793\pi$
$212$	25.5303	1.75343
$213$	13.1762	0.902817
$214$	13.1592	0.899546
$215$	−12.1390	−0.827872
$216$	−0.913167	−0.0621332
$217$	−4.35043	−0.295326
$218$	32.3391	2.19028
$219$	7.58330	0.512432
$220$	7.62889	0.514340
$221$	1.58535	0.106642
$222$	−3.81507	−0.256050
$223$	−5.33232	−0.357079	−0.178539	−	0.983933i	$-0.557137\pi$
$223$	−5.33232	−0.357079	−0.178539	+	0.983933i	$0.557137\pi$
$224$	6.08472	0.406552
$225$	−4.09579	−0.273052
$226$	−12.6459	−0.841193
$227$	−16.1141	−1.06953	−0.534766	−	0.845000i	$-0.679600\pi$
$227$	−16.1141	−1.06953	−0.534766	+	0.845000i	$0.679600\pi$
$228$	−14.6728	−0.971730
$229$	11.6914	0.772587	0.386294	−	0.922376i	$-0.373755\pi$
$229$	11.6914	0.772587	0.386294	+	0.922376i	$0.373755\pi$
$230$	1.65425	0.109078
$231$	2.49906	0.164426
$232$	4.06871	0.267124
$233$	5.93258	0.388656	0.194328	−	0.980937i	$-0.437747\pi$
$233$	5.93258	0.388656	0.194328	+	0.980937i	$0.437747\pi$
$234$	3.33816	0.218223
$235$	10.6434	0.694299
$236$	−7.33682	−0.477586
$237$	0.909801	0.0590979
$238$	−1.59623	−0.103468
$239$	−23.2346	−1.50292	−0.751460	−	0.659779i	$-0.770650\pi$
$239$	−23.2346	−1.50292	−0.751460	+	0.659779i	$0.770650\pi$
$240$	2.79999	0.180739
$241$	−22.2342	−1.43223	−0.716116	−	0.697981i	$-0.754082\pi$
$241$	−22.2342	−1.43223	−0.716116	+	0.697981i	$0.754082\pi$
$242$	−0.279242	−0.0179504
$243$	−1.00000	−0.0641500
$244$	24.7743	1.58601
$245$	−6.10984	−0.390344
$246$	4.36809	0.278499
$247$	9.55818	0.608172
$248$	5.24045	0.332769
$249$	−17.1339	−1.08581
$250$	−18.2120	−1.15183
$251$	−0.705844	−0.0445525	−0.0222763	−	0.999752i	$-0.507091\pi$
$251$	−0.705844	−0.0445525	−0.0222763	+	0.999752i	$0.507091\pi$
$252$	−1.84492	−0.116219
$253$	2.72362	0.171232
$254$	14.6963	0.922129
$255$	−0.950902	−0.0595478
$256$	7.00271	0.437670
$257$	7.03152	0.438614	0.219307	−	0.975656i	$-0.429620\pi$
$257$	7.03152	0.438614	0.219307	+	0.975656i	$0.429620\pi$
$258$	26.8800	1.67347
$259$	−1.37352	−0.0853462
$260$	3.66880	0.227530
$261$	4.45560	0.275795
$262$	12.7999	0.790778
$263$	−3.63296	−0.224018	−0.112009	−	0.993707i	$-0.535729\pi$
$263$	−3.63296	−0.224018	−0.112009	+	0.993707i	$0.535729\pi$
$264$	−3.01032	−0.185272
$265$	9.97537	0.612782
$266$	−9.62379	−0.590072
$267$	−5.22243	−0.319607
$268$	−39.3917	−2.40623
$269$	15.7081	0.957739	0.478870	−	0.877886i	$-0.341047\pi$
$269$	15.7081	0.957739	0.478870	+	0.877886i	$0.341047\pi$
$270$	−2.00225	−0.121853
$271$	7.17330	0.435747	0.217873	−	0.975977i	$-0.430088\pi$
$271$	7.17330	0.435747	0.217873	+	0.975977i	$0.430088\pi$
$272$	−2.94456	−0.178540
$273$	1.20182	0.0727375
$274$	46.6315	2.81711
$275$	−13.5021	−0.814204
$276$	−2.01070	−0.121030
$277$	17.0409	1.02389	0.511944	−	0.859019i	$-0.328925\pi$
$277$	17.0409	1.02389	0.511944	+	0.859019i	$0.328925\pi$
$278$	30.8890	1.85260
$279$	5.73876	0.343570
$280$	−0.658264	−0.0393388
$281$	−9.20527	−0.549141	−0.274570	−	0.961567i	$-0.588536\pi$
$281$	−9.20527	−0.549141	−0.274570	+	0.961567i	$0.588536\pi$
$282$	−23.5682	−1.40347
$283$	17.6949	1.05185	0.525926	−	0.850530i	$-0.323719\pi$
$283$	17.6949	1.05185	0.525926	+	0.850530i	$0.323719\pi$
$284$	−32.0666	−1.90280
$285$	−5.73304	−0.339596
$286$	11.0045	0.650710
$287$	1.57262	0.0928288
$288$	−8.02650	−0.472966
$289$	1.00000	0.0588235
$290$	8.92122	0.523872
$291$	−15.5144	−0.909470
$292$	−18.4553	−1.08002
$293$	10.6837	0.624148	0.312074	−	0.950058i	$-0.398976\pi$
$293$	10.6837	0.624148	0.312074	+	0.950058i	$0.398976\pi$
$294$	13.5293	0.789047
$295$	−2.86668	−0.166905
$296$	1.65451	0.0961666
$297$	−3.29657	−0.191286
$298$	12.4634	0.721985
$299$	1.30981	0.0757485
$300$	9.96783	0.575493
$301$	9.67746	0.557799
$302$	38.8385	2.23490
$303$	2.63246	0.151231
$304$	−17.7530	−1.01820
$305$	9.67998	0.554274
$306$	2.10563	0.120371
$307$	12.4484	0.710470	0.355235	−	0.934777i	$-0.384401\pi$
$307$	12.4484	0.710470	0.355235	+	0.934777i	$0.384401\pi$
$308$	−6.08191	−0.346549
$309$	−19.5565	−1.11253
$310$	11.4904	0.652612
$311$	−12.6981	−0.720044	−0.360022	−	0.932944i	$-0.617231\pi$
$311$	−12.6981	−0.720044	−0.360022	+	0.932944i	$0.617231\pi$
$312$	−1.44769	−0.0819594
$313$	−31.8177	−1.79845	−0.899223	−	0.437491i	$-0.855867\pi$
$313$	−31.8177	−1.79845	−0.899223	+	0.437491i	$0.855867\pi$
$314$	−2.10563	−0.118828
$315$	−0.720858	−0.0406158
$316$	−2.21416	−0.124556
$317$	9.32318	0.523642	0.261821	−	0.965116i	$-0.415677\pi$
$317$	9.32318	0.523642	0.261821	+	0.965116i	$0.415677\pi$
$318$	−22.0890	−1.23869
$319$	14.6882	0.822382
$320$	−10.4711	−0.585350
$321$	−6.24954	−0.348815
$322$	−1.31880	−0.0734941
$323$	6.02906	0.335466
$324$	2.43368	0.135204
$325$	−6.49326	−0.360181
$326$	−39.5273	−2.18921
$327$	−15.3584	−0.849321
$328$	−1.89435	−0.104598
$329$	−8.48515	−0.467801
$330$	−6.60055	−0.363348
$331$	−8.43908	−0.463854	−0.231927	−	0.972733i	$-0.574503\pi$
$331$	−8.43908	−0.463854	−0.231927	+	0.972733i	$0.574503\pi$
$332$	41.6983	2.28849
$333$	1.81184	0.0992882
$334$	30.3097	1.65847
$335$	−15.3913	−0.840919
$336$	−2.23221	−0.121777
$337$	−34.6225	−1.88601	−0.943005	−	0.332778i	$-0.892014\pi$
$337$	−34.6225	−1.88601	−0.943005	+	0.332778i	$0.892014\pi$
$338$	−22.0810	−1.20105
$339$	6.00576	0.326188
$340$	2.31419	0.125505
$341$	18.9182	1.02448
$342$	12.6950	0.686465
$343$	10.1774	0.549530
$344$	−11.6573	−0.628519
$345$	−0.785633	−0.0422970
$346$	−27.4357	−1.47495
$347$	30.0264	1.61190	0.805952	−	0.591981i	$-0.201654\pi$
$347$	30.0264	1.61190	0.805952	+	0.591981i	$0.201654\pi$
$348$	−10.8435	−0.581273
$349$	15.9263	0.852518	0.426259	−	0.904601i	$-0.359831\pi$
$349$	15.9263	0.852518	0.426259	+	0.904601i	$0.359831\pi$
$350$	6.53783	0.349462
$351$	−1.58535	−0.0846198
$352$	−26.4599	−1.41032
$353$	8.09634	0.430925	0.215462	−	0.976512i	$-0.430874\pi$
$353$	8.09634	0.430925	0.215462	+	0.976512i	$0.430874\pi$
$354$	6.34785	0.337384
$355$	−12.5293	−0.664984
$356$	12.7097	0.673614
$357$	0.758079	0.0401218
$358$	−34.3540	−1.81566
$359$	8.59486	0.453619	0.226810	−	0.973939i	$-0.427170\pi$
$359$	8.59486	0.453619	0.226810	+	0.973939i	$0.427170\pi$
$360$	0.868332	0.0457651
$361$	17.3496	0.913135
$362$	−20.8089	−1.09369
$363$	0.132617	0.00696059
$364$	−2.92485	−0.153304
$365$	−7.21097	−0.377440
$366$	−21.4349	−1.12042
$367$	−12.8285	−0.669643	−0.334821	−	0.942282i	$-0.608676\pi$
$367$	−12.8285	−0.669643	−0.334821	+	0.942282i	$0.608676\pi$
$368$	−2.43279	−0.126818
$369$	−2.07448	−0.107993
$370$	3.62775	0.188598
$371$	−7.95257	−0.412877
$372$	−13.9663	−0.724119
$373$	12.0494	0.623896	0.311948	−	0.950099i	$-0.399019\pi$
$373$	12.0494	0.623896	0.311948	+	0.950099i	$0.399019\pi$
$374$	6.94136	0.358929
$375$	8.64920	0.446643
$376$	10.2210	0.527110
$377$	7.06370	0.363799
$378$	1.59623	0.0821014
$379$	−1.21217	−0.0622651	−0.0311325	−	0.999515i	$-0.509911\pi$
$379$	−1.21217	−0.0622651	−0.0311325	+	0.999515i	$0.509911\pi$
$380$	13.9524	0.715742
$381$	−6.97953	−0.357572
$382$	51.2776	2.62359
$383$	−28.4133	−1.45185	−0.725926	−	0.687772i	$-0.758589\pi$
$383$	−28.4133	−1.45185	−0.725926	+	0.687772i	$0.758589\pi$
$384$	7.13359	0.364035
$385$	−2.37636	−0.121111
$386$	48.5149	2.46934
$387$	−12.7658	−0.648920
$388$	37.7571	1.91683
$389$	11.8226	0.599429	0.299714	−	0.954029i	$-0.403109\pi$
$389$	11.8226	0.599429	0.299714	+	0.954029i	$0.403109\pi$
$390$	−3.17427	−0.160735
$391$	0.826198	0.0417826
$392$	−5.86739	−0.296348
$393$	−6.07887	−0.306639
$394$	−4.37271	−0.220294
$395$	−0.865131	−0.0435295
$396$	8.02280	0.403161
$397$	−22.3227	−1.12035	−0.560173	−	0.828376i	$-0.689265\pi$
$397$	−22.3227	−1.12035	−0.560173	+	0.828376i	$0.689265\pi$
$398$	−45.5310	−2.28226
$399$	4.57050	0.228811
$400$	12.0603	0.603015
$401$	12.7941	0.638907	0.319454	−	0.947602i	$-0.396501\pi$
$401$	12.7941	0.638907	0.319454	+	0.947602i	$0.396501\pi$
$402$	34.0819	1.69985
$403$	9.09795	0.453201
$404$	−6.40656	−0.318738
$405$	0.950902	0.0472507
$406$	−7.11218	−0.352972
$407$	5.97286	0.296064
$408$	−0.913167	−0.0452085
$409$	−24.5815	−1.21548	−0.607739	−	0.794137i	$-0.707923\pi$
$409$	−24.5815	−1.21548	−0.607739	+	0.794137i	$0.707923\pi$
$410$	−4.15362	−0.205133
$411$	−22.1461	−1.09239
$412$	47.5942	2.34480
$413$	2.28538	0.112456
$414$	1.73967	0.0854999
$415$	16.2926	0.799773
$416$	−12.7248	−0.623886
$417$	−14.6697	−0.718378
$418$	41.8499	2.04694
$419$	−31.1007	−1.51937	−0.759685	−	0.650291i	$-0.774647\pi$
$419$	−31.1007	−1.51937	−0.759685	+	0.650291i	$0.774647\pi$
$420$	1.75434	0.0856029
$421$	2.53800	0.123694	0.0618472	−	0.998086i	$-0.480301\pi$
$421$	2.53800	0.123694	0.0618472	+	0.998086i	$0.480301\pi$
$422$	−11.4234	−0.556085
$423$	11.1930	0.544220
$424$	9.57952	0.465223
$425$	−4.09579	−0.198675
$426$	27.7442	1.34421
$427$	−7.71708	−0.373456
$428$	15.2094	0.735173
$429$	−5.22622	−0.252324
$430$	−25.5602	−1.23262
$431$	26.3868	1.27101	0.635504	−	0.772098i	$-0.280793\pi$
$431$	26.3868	1.27101	0.635504	+	0.772098i	$0.280793\pi$
$432$	2.94456	0.141670
$433$	−25.2850	−1.21512	−0.607560	−	0.794274i	$-0.707851\pi$
$433$	−25.2850	−1.21512	−0.607560	+	0.794274i	$0.707851\pi$
$434$	−9.16040	−0.439713
$435$	−4.23684	−0.203141
$436$	37.3774	1.79005
$437$	4.98119	0.238283
$438$	15.9676	0.762963
$439$	11.3317	0.540833	0.270417	−	0.962743i	$-0.412839\pi$
$439$	11.3317	0.540833	0.270417	+	0.962743i	$0.412839\pi$
$440$	2.86252	0.136465
$441$	−6.42532	−0.305967
$442$	3.33816	0.158780
$443$	7.52296	0.357427	0.178713	−	0.983901i	$-0.442807\pi$
$443$	7.52296	0.357427	0.178713	+	0.983901i	$0.442807\pi$
$444$	−4.40944	−0.209263
$445$	4.96602	0.235412
$446$	−11.2279	−0.531656
$447$	−5.91908	−0.279963
$448$	8.34774	0.394394
$449$	−17.9338	−0.846346	−0.423173	−	0.906049i	$-0.639084\pi$
$449$	−17.9338	−0.846346	−0.423173	+	0.906049i	$0.639084\pi$
$450$	−8.62421	−0.406549
$451$	−6.83867	−0.322021
$452$	−14.6161	−0.687483
$453$	−18.4451	−0.866624
$454$	−33.9304	−1.59243
$455$	−1.14281	−0.0535759
$456$	−5.50554	−0.257821
$457$	21.1603	0.989838	0.494919	−	0.868939i	$-0.335198\pi$
$457$	21.1603	0.989838	0.494919	+	0.868939i	$0.335198\pi$
$458$	24.6177	1.15031
$459$	−1.00000	−0.0466760
$460$	1.91198	0.0891464
$461$	−32.2711	−1.50301	−0.751507	−	0.659725i	$-0.770673\pi$
$461$	−32.2711	−1.50301	−0.751507	+	0.659725i	$0.770673\pi$
$462$	5.26210	0.244815
$463$	11.6986	0.543680	0.271840	−	0.962342i	$-0.412368\pi$
$463$	11.6986	0.543680	0.271840	+	0.962342i	$0.412368\pi$
$464$	−13.1198	−0.609072
$465$	−5.45699	−0.253062
$466$	12.4918	0.578673
$467$	20.0662	0.928554	0.464277	−	0.885690i	$-0.346314\pi$
$467$	20.0662	0.928554	0.464277	+	0.885690i	$0.346314\pi$
$468$	3.85824	0.178347
$469$	12.2703	0.566590
$470$	22.4111	1.03375
$471$	1.00000	0.0460776
$472$	−2.75293	−0.126714
$473$	−42.0833	−1.93499
$474$	1.91570	0.0879912
$475$	−24.6937	−1.13303
$476$	−1.84492	−0.0845618
$477$	10.4904	0.480324
$478$	−48.9234	−2.23771
$479$	−20.6893	−0.945317	−0.472659	−	0.881246i	$-0.656706\pi$
$479$	−20.6893	−0.945317	−0.472659	+	0.881246i	$0.656706\pi$
$480$	7.63241	0.348370
$481$	2.87240	0.130970
$482$	−46.8171	−2.13246
$483$	0.626323	0.0284987
$484$	−0.322747	−0.0146703
$485$	14.7527	0.669884
$486$	−2.10563	−0.0955133
$487$	7.97836	0.361534	0.180767	−	0.983526i	$-0.442142\pi$
$487$	7.97836	0.361534	0.180767	+	0.983526i	$0.442142\pi$
$488$	9.29585	0.420804
$489$	18.7722	0.848907
$490$	−12.8651	−0.581185
$491$	31.8480	1.43728	0.718640	−	0.695382i	$-0.244765\pi$
$491$	31.8480	1.43728	0.718640	+	0.695382i	$0.244765\pi$
$492$	5.04862	0.227609
$493$	4.45560	0.200670
$494$	20.1260	0.905511
$495$	3.13471	0.140895
$496$	−16.8981	−0.758749
$497$	9.98859	0.448049
$498$	−36.0776	−1.61667
$499$	9.67010	0.432893	0.216447	−	0.976294i	$-0.430553\pi$
$499$	9.67010	0.432893	0.216447	+	0.976294i	$0.430553\pi$
$500$	−21.0494	−0.941356
$501$	−14.3946	−0.643102
$502$	−1.48625	−0.0663345
$503$	−17.5530	−0.782649	−0.391324	−	0.920253i	$-0.627983\pi$
$503$	−17.5530	−0.782649	−0.391324	+	0.920253i	$0.627983\pi$
$504$	−0.692253	−0.0308354
$505$	−2.50321	−0.111391
$506$	5.73494	0.254949
$507$	10.4867	0.465729
$508$	16.9859	0.753629
$509$	3.11825	0.138214	0.0691071	−	0.997609i	$-0.477985\pi$
$509$	3.11825	0.138214	0.0691071	+	0.997609i	$0.477985\pi$
$510$	−2.00225	−0.0886610
$511$	5.74874	0.254309
$512$	29.0123	1.28218
$513$	−6.02906	−0.266190
$514$	14.8058	0.653055
$515$	18.5963	0.819451
$516$	31.0678	1.36768
$517$	36.8984	1.62279
$518$	−2.89212	−0.127072
$519$	13.0297	0.571940
$520$	1.37661	0.0603684
$521$	−38.8095	−1.70027	−0.850137	−	0.526561i	$-0.823481\pi$
$521$	−38.8095	−1.70027	−0.850137	+	0.526561i	$0.823481\pi$
$522$	9.38185	0.410632
$523$	−5.12317	−0.224020	−0.112010	−	0.993707i	$-0.535729\pi$
$523$	−5.12317	−0.224020	−0.112010	+	0.993707i	$0.535729\pi$
$524$	14.7940	0.646280
$525$	−3.10493	−0.135510
$526$	−7.64966	−0.333541
$527$	5.73876	0.249984
$528$	9.70697	0.422442
$529$	−22.3174	−0.970322
$530$	21.0044	0.912374
$531$	−3.01470	−0.130827
$532$	−11.1231	−0.482249
$533$	−3.28878	−0.142453
$534$	−10.9965	−0.475865
$535$	5.94270	0.256925
$536$	−14.7806	−0.638424
$537$	16.3153	0.704057
$538$	33.0754	1.42598
$539$	−21.1815	−0.912352
$540$	−2.31419	−0.0995868
$541$	−20.2546	−0.870814	−0.435407	−	0.900234i	$-0.643396\pi$
$541$	−20.2546	−0.870814	−0.435407	+	0.900234i	$0.643396\pi$
$542$	15.1043	0.648786
$543$	9.88249	0.424098
$544$	−8.02650	−0.344133
$545$	14.6043	0.625580
$546$	2.53059	0.108299
$547$	−6.36995	−0.272359	−0.136180	−	0.990684i	$-0.543482\pi$
$547$	−6.36995	−0.272359	−0.136180	+	0.990684i	$0.543482\pi$
$548$	53.8965	2.30235
$549$	10.1798	0.434463
$550$	−28.4303	−1.21227
$551$	26.8631	1.14441
$552$	−0.754457	−0.0321118
$553$	0.689700	0.0293290
$554$	35.8819	1.52447
$555$	−1.72288	−0.0731323
$556$	35.7013	1.51407
$557$	−30.9550	−1.31160	−0.655802	−	0.754933i	$-0.727669\pi$
$557$	−30.9550	−1.31160	−0.655802	+	0.754933i	$0.727669\pi$
$558$	12.0837	0.511544
$559$	−20.2382	−0.855986
$560$	2.12261	0.0896968
$561$	−3.29657	−0.139181
$562$	−19.3829	−0.817618
$563$	−7.63841	−0.321921	−0.160960	−	0.986961i	$-0.551459\pi$
$563$	−7.63841	−0.321921	−0.160960	+	0.986961i	$0.551459\pi$
$564$	−27.2401	−1.14701
$565$	−5.71088	−0.240259
$566$	37.2589	1.56611
$567$	−0.758079	−0.0318363
$568$	−12.0321	−0.504854
$569$	−27.4430	−1.15047	−0.575236	−	0.817987i	$-0.695090\pi$
$569$	−27.4430	−1.15047	−0.575236	+	0.817987i	$0.695090\pi$
$570$	−12.0717	−0.505627
$571$	−34.1122	−1.42755	−0.713775	−	0.700375i	$-0.753016\pi$
$571$	−34.1122	−1.42755	−0.713775	+	0.700375i	$0.753016\pi$
$572$	12.7190	0.531806
$573$	−24.3526	−1.01735
$574$	3.31136	0.138213
$575$	−3.38393	−0.141120
$576$	−11.0117	−0.458821
$577$	23.5493	0.980370	0.490185	−	0.871618i	$-0.336929\pi$
$577$	23.5493	0.980370	0.490185	+	0.871618i	$0.336929\pi$
$578$	2.10563	0.0875827
$579$	−23.0406	−0.957533
$580$	10.3111	0.428145
$581$	−12.9888	−0.538867
$582$	−32.6676	−1.35412
$583$	34.5825	1.43226
$584$	−6.92482	−0.286551
$585$	1.50751	0.0623280
$586$	22.4959	0.929297
$587$	2.53364	0.104575	0.0522873	−	0.998632i	$-0.483349\pi$
$587$	2.53364	0.104575	0.0522873	+	0.998632i	$0.483349\pi$
$588$	15.6372	0.644866
$589$	34.5993	1.42564
$590$	−6.03618	−0.248505
$591$	2.07667	0.0854230
$592$	−5.33508	−0.219271
$593$	3.20900	0.131778	0.0658888	−	0.997827i	$-0.479012\pi$
$593$	3.20900	0.131778	0.0658888	+	0.997827i	$0.479012\pi$
$594$	−6.94136	−0.284807
$595$	−0.720858	−0.0295523
$596$	14.4051	0.590057
$597$	21.6234	0.884989
$598$	2.75798	0.112782
$599$	5.91472	0.241669	0.120834	−	0.992673i	$-0.461443\pi$
$599$	5.91472	0.241669	0.120834	+	0.992673i	$0.461443\pi$
$600$	3.74014	0.152691
$601$	−25.3652	−1.03467	−0.517334	−	0.855784i	$-0.673075\pi$
$601$	−25.3652	−1.03467	−0.517334	+	0.855784i	$0.673075\pi$
$602$	20.3771	0.830510
$603$	−16.1861	−0.659147
$604$	44.8893	1.82652
$605$	−0.126106	−0.00512693
$606$	5.54299	0.225168
$607$	−37.8454	−1.53610	−0.768048	−	0.640392i	$-0.778772\pi$
$607$	−37.8454	−1.53610	−0.768048	+	0.640392i	$0.778772\pi$
$608$	−48.3922	−1.96256
$609$	3.37770	0.136871
$610$	20.3825	0.825262
$611$	17.7448	0.717877
$612$	2.43368	0.0983756
$613$	40.3430	1.62944	0.814720	−	0.579855i	$-0.196891\pi$
$613$	40.3430	1.62944	0.814720	+	0.579855i	$0.196891\pi$
$614$	26.2118	1.05782
$615$	1.97263	0.0795440
$616$	−2.28206	−0.0919468
$617$	−7.94271	−0.319761	−0.159881	−	0.987136i	$-0.551111\pi$
$617$	−7.94271	−0.319761	−0.159881	+	0.987136i	$0.551111\pi$
$618$	−41.1787	−1.65645
$619$	−2.36047	−0.0948754	−0.0474377	−	0.998874i	$-0.515106\pi$
$619$	−2.36047	−0.0948754	−0.0474377	+	0.998874i	$0.515106\pi$
$620$	13.2806	0.533361
$621$	−0.826198	−0.0331542
$622$	−26.7375	−1.07208
$623$	−3.95901	−0.158614
$624$	4.66817	0.186876
$625$	12.2544	0.490176
$626$	−66.9964	−2.67772
$627$	−19.8752	−0.793740
$628$	−2.43368	−0.0971144
$629$	1.81184	0.0722428
$630$	−1.51786	−0.0604730
$631$	1.35333	0.0538752	0.0269376	−	0.999637i	$-0.491424\pi$
$631$	1.35333	0.0538752	0.0269376	+	0.999637i	$0.491424\pi$
$632$	−0.830800	−0.0330475
$633$	5.42519	0.215632
$634$	19.6312	0.779653
$635$	6.63685	0.263375
$636$	−25.5303	−1.01234
$637$	−10.1864	−0.403599
$638$	30.9279	1.22445
$639$	−13.1762	−0.521242
$640$	−6.78334	−0.268135
$641$	−33.0676	−1.30609	−0.653045	−	0.757319i	$-0.726509\pi$
$641$	−33.0676	−1.30609	−0.653045	+	0.757319i	$0.726509\pi$
$642$	−13.1592	−0.519353
$643$	−16.2799	−0.642018	−0.321009	−	0.947076i	$-0.604022\pi$
$643$	−16.2799	−0.642018	−0.321009	+	0.947076i	$0.604022\pi$
$644$	−1.52427	−0.0600646
$645$	12.1390	0.477972
$646$	12.6950	0.499477
$647$	−9.74983	−0.383306	−0.191653	−	0.981463i	$-0.561385\pi$
$647$	−9.74983	−0.383306	−0.191653	+	0.981463i	$0.561385\pi$
$648$	0.913167	0.0358726
$649$	−9.93818	−0.390108
$650$	−13.6724	−0.536276
$651$	4.35043	0.170507
$652$	−45.6855	−1.78918
$653$	28.9387	1.13246	0.566229	−	0.824248i	$-0.308402\pi$
$653$	28.9387	1.13246	0.566229	+	0.824248i	$0.308402\pi$
$654$	−32.3391	−1.26456
$655$	5.78041	0.225859
$656$	6.10844	0.238495
$657$	−7.58330	−0.295853
$658$	−17.8666	−0.696512
$659$	6.99461	0.272471	0.136236	−	0.990676i	$-0.456500\pi$
$659$	6.99461	0.272471	0.136236	+	0.990676i	$0.456500\pi$
$660$	−7.62889	−0.296954
$661$	18.8913	0.734785	0.367393	−	0.930066i	$-0.380251\pi$
$661$	18.8913	0.734785	0.367393	+	0.930066i	$0.380251\pi$
$662$	−17.7696	−0.690635
$663$	−1.58535	−0.0615700
$664$	15.6461	0.607186
$665$	−4.34610	−0.168534
$666$	3.81507	0.147831
$667$	3.68121	0.142537
$668$	35.0318	1.35542
$669$	5.33232	0.206159
$670$	−32.4085	−1.25205
$671$	33.5584	1.29551
$672$	−6.08472	−0.234723
$673$	−17.7583	−0.684533	−0.342267	−	0.939603i	$-0.611195\pi$
$673$	−17.7583	−0.684533	−0.342267	+	0.939603i	$0.611195\pi$
$674$	−72.9023	−2.80809
$675$	4.09579	0.157647
$676$	−25.5212	−0.981583
$677$	17.2707	0.663767	0.331884	−	0.943320i	$-0.392316\pi$
$677$	17.2707	0.663767	0.331884	+	0.943320i	$0.392316\pi$
$678$	12.6459	0.485663
$679$	−11.7611	−0.451351
$680$	0.868332	0.0332990
$681$	16.1141	0.617494
$682$	39.8348	1.52535
$683$	−11.3037	−0.432522	−0.216261	−	0.976336i	$-0.569386\pi$
$683$	−11.3037	−0.432522	−0.216261	+	0.976336i	$0.569386\pi$
$684$	14.6728	0.561028
$685$	21.0588	0.804614
$686$	21.4299	0.818199
$687$	−11.6914	−0.446053
$688$	37.5896	1.43309
$689$	16.6310	0.633591
$690$	−1.65425	−0.0629763
$691$	28.6946	1.09160	0.545798	−	0.837917i	$-0.316227\pi$
$691$	28.6946	1.09160	0.545798	+	0.837917i	$0.316227\pi$
$692$	−31.7101	−1.20544
$693$	−2.49906	−0.0949315
$694$	63.2246	2.39997
$695$	13.9494	0.529132
$696$	−4.06871	−0.154224
$697$	−2.07448	−0.0785766
$698$	33.5350	1.26932
$699$	−5.93258	−0.224391
$700$	7.55640	0.285605
$701$	22.1440	0.836366	0.418183	−	0.908363i	$-0.362667\pi$
$701$	22.1440	0.836366	0.418183	+	0.908363i	$0.362667\pi$
$702$	−3.33816	−0.125991
$703$	10.9237	0.411995
$704$	−36.3009	−1.36814
$705$	−10.6434	−0.400854
$706$	17.0479	0.641606
$707$	1.99561	0.0750527
$708$	7.33682	0.275734
$709$	6.83695	0.256767	0.128384	−	0.991725i	$-0.459021\pi$
$709$	6.83695	0.256767	0.128384	+	0.991725i	$0.459021\pi$
$710$	−26.3820	−0.990098
$711$	−0.909801	−0.0341202
$712$	4.76895	0.178724
$713$	4.74135	0.177565
$714$	1.59623	0.0597375
$715$	4.96962	0.185853
$716$	−39.7062	−1.48389
$717$	23.2346	0.867711
$718$	18.0976	0.675396
$719$	−38.8806	−1.45000	−0.725001	−	0.688748i	$-0.758161\pi$
$719$	−38.8806	−1.45000	−0.725001	+	0.688748i	$0.758161\pi$
$720$	−2.79999	−0.104350
$721$	−14.8254	−0.552125
$722$	36.5318	1.35957
$723$	22.2342	0.826900
$724$	−24.0508	−0.893841
$725$	−18.2492	−0.677758
$726$	0.279242	0.0103637
$727$	−24.3545	−0.903258	−0.451629	−	0.892206i	$-0.649157\pi$
$727$	−24.3545	−0.903258	−0.451629	+	0.892206i	$0.649157\pi$
$728$	−1.09746	−0.0406747
$729$	1.00000	0.0370370
$730$	−15.1836	−0.561972
$731$	−12.7658	−0.472159
$732$	−24.7743	−0.915686
$733$	16.7165	0.617439	0.308720	−	0.951153i	$-0.400100\pi$
$733$	16.7165	0.617439	0.308720	+	0.951153i	$0.400100\pi$
$734$	−27.0121	−0.997034
$735$	6.10984	0.225365
$736$	−6.63147	−0.244439
$737$	−53.3585	−1.96549
$738$	−4.36809	−0.160792
$739$	−42.1610	−1.55092	−0.775459	−	0.631398i	$-0.782482\pi$
$739$	−42.1610	−1.55092	−0.775459	+	0.631398i	$0.782482\pi$
$740$	4.19294	0.154136
$741$	−9.55818	−0.351128
$742$	−16.7452	−0.614735
$743$	23.4624	0.860751	0.430376	−	0.902650i	$-0.358381\pi$
$743$	23.4624	0.860751	0.430376	+	0.902650i	$0.358381\pi$
$744$	−5.24045	−0.192124
$745$	5.62846	0.206211
$746$	25.3717	0.928922
$747$	17.1339	0.626895
$748$	8.02280	0.293342
$749$	−4.73764	−0.173110
$750$	18.2120	0.665009
$751$	−35.0055	−1.27737	−0.638685	−	0.769468i	$-0.720521\pi$
$751$	−35.0055	−1.27737	−0.638685	+	0.769468i	$0.720521\pi$
$752$	−32.9584	−1.20187
$753$	0.705844	0.0257224
$754$	14.8735	0.541662
$755$	17.5394	0.638325
$756$	1.84492	0.0670991
$757$	36.2774	1.31853	0.659263	−	0.751913i	$-0.270868\pi$
$757$	36.2774	1.31853	0.659263	+	0.751913i	$0.270868\pi$
$758$	−2.55238	−0.0927068
$759$	−2.72362	−0.0988611
$760$	5.23523	0.189902
$761$	−40.4450	−1.46613	−0.733065	−	0.680158i	$-0.761911\pi$
$761$	−40.4450	−1.46613	−0.733065	+	0.680158i	$0.761911\pi$
$762$	−14.6963	−0.532391
$763$	−11.6429	−0.421500
$764$	59.2665	2.14419
$765$	0.950902	0.0343799
$766$	−59.8279	−2.16167
$767$	−4.77936	−0.172573
$768$	−7.00271	−0.252689
$769$	−35.4664	−1.27895	−0.639475	−	0.768812i	$-0.720848\pi$
$769$	−35.4664	−1.27895	−0.639475	+	0.768812i	$0.720848\pi$
$770$	−5.00374	−0.180322
$771$	−7.03152	−0.253234
$772$	56.0733	2.01812
$773$	5.29481	0.190441	0.0952205	−	0.995456i	$-0.469644\pi$
$773$	5.29481	0.190441	0.0952205	+	0.995456i	$0.469644\pi$
$774$	−26.8800	−0.966181
$775$	−23.5047	−0.844315
$776$	14.1672	0.508575
$777$	1.37352	0.0492747
$778$	24.8940	0.892493
$779$	−12.5072	−0.448116
$780$	−3.66880	−0.131364
$781$	−43.4362	−1.55427
$782$	1.73967	0.0622103
$783$	−4.45560	−0.159230
$784$	18.9198	0.675706
$785$	−0.950902	−0.0339391
$786$	−12.7999	−0.456556
$787$	15.9614	0.568964	0.284482	−	0.958681i	$-0.408178\pi$
$787$	15.9614	0.568964	0.284482	+	0.958681i	$0.408178\pi$
$788$	−5.05396	−0.180040
$789$	3.63296	0.129337
$790$	−1.82165	−0.0648112
$791$	4.55284	0.161880
$792$	3.01032	0.106967
$793$	16.1385	0.573097
$794$	−47.0034	−1.66809
$795$	−9.97537	−0.353790
$796$	−52.6245	−1.86523
$797$	−15.4994	−0.549018	−0.274509	−	0.961585i	$-0.588515\pi$
$797$	−15.4994	−0.549018	−0.274509	+	0.961585i	$0.588515\pi$
$798$	9.62379	0.340678
$799$	11.1930	0.395979
$800$	32.8748	1.16230
$801$	5.22243	0.184525
$802$	26.9397	0.951273
$803$	−24.9989	−0.882192
$804$	39.3917	1.38924
$805$	−0.595571	−0.0209911
$806$	19.1569	0.674774
$807$	−15.7081	−0.552951
$808$	−2.40388	−0.0845681
$809$	−5.93477	−0.208655	−0.104328	−	0.994543i	$-0.533269\pi$
$809$	−5.93477	−0.208655	−0.104328	+	0.994543i	$0.533269\pi$
$810$	2.00225	0.0703518
$811$	8.51292	0.298929	0.149465	−	0.988767i	$-0.452245\pi$
$811$	8.51292	0.298929	0.149465	+	0.988767i	$0.452245\pi$
$812$	−8.22023	−0.288474
$813$	−7.17330	−0.251579
$814$	12.5766	0.440811
$815$	−17.8505	−0.625275
$816$	2.94456	0.103080
$817$	−76.9656	−2.69268
$818$	−51.7596	−1.80973
$819$	−1.20182	−0.0419950
$820$	−4.80074	−0.167649
$821$	18.6294	0.650171	0.325085	−	0.945685i	$-0.394607\pi$
$821$	18.6294	0.650171	0.325085	+	0.945685i	$0.394607\pi$
$822$	−46.6315	−1.62646
$823$	−41.5591	−1.44866	−0.724330	−	0.689453i	$-0.757851\pi$
$823$	−41.5591	−1.44866	−0.724330	+	0.689453i	$0.757851\pi$
$824$	17.8583	0.622125
$825$	13.5021	0.470081
$826$	4.81217	0.167437
$827$	−53.3157	−1.85397	−0.926985	−	0.375099i	$-0.877609\pi$
$827$	−53.3157	−1.85397	−0.926985	+	0.375099i	$0.877609\pi$
$828$	2.01070	0.0698766
$829$	0.0395649	0.00137414	0.000687072	−	1.00000i	$-0.499781\pi$
$829$	0.0395649	0.00137414	0.000687072		1.00000i	$0.499781\pi$
$830$	34.3062	1.19079
$831$	−17.0409	−0.591143
$832$	−17.4574	−0.605228
$833$	−6.42532	−0.222624
$834$	−30.8890	−1.06960
$835$	13.6878	0.473687
$836$	48.3699	1.67291
$837$	−5.73876	−0.198360
$838$	−65.4867	−2.26220
$839$	−13.6166	−0.470099	−0.235049	−	0.971983i	$-0.575525\pi$
$839$	−13.6166	−0.470099	−0.235049	+	0.971983i	$0.575525\pi$
$840$	0.658264	0.0227123
$841$	−9.14761	−0.315435
$842$	5.34409	0.184169
$843$	9.20527	0.317046
$844$	−13.2032	−0.454472
$845$	−9.97178	−0.343040
$846$	23.5682	0.810293
$847$	0.100534	0.00345439
$848$	−30.8898	−1.06076
$849$	−17.6949	−0.607287
$850$	−8.62421	−0.295808
$851$	1.49694	0.0513144
$852$	32.0666	1.09858
$853$	51.6888	1.76979	0.884895	−	0.465791i	$-0.154230\pi$
$853$	51.6888	1.76979	0.884895	+	0.465791i	$0.154230\pi$
$854$	−16.2493	−0.556040
$855$	5.73304	0.196066
$856$	5.70688	0.195057
$857$	21.8295	0.745681	0.372840	−	0.927896i	$-0.378384\pi$
$857$	21.8295	0.745681	0.372840	+	0.927896i	$0.378384\pi$
$858$	−11.0045	−0.375687
$859$	−49.5754	−1.69149	−0.845745	−	0.533587i	$-0.820844\pi$
$859$	−49.5754	−1.69149	−0.845745	+	0.533587i	$0.820844\pi$
$860$	−29.5424	−1.00739
$861$	−1.57262	−0.0535947
$862$	55.5608	1.89241
$863$	4.88784	0.166384	0.0831921	−	0.996534i	$-0.473489\pi$
$863$	4.88784	0.166384	0.0831921	+	0.996534i	$0.473489\pi$
$864$	8.02650	0.273067
$865$	−12.3900	−0.421271
$866$	−53.2408	−1.80920
$867$	−1.00000	−0.0339618
$868$	−10.5876	−0.359365
$869$	−2.99922	−0.101742
$870$	−8.92122	−0.302458
$871$	−25.6606	−0.869476
$872$	14.0248	0.474939
$873$	15.5144	0.525083
$874$	10.4886	0.354781
$875$	6.55677	0.221659
$876$	18.4553	0.623547
$877$	7.80503	0.263557	0.131779	−	0.991279i	$-0.457931\pi$
$877$	7.80503	0.263557	0.131779	+	0.991279i	$0.457931\pi$
$878$	23.8604	0.805250
$879$	−10.6837	−0.360352
$880$	−9.23037	−0.311156
$881$	−8.94314	−0.301302	−0.150651	−	0.988587i	$-0.548137\pi$
$881$	−8.94314	−0.301302	−0.150651	+	0.988587i	$0.548137\pi$
$882$	−13.5293	−0.455557
$883$	−52.4214	−1.76412	−0.882060	−	0.471137i	$-0.843844\pi$
$883$	−52.4214	−1.76412	−0.882060	+	0.471137i	$0.843844\pi$
$884$	3.85824	0.129767
$885$	2.86668	0.0963625
$886$	15.8406	0.532175
$887$	20.3527	0.683378	0.341689	−	0.939813i	$-0.389001\pi$
$887$	20.3527	0.683378	0.341689	+	0.939813i	$0.389001\pi$
$888$	−1.65451	−0.0555218
$889$	−5.29103	−0.177456
$890$	10.4566	0.350506
$891$	3.29657	0.110439
$892$	−12.9772	−0.434507
$893$	67.4830	2.25823
$894$	−12.4634	−0.416838
$895$	−15.5142	−0.518584
$896$	5.40782	0.180663
$897$	−1.30981	−0.0437334
$898$	−37.7619	−1.26013
$899$	25.5696	0.852795
$900$	−9.96783	−0.332261
$901$	10.4904	0.349487
$902$	−14.3997	−0.479458
$903$	−9.67746	−0.322046
$904$	−5.48426	−0.182404
$905$	−9.39727	−0.312376
$906$	−38.8385	−1.29032
$907$	19.4973	0.647399	0.323699	−	0.946160i	$-0.395073\pi$
$907$	19.4973	0.647399	0.323699	+	0.946160i	$0.395073\pi$
$908$	−39.2166	−1.30145
$909$	−2.63246	−0.0873132
$910$	−2.40634	−0.0797695
$911$	−55.3845	−1.83497	−0.917485	−	0.397770i	$-0.869784\pi$
$911$	−55.3845	−1.83497	−0.917485	+	0.397770i	$0.869784\pi$
$912$	17.7530	0.587859
$913$	56.4830	1.86931
$914$	44.5558	1.47377
$915$	−9.67998	−0.320010
$916$	28.4530	0.940114
$917$	−4.60826	−0.152178
$918$	−2.10563	−0.0694962
$919$	21.0077	0.692981	0.346491	−	0.938053i	$-0.387373\pi$
$919$	21.0077	0.692981	0.346491	+	0.938053i	$0.387373\pi$
$920$	0.717414	0.0236524
$921$	−12.4484	−0.410190
$922$	−67.9510	−2.23785
$923$	−20.8889	−0.687566
$924$	6.08191	0.200080
$925$	−7.42091	−0.243998
$926$	24.6329	0.809488
$927$	19.5565	0.642319
$928$	−35.7629	−1.17397
$929$	54.9016	1.80126	0.900631	−	0.434584i	$-0.143105\pi$
$929$	54.9016	1.80126	0.900631	+	0.434584i	$0.143105\pi$
$930$	−11.4904	−0.376785
$931$	−38.7386	−1.26961
$932$	14.4380	0.472932
$933$	12.6981	0.415718
$934$	42.2520	1.38253
$935$	3.13471	0.102516
$936$	1.44769	0.0473193
$937$	22.4276	0.732678	0.366339	−	0.930482i	$-0.380611\pi$
$937$	22.4276	0.732678	0.366339	+	0.930482i	$0.380611\pi$
$938$	25.8367	0.843599
$939$	31.8177	1.03833
$940$	25.9026	0.844851
$941$	−4.18343	−0.136376	−0.0681879	−	0.997672i	$-0.521722\pi$
$941$	−4.18343	−0.136376	−0.0681879	+	0.997672i	$0.521722\pi$
$942$	2.10563	0.0686051
$943$	−1.71393	−0.0558133
$944$	8.87698	0.288921
$945$	0.720858	0.0234495
$946$	−88.6118	−2.88102
$947$	−34.4004	−1.11786	−0.558931	−	0.829214i	$-0.688788\pi$
$947$	−34.4004	−1.11786	−0.558931	+	0.829214i	$0.688788\pi$
$948$	2.21416	0.0719127
$949$	−12.0222	−0.390257
$950$	−51.9959	−1.68697
$951$	−9.32318	−0.302325
$952$	−0.692253	−0.0224360
$953$	7.05160	0.228424	0.114212	−	0.993456i	$-0.463566\pi$
$953$	7.05160	0.228424	0.114212	+	0.993456i	$0.463566\pi$
$954$	22.0890	0.715157
$955$	23.1570	0.749341
$956$	−56.5455	−1.82881
$957$	−14.6882	−0.474802
$958$	−43.5640	−1.40749
$959$	−16.7885	−0.542129
$960$	10.4711	0.337952
$961$	1.93334	0.0623659
$962$	6.04822	0.195002
$963$	6.24954	0.201389
$964$	−54.1110	−1.74280
$965$	21.9093	0.705285
$966$	1.31880	0.0424318
$967$	−2.17517	−0.0699487	−0.0349744	−	0.999388i	$-0.511135\pi$
$967$	−2.17517	−0.0699487	−0.0349744	+	0.999388i	$0.511135\pi$
$968$	−0.121102	−0.00389235
$969$	−6.02906	−0.193681
$970$	31.0637	0.997394
$971$	24.6505	0.791071	0.395536	−	0.918451i	$-0.370559\pi$
$971$	24.6505	0.791071	0.395536	+	0.918451i	$0.370559\pi$
$972$	−2.43368	−0.0780603
$973$	−11.1208	−0.356516
$974$	16.7995	0.538290
$975$	6.49326	0.207951
$976$	−29.9751	−0.959478
$977$	22.5645	0.721902	0.360951	−	0.932585i	$-0.382452\pi$
$977$	22.5645	0.721902	0.360951	+	0.932585i	$0.382452\pi$
$978$	39.5273	1.26394
$979$	17.2161	0.550229
$980$	−14.8694	−0.474985
$981$	15.3584	0.490356
$982$	67.0601	2.13998
$983$	−23.8174	−0.759657	−0.379828	−	0.925057i	$-0.624017\pi$
$983$	−23.8174	−0.759657	−0.379828	+	0.925057i	$0.624017\pi$
$984$	1.89435	0.0603896
$985$	−1.97471	−0.0629196
$986$	9.38185	0.298779
$987$	8.48515	0.270085
$988$	23.2615	0.740048
$989$	−10.5470	−0.335377
$990$	6.60055	0.209779
$991$	−26.3042	−0.835582	−0.417791	−	0.908543i	$-0.637196\pi$
$991$	−26.3042	−0.835582	−0.417791	+	0.908543i	$0.637196\pi$
$992$	−46.0621	−1.46247
$993$	8.43908	0.267806
$994$	21.0323	0.667103
$995$	−20.5618	−0.651852
$996$	−41.6983	−1.32126
$997$	18.8115	0.595767	0.297883	−	0.954602i	$-0.403719\pi$
$997$	18.8115	0.595767	0.297883	+	0.954602i	$0.403719\pi$
$998$	20.3617	0.644537
$999$	−1.81184	−0.0573241

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.53	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.53	✓	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)

\(f(q)\)	\(=\)	\(q+2.10563 q^{2} -1.00000 q^{3} +2.43368 q^{4} +0.950902 q^{5} -2.10563 q^{6} -0.758079 q^{7} +0.913167 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.10563 q^{2} -1.00000 q^{3} +2.43368 q^{4} +0.950902 q^{5} -2.10563 q^{6} -0.758079 q^{7} +0.913167 q^{8} +1.00000 q^{9} +2.00225 q^{10} +3.29657 q^{11} -2.43368 q^{12} +1.58535 q^{13} -1.59623 q^{14} -0.950902 q^{15} -2.94456 q^{16} +1.00000 q^{17} +2.10563 q^{18} +6.02906 q^{19} +2.31419 q^{20} +0.758079 q^{21} +6.94136 q^{22} +0.826198 q^{23} -0.913167 q^{24} -4.09579 q^{25} +3.33816 q^{26} -1.00000 q^{27} -1.84492 q^{28} +4.45560 q^{29} -2.00225 q^{30} +5.73876 q^{31} -8.02650 q^{32} -3.29657 q^{33} +2.10563 q^{34} -0.720858 q^{35} +2.43368 q^{36} +1.81184 q^{37} +12.6950 q^{38} -1.58535 q^{39} +0.868332 q^{40} -2.07448 q^{41} +1.59623 q^{42} -12.7658 q^{43} +8.02280 q^{44} +0.950902 q^{45} +1.73967 q^{46} +11.1930 q^{47} +2.94456 q^{48} -6.42532 q^{49} -8.62421 q^{50} -1.00000 q^{51} +3.85824 q^{52} +10.4904 q^{53} -2.10563 q^{54} +3.13471 q^{55} -0.692253 q^{56} -6.02906 q^{57} +9.38185 q^{58} -3.01470 q^{59} -2.31419 q^{60} +10.1798 q^{61} +12.0837 q^{62} -0.758079 q^{63} -11.0117 q^{64} +1.50751 q^{65} -6.94136 q^{66} -16.1861 q^{67} +2.43368 q^{68} -0.826198 q^{69} -1.51786 q^{70} -13.1762 q^{71} +0.913167 q^{72} -7.58330 q^{73} +3.81507 q^{74} +4.09579 q^{75} +14.6728 q^{76} -2.49906 q^{77} -3.33816 q^{78} -0.909801 q^{79} -2.79999 q^{80} +1.00000 q^{81} -4.36809 q^{82} +17.1339 q^{83} +1.84492 q^{84} +0.950902 q^{85} -26.8800 q^{86} -4.45560 q^{87} +3.01032 q^{88} +5.22243 q^{89} +2.00225 q^{90} -1.20182 q^{91} +2.01070 q^{92} -5.73876 q^{93} +23.5682 q^{94} +5.73304 q^{95} +8.02650 q^{96} +15.5144 q^{97} -13.5293 q^{98} +3.29657 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 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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