LMFDB - Embedded newform 8007.2.a.i.1.9

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:	$63$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-2.12676 q^{2} +1.00000 q^{3} +2.52310 q^{4} -0.0337885 q^{5} -2.12676 q^{6} +4.05166 q^{7} -1.11251 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.12676 q^{2} +1.00000 q^{3} +2.52310 q^{4} -0.0337885 q^{5} -2.12676 q^{6} +4.05166 q^{7} -1.11251 q^{8} +1.00000 q^{9} +0.0718600 q^{10} +1.94603 q^{11} +2.52310 q^{12} +0.842858 q^{13} -8.61690 q^{14} -0.0337885 q^{15} -2.68017 q^{16} +1.00000 q^{17} -2.12676 q^{18} -4.07144 q^{19} -0.0852518 q^{20} +4.05166 q^{21} -4.13873 q^{22} +1.71590 q^{23} -1.11251 q^{24} -4.99886 q^{25} -1.79256 q^{26} +1.00000 q^{27} +10.2227 q^{28} -0.704078 q^{29} +0.0718600 q^{30} +4.84318 q^{31} +7.92508 q^{32} +1.94603 q^{33} -2.12676 q^{34} -0.136899 q^{35} +2.52310 q^{36} -2.12078 q^{37} +8.65898 q^{38} +0.842858 q^{39} +0.0375899 q^{40} +4.65332 q^{41} -8.61690 q^{42} -7.09870 q^{43} +4.91002 q^{44} -0.0337885 q^{45} -3.64930 q^{46} -13.1243 q^{47} -2.68017 q^{48} +9.41593 q^{49} +10.6314 q^{50} +1.00000 q^{51} +2.12662 q^{52} +7.98981 q^{53} -2.12676 q^{54} -0.0657533 q^{55} -4.50750 q^{56} -4.07144 q^{57} +1.49740 q^{58} +6.03247 q^{59} -0.0852518 q^{60} -14.4559 q^{61} -10.3003 q^{62} +4.05166 q^{63} -11.4944 q^{64} -0.0284789 q^{65} -4.13873 q^{66} +8.01358 q^{67} +2.52310 q^{68} +1.71590 q^{69} +0.291152 q^{70} +7.58612 q^{71} -1.11251 q^{72} +6.28488 q^{73} +4.51038 q^{74} -4.99886 q^{75} -10.2727 q^{76} +7.88463 q^{77} -1.79256 q^{78} -15.7332 q^{79} +0.0905588 q^{80} +1.00000 q^{81} -9.89648 q^{82} -10.1331 q^{83} +10.2227 q^{84} -0.0337885 q^{85} +15.0972 q^{86} -0.704078 q^{87} -2.16497 q^{88} +14.3287 q^{89} +0.0718600 q^{90} +3.41497 q^{91} +4.32938 q^{92} +4.84318 q^{93} +27.9121 q^{94} +0.137568 q^{95} +7.92508 q^{96} +12.9447 q^{97} -20.0254 q^{98} +1.94603 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) $ 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * 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 $

$2$	−2.12676	−1.50385	−0.751923	−	0.659251i	$-0.770873\pi$
$2$	−2.12676	−1.50385	−0.751923	+	0.659251i	$0.770873\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.52310	1.26155
$5$	−0.0337885	−0.0151107	−0.00755534	−	0.999971i	$-0.502405\pi$
$5$	−0.0337885	−0.0151107	−0.00755534	+	0.999971i	$0.502405\pi$
$6$	−2.12676	−0.868245
$7$	4.05166	1.53138	0.765691	−	0.643208i	$-0.222397\pi$
$7$	4.05166	1.53138	0.765691	+	0.643208i	$0.222397\pi$
$8$	−1.11251	−0.393331
$9$	1.00000	0.333333
$10$	0.0718600	0.0227241
$11$	1.94603	0.586749	0.293375	−	0.955998i	$-0.405222\pi$
$11$	1.94603	0.586749	0.293375	+	0.955998i	$0.405222\pi$
$12$	2.52310	0.728356
$13$	0.842858	0.233767	0.116883	−	0.993146i	$-0.462710\pi$
$13$	0.842858	0.233767	0.116883	+	0.993146i	$0.462710\pi$
$14$	−8.61690	−2.30296
$15$	−0.0337885	−0.00872416
$16$	−2.68017	−0.670042
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.12676	−0.501282
$19$	−4.07144	−0.934053	−0.467027	−	0.884243i	$-0.654675\pi$
$19$	−4.07144	−0.934053	−0.467027	+	0.884243i	$0.654675\pi$
$20$	−0.0852518	−0.0190629
$21$	4.05166	0.884144
$22$	−4.13873	−0.882380
$23$	1.71590	0.357789	0.178894	−	0.983868i	$-0.442748\pi$
$23$	1.71590	0.357789	0.178894	+	0.983868i	$0.442748\pi$
$24$	−1.11251	−0.227090
$25$	−4.99886	−0.999772
$26$	−1.79256	−0.351549
$27$	1.00000	0.192450
$28$	10.2227	1.93192
$29$	−0.704078	−0.130744	−0.0653720	−	0.997861i	$-0.520823\pi$
$29$	−0.704078	−0.130744	−0.0653720	+	0.997861i	$0.520823\pi$
$30$	0.0718600	0.0131198
$31$	4.84318	0.869861	0.434930	−	0.900464i	$-0.356773\pi$
$31$	4.84318	0.869861	0.434930	+	0.900464i	$0.356773\pi$
$32$	7.92508	1.40097
$33$	1.94603	0.338760
$34$	−2.12676	−0.364736
$35$	−0.136899	−0.0231402
$36$	2.52310	0.420517
$37$	−2.12078	−0.348653	−0.174327	−	0.984688i	$-0.555775\pi$
$37$	−2.12078	−0.348653	−0.174327	+	0.984688i	$0.555775\pi$
$38$	8.65898	1.40467
$39$	0.842858	0.134965
$40$	0.0375899	0.00594349
$41$	4.65332	0.726726	0.363363	−	0.931648i	$-0.381628\pi$
$41$	4.65332	0.726726	0.363363	+	0.931648i	$0.381628\pi$
$42$	−8.61690	−1.32962
$43$	−7.09870	−1.08254	−0.541271	−	0.840849i	$-0.682057\pi$
$43$	−7.09870	−1.08254	−0.541271	+	0.840849i	$0.682057\pi$
$44$	4.91002	0.740213
$45$	−0.0337885	−0.00503689
$46$	−3.64930	−0.538059
$47$	−13.1243	−1.91437	−0.957185	−	0.289479i	$-0.906518\pi$
$47$	−13.1243	−1.91437	−0.957185	+	0.289479i	$0.906518\pi$
$48$	−2.68017	−0.386849
$49$	9.41593	1.34513
$50$	10.6314	1.50350
$51$	1.00000	0.140028
$52$	2.12662	0.294909
$53$	7.98981	1.09749	0.548743	−	0.835991i	$-0.315107\pi$
$53$	7.98981	1.09749	0.548743	+	0.835991i	$0.315107\pi$
$54$	−2.12676	−0.289415
$55$	−0.0657533	−0.00886618
$56$	−4.50750	−0.602340
$57$	−4.07144	−0.539276
$58$	1.49740	0.196619
$59$	6.03247	0.785361	0.392680	−	0.919675i	$-0.371548\pi$
$59$	6.03247	0.785361	0.392680	+	0.919675i	$0.371548\pi$
$60$	−0.0852518	−0.0110060
$61$	−14.4559	−1.85089	−0.925443	−	0.378888i	$-0.876307\pi$
$61$	−14.4559	−1.85089	−0.925443	+	0.378888i	$0.876307\pi$
$62$	−10.3003	−1.30814
$63$	4.05166	0.510461
$64$	−11.4944	−1.43680
$65$	−0.0284789	−0.00353238
$66$	−4.13873	−0.509442
$67$	8.01358	0.979014	0.489507	−	0.871999i	$-0.337177\pi$
$67$	8.01358	0.979014	0.489507	+	0.871999i	$0.337177\pi$
$68$	2.52310	0.305971
$69$	1.71590	0.206570
$70$	0.291152	0.0347993
$71$	7.58612	0.900307	0.450154	−	0.892951i	$-0.351369\pi$
$71$	7.58612	0.900307	0.450154	+	0.892951i	$0.351369\pi$
$72$	−1.11251	−0.131110
$73$	6.28488	0.735590	0.367795	−	0.929907i	$-0.380113\pi$
$73$	6.28488	0.735590	0.367795	+	0.929907i	$0.380113\pi$
$74$	4.51038	0.524321
$75$	−4.99886	−0.577218
$76$	−10.2727	−1.17835
$77$	7.88463	0.898537
$78$	−1.79256	−0.202967
$79$	−15.7332	−1.77012	−0.885062	−	0.465472i	$-0.845884\pi$
$79$	−15.7332	−1.77012	−0.885062	+	0.465472i	$0.845884\pi$
$80$	0.0905588	0.0101248
$81$	1.00000	0.111111
$82$	−9.89648	−1.09288
$83$	−10.1331	−1.11225	−0.556126	−	0.831098i	$-0.687713\pi$
$83$	−10.1331	−1.11225	−0.556126	+	0.831098i	$0.687713\pi$
$84$	10.2227	1.11539
$85$	−0.0337885	−0.00366488
$86$	15.0972	1.62797
$87$	−0.704078	−0.0754850
$88$	−2.16497	−0.230786
$89$	14.3287	1.51884	0.759418	−	0.650603i	$-0.225484\pi$
$89$	14.3287	1.51884	0.759418	+	0.650603i	$0.225484\pi$
$90$	0.0718600	0.00757471
$91$	3.41497	0.357987
$92$	4.32938	0.451369
$93$	4.84318	0.502214
$94$	27.9121	2.87891
$95$	0.137568	0.0141142
$96$	7.92508	0.808850
$97$	12.9447	1.31434	0.657168	−	0.753744i	$-0.271754\pi$
$97$	12.9447	1.31434	0.657168	+	0.753744i	$0.271754\pi$
$98$	−20.0254	−2.02287
$99$	1.94603	0.195583
$100$	−12.6126	−1.26126
$101$	15.7911	1.57127	0.785637	−	0.618688i	$-0.212335\pi$
$101$	15.7911	1.57127	0.785637	+	0.618688i	$0.212335\pi$
$102$	−2.12676	−0.210580
$103$	13.7794	1.35773	0.678865	−	0.734263i	$-0.262472\pi$
$103$	13.7794	1.35773	0.678865	+	0.734263i	$0.262472\pi$
$104$	−0.937686	−0.0919476
$105$	−0.136899	−0.0133600
$106$	−16.9924	−1.65045
$107$	6.07586	0.587375	0.293688	−	0.955901i	$-0.405117\pi$
$107$	6.07586	0.587375	0.293688	+	0.955901i	$0.405117\pi$
$108$	2.52310	0.242785
$109$	17.0482	1.63293	0.816463	−	0.577398i	$-0.195932\pi$
$109$	17.0482	1.63293	0.816463	+	0.577398i	$0.195932\pi$
$110$	0.139841	0.0133334
$111$	−2.12078	−0.201295
$112$	−10.8591	−1.02609
$113$	1.33930	0.125990	0.0629951	−	0.998014i	$-0.479935\pi$
$113$	1.33930	0.125990	0.0629951	+	0.998014i	$0.479935\pi$
$114$	8.65898	0.810987
$115$	−0.0579776	−0.00540644
$116$	−1.77646	−0.164940
$117$	0.842858	0.0779223
$118$	−12.8296	−1.18106
$119$	4.05166	0.371415
$120$	0.0375899	0.00343148
$121$	−7.21298	−0.655726
$122$	30.7442	2.78344
$123$	4.65332	0.419576
$124$	12.2198	1.09737
$125$	0.337847	0.0302179
$126$	−8.61690	−0.767654
$127$	18.8315	1.67103	0.835514	−	0.549469i	$-0.185170\pi$
$127$	18.8315	1.67103	0.835514	+	0.549469i	$0.185170\pi$
$128$	8.59564	0.759754
$129$	−7.09870	−0.625005
$130$	0.0605678	0.00531215
$131$	2.65291	0.231786	0.115893	−	0.993262i	$-0.463027\pi$
$131$	2.65291	0.231786	0.115893	+	0.993262i	$0.463027\pi$
$132$	4.91002	0.427362
$133$	−16.4961	−1.43039
$134$	−17.0429	−1.47229
$135$	−0.0337885	−0.00290805
$136$	−1.11251	−0.0953967
$137$	21.3866	1.82718	0.913589	−	0.406640i	$-0.133300\pi$
$137$	21.3866	1.82718	0.913589	+	0.406640i	$0.133300\pi$
$138$	−3.64930	−0.310649
$139$	−2.85937	−0.242528	−0.121264	−	0.992620i	$-0.538695\pi$
$139$	−2.85937	−0.242528	−0.121264	+	0.992620i	$0.538695\pi$
$140$	−0.345411	−0.0291926
$141$	−13.1243	−1.10526
$142$	−16.1339	−1.35392
$143$	1.64022	0.137162
$144$	−2.68017	−0.223347
$145$	0.0237897	0.00197563
$146$	−13.3664	−1.10621
$147$	9.41593	0.776613
$148$	−5.35093	−0.439844
$149$	12.1031	0.991524	0.495762	−	0.868458i	$-0.334889\pi$
$149$	12.1031	0.991524	0.495762	+	0.868458i	$0.334889\pi$
$150$	10.6314	0.868047
$151$	6.04712	0.492108	0.246054	−	0.969256i	$-0.420866\pi$
$151$	6.04712	0.492108	0.246054	+	0.969256i	$0.420866\pi$
$152$	4.52951	0.367392
$153$	1.00000	0.0808452
$154$	−16.7687	−1.35126
$155$	−0.163644	−0.0131442
$156$	2.12662	0.170266
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	33.4607	2.66199
$159$	7.98981	0.633633
$160$	−0.267777	−0.0211696
$161$	6.95222	0.547912
$162$	−2.12676	−0.167094
$163$	−10.8532	−0.850092	−0.425046	−	0.905172i	$-0.639742\pi$
$163$	−10.8532	−0.850092	−0.425046	+	0.905172i	$0.639742\pi$
$164$	11.7408	0.916801
$165$	−0.0657533	−0.00511889
$166$	21.5506	1.67265
$167$	20.6878	1.60087	0.800436	−	0.599418i	$-0.204601\pi$
$167$	20.6878	1.60087	0.800436	+	0.599418i	$0.204601\pi$
$168$	−4.50750	−0.347761
$169$	−12.2896	−0.945353
$170$	0.0718600	0.00551141
$171$	−4.07144	−0.311351
$172$	−17.9107	−1.36568
$173$	4.18027	0.317820	0.158910	−	0.987293i	$-0.449202\pi$
$173$	4.18027	0.317820	0.158910	+	0.987293i	$0.449202\pi$
$174$	1.49740	0.113518
$175$	−20.2537	−1.53103
$176$	−5.21568	−0.393146
$177$	6.03247	0.453428
$178$	−30.4736	−2.28409
$179$	3.03705	0.227000	0.113500	−	0.993538i	$-0.463794\pi$
$179$	3.03705	0.227000	0.113500	+	0.993538i	$0.463794\pi$
$180$	−0.0852518	−0.00635429
$181$	−0.370034	−0.0275044	−0.0137522	−	0.999905i	$-0.504378\pi$
$181$	−0.370034	−0.0275044	−0.0137522	+	0.999905i	$0.504378\pi$
$182$	−7.26282	−0.538356
$183$	−14.4559	−1.06861
$184$	−1.90895	−0.140729
$185$	0.0716579	0.00526839
$186$	−10.3003	−0.755252
$187$	1.94603	0.142308
$188$	−33.1138	−2.41507
$189$	4.05166	0.294715
$190$	−0.292574	−0.0212255
$191$	14.8900	1.07740	0.538701	−	0.842497i	$-0.318915\pi$
$191$	14.8900	1.07740	0.538701	+	0.842497i	$0.318915\pi$
$192$	−11.4944	−0.829536
$193$	−10.4219	−0.750185	−0.375093	−	0.926987i	$-0.622389\pi$
$193$	−10.4219	−0.750185	−0.375093	+	0.926987i	$0.622389\pi$
$194$	−27.5303	−1.97656
$195$	−0.0284789	−0.00203942
$196$	23.7573	1.69695
$197$	−13.2484	−0.943911	−0.471956	−	0.881622i	$-0.656452\pi$
$197$	−13.2484	−0.943911	−0.471956	+	0.881622i	$0.656452\pi$
$198$	−4.13873	−0.294127
$199$	2.21865	0.157276	0.0786380	−	0.996903i	$-0.474943\pi$
$199$	2.21865	0.157276	0.0786380	+	0.996903i	$0.474943\pi$
$200$	5.56126	0.393241
$201$	8.01358	0.565234
$202$	−33.5839	−2.36295
$203$	−2.85268	−0.200219
$204$	2.52310	0.176652
$205$	−0.157229	−0.0109813
$206$	−29.3056	−2.04181
$207$	1.71590	0.119263
$208$	−2.25900	−0.156634
$209$	−7.92314	−0.548055
$210$	0.291152	0.0200914
$211$	0.354591	0.0244111	0.0122055	−	0.999926i	$-0.496115\pi$
$211$	0.354591	0.0244111	0.0122055	+	0.999926i	$0.496115\pi$
$212$	20.1591	1.38453
$213$	7.58612	0.519793
$214$	−12.9219	−0.883321
$215$	0.239854	0.0163579
$216$	−1.11251	−0.0756965
$217$	19.6229	1.33209
$218$	−36.2575	−2.45567
$219$	6.28488	0.424693
$220$	−0.165902	−0.0111851
$221$	0.842858	0.0566968
$222$	4.51038	0.302717
$223$	5.86293	0.392611	0.196305	−	0.980543i	$-0.437106\pi$
$223$	5.86293	0.392611	0.196305	+	0.980543i	$0.437106\pi$
$224$	32.1097	2.14542
$225$	−4.99886	−0.333257
$226$	−2.84836	−0.189470
$227$	2.02617	0.134482	0.0672409	−	0.997737i	$-0.478580\pi$
$227$	2.02617	0.134482	0.0672409	+	0.997737i	$0.478580\pi$
$228$	−10.2727	−0.680324
$229$	17.4044	1.15011	0.575057	−	0.818113i	$-0.304980\pi$
$229$	17.4044	1.15011	0.575057	+	0.818113i	$0.304980\pi$
$230$	0.123304	0.00813044
$231$	7.88463	0.518771
$232$	0.783291	0.0514256
$233$	9.90283	0.648756	0.324378	−	0.945928i	$-0.394845\pi$
$233$	9.90283	0.648756	0.324378	+	0.945928i	$0.394845\pi$
$234$	−1.79256	−0.117183
$235$	0.443449	0.0289274
$236$	15.2205	0.990772
$237$	−15.7332	−1.02198
$238$	−8.61690	−0.558550
$239$	−2.12986	−0.137769	−0.0688845	−	0.997625i	$-0.521944\pi$
$239$	−2.12986	−0.137769	−0.0688845	+	0.997625i	$0.521944\pi$
$240$	0.0905588	0.00584555
$241$	14.2144	0.915629	0.457814	−	0.889048i	$-0.348632\pi$
$241$	14.2144	0.915629	0.457814	+	0.889048i	$0.348632\pi$
$242$	15.3403	0.986110
$243$	1.00000	0.0641500
$244$	−36.4736	−2.33498
$245$	−0.318150	−0.0203259
$246$	−9.89648	−0.630977
$247$	−3.43165	−0.218351
$248$	−5.38807	−0.342143
$249$	−10.1331	−0.642159
$250$	−0.718518	−0.0454431
$251$	−18.1950	−1.14846	−0.574229	−	0.818694i	$-0.694698\pi$
$251$	−18.1950	−1.14846	−0.574229	+	0.818694i	$0.694698\pi$
$252$	10.2227	0.643972
$253$	3.33918	0.209932
$254$	−40.0501	−2.51297
$255$	−0.0337885	−0.00211592
$256$	4.70795	0.294247
$257$	−11.0920	−0.691900	−0.345950	−	0.938253i	$-0.612443\pi$
$257$	−11.0920	−0.691900	−0.345950	+	0.938253i	$0.612443\pi$
$258$	15.0972	0.939911
$259$	−8.59266	−0.533922
$260$	−0.0718552	−0.00445627
$261$	−0.704078	−0.0435813
$262$	−5.64211	−0.348570
$263$	−18.1573	−1.11963	−0.559813	−	0.828619i	$-0.689127\pi$
$263$	−18.1573	−1.11963	−0.559813	+	0.828619i	$0.689127\pi$
$264$	−2.16497	−0.133245
$265$	−0.269964	−0.0165838
$266$	35.0832	2.15109
$267$	14.3287	0.876900
$268$	20.2191	1.23508
$269$	−1.33776	−0.0815649	−0.0407825	−	0.999168i	$-0.512985\pi$
$269$	−1.33776	−0.0815649	−0.0407825	+	0.999168i	$0.512985\pi$
$270$	0.0718600	0.00437326
$271$	−2.30689	−0.140133	−0.0700667	−	0.997542i	$-0.522321\pi$
$271$	−2.30689	−0.140133	−0.0700667	+	0.997542i	$0.522321\pi$
$272$	−2.68017	−0.162509
$273$	3.41497	0.206684
$274$	−45.4840	−2.74779
$275$	−9.72791	−0.586615
$276$	4.32938	0.260598
$277$	−21.0537	−1.26499	−0.632497	−	0.774563i	$-0.717970\pi$
$277$	−21.0537	−1.26499	−0.632497	+	0.774563i	$0.717970\pi$
$278$	6.08119	0.364725
$279$	4.84318	0.289954
$280$	0.152302	0.00910176
$281$	18.6356	1.11171	0.555854	−	0.831280i	$-0.312391\pi$
$281$	18.6356	1.11171	0.555854	+	0.831280i	$0.312391\pi$
$282$	27.9121	1.66214
$283$	16.8674	1.00266	0.501331	−	0.865256i	$-0.332844\pi$
$283$	16.8674	1.00266	0.501331	+	0.865256i	$0.332844\pi$
$284$	19.1406	1.13578
$285$	0.137568	0.00814883
$286$	−3.48836	−0.206271
$287$	18.8537	1.11290
$288$	7.92508	0.466990
$289$	1.00000	0.0588235
$290$	−0.0505950	−0.00297104
$291$	12.9447	0.758832
$292$	15.8574	0.927984
$293$	2.28648	0.133578	0.0667888	−	0.997767i	$-0.478725\pi$
$293$	2.28648	0.133578	0.0667888	+	0.997767i	$0.478725\pi$
$294$	−20.0254	−1.16791
$295$	−0.203828	−0.0118673
$296$	2.35938	0.137136
$297$	1.94603	0.112920
$298$	−25.7404	−1.49110
$299$	1.44626	0.0836392
$300$	−12.6126	−0.728190
$301$	−28.7615	−1.65778
$302$	−12.8608	−0.740054
$303$	15.7911	0.907176
$304$	10.9121	0.625855
$305$	0.488443	0.0279681
$306$	−2.12676	−0.121579
$307$	−23.6819	−1.35160	−0.675799	−	0.737086i	$-0.736201\pi$
$307$	−23.6819	−1.35160	−0.675799	+	0.737086i	$0.736201\pi$
$308$	19.8937	1.13355
$309$	13.7794	0.783885
$310$	0.348031	0.0197668
$311$	−8.04185	−0.456012	−0.228006	−	0.973660i	$-0.573221\pi$
$311$	−8.04185	−0.456012	−0.228006	+	0.973660i	$0.573221\pi$
$312$	−0.937686	−0.0530860
$313$	−15.5760	−0.880408	−0.440204	−	0.897898i	$-0.645094\pi$
$313$	−15.5760	−0.880408	−0.440204	+	0.897898i	$0.645094\pi$
$314$	−2.12676	−0.120020
$315$	−0.136899	−0.00771341
$316$	−39.6965	−2.23310
$317$	−13.5629	−0.761768	−0.380884	−	0.924623i	$-0.624380\pi$
$317$	−13.5629	−0.761768	−0.380884	+	0.924623i	$0.624380\pi$
$318$	−16.9924	−0.952887
$319$	−1.37015	−0.0767139
$320$	0.388378	0.0217110
$321$	6.07586	0.339121
$322$	−14.7857	−0.823975
$323$	−4.07144	−0.226541
$324$	2.52310	0.140172
$325$	−4.21333	−0.233713
$326$	23.0822	1.27841
$327$	17.0482	0.942770
$328$	−5.17685	−0.285844
$329$	−53.1750	−2.93163
$330$	0.139841	0.00769802
$331$	12.8217	0.704744	0.352372	−	0.935860i	$-0.385375\pi$
$331$	12.8217	0.704744	0.352372	+	0.935860i	$0.385375\pi$
$332$	−25.5668	−1.40316
$333$	−2.12078	−0.116218
$334$	−43.9980	−2.40746
$335$	−0.270767	−0.0147936
$336$	−10.8591	−0.592414
$337$	−1.85285	−0.100931	−0.0504657	−	0.998726i	$-0.516071\pi$
$337$	−1.85285	−0.100931	−0.0504657	+	0.998726i	$0.516071\pi$
$338$	26.1370	1.42166
$339$	1.33930	0.0727405
$340$	−0.0852518	−0.00462343
$341$	9.42495	0.510390
$342$	8.65898	0.468224
$343$	9.78852	0.528531
$344$	7.89735	0.425796
$345$	−0.0579776	−0.00312141
$346$	−8.89042	−0.477952
$347$	15.9793	0.857812	0.428906	−	0.903349i	$-0.358899\pi$
$347$	15.9793	0.857812	0.428906	+	0.903349i	$0.358899\pi$
$348$	−1.77646	−0.0952281
$349$	1.61860	0.0866418	0.0433209	−	0.999061i	$-0.486206\pi$
$349$	1.61860	0.0866418	0.0433209	+	0.999061i	$0.486206\pi$
$350$	43.0746	2.30244
$351$	0.842858	0.0449885
$352$	15.4224	0.822018
$353$	24.5075	1.30440	0.652200	−	0.758047i	$-0.273846\pi$
$353$	24.5075	1.30440	0.652200	+	0.758047i	$0.273846\pi$
$354$	−12.8296	−0.681886
$355$	−0.256324	−0.0136043
$356$	36.1526	1.91609
$357$	4.05166	0.214436
$358$	−6.45907	−0.341373
$359$	−8.28001	−0.437002	−0.218501	−	0.975837i	$-0.570117\pi$
$359$	−8.28001	−0.437002	−0.218501	+	0.975837i	$0.570117\pi$
$360$	0.0375899	0.00198116
$361$	−2.42334	−0.127544
$362$	0.786973	0.0413624
$363$	−7.21298	−0.378583
$364$	8.61632	0.451618
$365$	−0.212357	−0.0111153
$366$	30.7442	1.60702
$367$	33.0285	1.72408	0.862038	−	0.506844i	$-0.169188\pi$
$367$	33.0285	1.72408	0.862038	+	0.506844i	$0.169188\pi$
$368$	−4.59889	−0.239734
$369$	4.65332	0.242242
$370$	−0.152399	−0.00792284
$371$	32.3720	1.68067
$372$	12.2198	0.633568
$373$	−29.7343	−1.53958	−0.769792	−	0.638295i	$-0.779640\pi$
$373$	−29.7343	−1.53958	−0.769792	+	0.638295i	$0.779640\pi$
$374$	−4.13873	−0.214009
$375$	0.337847	0.0174463
$376$	14.6008	0.752980
$377$	−0.593438	−0.0305636
$378$	−8.61690	−0.443205
$379$	26.3256	1.35225	0.676127	−	0.736785i	$-0.263657\pi$
$379$	26.3256	1.35225	0.676127	+	0.736785i	$0.263657\pi$
$380$	0.347098	0.0178057
$381$	18.8315	0.964768
$382$	−31.6674	−1.62025
$383$	−35.8628	−1.83250	−0.916250	−	0.400606i	$-0.868800\pi$
$383$	−35.8628	−1.83250	−0.916250	+	0.400606i	$0.868800\pi$
$384$	8.59564	0.438644
$385$	−0.266410	−0.0135775
$386$	22.1649	1.12816
$387$	−7.09870	−0.360847
$388$	32.6608	1.65810
$389$	−23.6100	−1.19707	−0.598537	−	0.801095i	$-0.704251\pi$
$389$	−23.6100	−1.19707	−0.598537	+	0.801095i	$0.704251\pi$
$390$	0.0605678	0.00306697
$391$	1.71590	0.0867766
$392$	−10.4753	−0.529082
$393$	2.65291	0.133822
$394$	28.1762	1.41950
$395$	0.531602	0.0267478
$396$	4.91002	0.246738
$397$	−9.58319	−0.480966	−0.240483	−	0.970653i	$-0.577306\pi$
$397$	−9.58319	−0.480966	−0.240483	+	0.970653i	$0.577306\pi$
$398$	−4.71854	−0.236519
$399$	−16.4961	−0.825838
$400$	13.3978	0.669889
$401$	16.5334	0.825638	0.412819	−	0.910813i	$-0.364544\pi$
$401$	16.5334	0.825638	0.412819	+	0.910813i	$0.364544\pi$
$402$	−17.0429	−0.850024
$403$	4.08211	0.203345
$404$	39.8425	1.98224
$405$	−0.0337885	−0.00167896
$406$	6.06696	0.301098
$407$	−4.12709	−0.204572
$408$	−1.11251	−0.0550773
$409$	13.3534	0.660282	0.330141	−	0.943932i	$-0.392904\pi$
$409$	13.3534	0.660282	0.330141	+	0.943932i	$0.392904\pi$
$410$	0.334387	0.0165142
$411$	21.3866	1.05492
$412$	34.7669	1.71284
$413$	24.4415	1.20269
$414$	−3.64930	−0.179353
$415$	0.342382	0.0168069
$416$	6.67972	0.327500
$417$	−2.85937	−0.140024
$418$	16.8506	0.824190
$419$	17.9253	0.875707	0.437853	−	0.899046i	$-0.355739\pi$
$419$	17.9253	0.875707	0.437853	+	0.899046i	$0.355739\pi$
$420$	−0.345411	−0.0168543
$421$	19.9325	0.971452	0.485726	−	0.874111i	$-0.338555\pi$
$421$	19.9325	0.971452	0.485726	+	0.874111i	$0.338555\pi$
$422$	−0.754130	−0.0367105
$423$	−13.1243	−0.638123
$424$	−8.88872	−0.431675
$425$	−4.99886	−0.242480
$426$	−16.1339	−0.781688
$427$	−58.5703	−2.83441
$428$	15.3300	0.741003
$429$	1.64022	0.0791908
$430$	−0.510112	−0.0245998
$431$	−2.67224	−0.128717	−0.0643586	−	0.997927i	$-0.520500\pi$
$431$	−2.67224	−0.128717	−0.0643586	+	0.997927i	$0.520500\pi$
$432$	−2.68017	−0.128950
$433$	−31.6496	−1.52098	−0.760491	−	0.649349i	$-0.775042\pi$
$433$	−31.6496	−1.52098	−0.760491	+	0.649349i	$0.775042\pi$
$434$	−41.7332	−2.00326
$435$	0.0237897	0.00114063
$436$	43.0144	2.06002
$437$	−6.98617	−0.334194
$438$	−13.3664	−0.638673
$439$	−4.56402	−0.217829	−0.108914	−	0.994051i	$-0.534737\pi$
$439$	−4.56402	−0.217829	−0.108914	+	0.994051i	$0.534737\pi$
$440$	0.0731510	0.00348734
$441$	9.41593	0.448378
$442$	−1.79256	−0.0852632
$443$	−19.4791	−0.925478	−0.462739	−	0.886495i	$-0.653133\pi$
$443$	−19.4791	−0.925478	−0.462739	+	0.886495i	$0.653133\pi$
$444$	−5.35093	−0.253944
$445$	−0.484144	−0.0229506
$446$	−12.4690	−0.590426
$447$	12.1031	0.572457
$448$	−46.5714	−2.20029
$449$	22.5595	1.06465	0.532324	−	0.846541i	$-0.321319\pi$
$449$	22.5595	1.06465	0.532324	+	0.846541i	$0.321319\pi$
$450$	10.6314	0.501167
$451$	9.05548	0.426406
$452$	3.37918	0.158943
$453$	6.04712	0.284118
$454$	−4.30918	−0.202240
$455$	−0.115387	−0.00540942
$456$	4.52951	0.212114
$457$	−3.79035	−0.177305	−0.0886525	−	0.996063i	$-0.528256\pi$
$457$	−3.79035	−0.177305	−0.0886525	+	0.996063i	$0.528256\pi$
$458$	−37.0149	−1.72959
$459$	1.00000	0.0466760
$460$	−0.146283	−0.00682049
$461$	25.5755	1.19117	0.595585	−	0.803293i	$-0.296920\pi$
$461$	25.5755	1.19117	0.595585	+	0.803293i	$0.296920\pi$
$462$	−16.7687	−0.780151
$463$	11.1155	0.516580	0.258290	−	0.966067i	$-0.416841\pi$
$463$	11.1155	0.516580	0.258290	+	0.966067i	$0.416841\pi$
$464$	1.88705	0.0876039
$465$	−0.163644	−0.00758880
$466$	−21.0609	−0.975628
$467$	−14.0487	−0.650096	−0.325048	−	0.945698i	$-0.605380\pi$
$467$	−14.0487	−0.650096	−0.325048	+	0.945698i	$0.605380\pi$
$468$	2.12662	0.0983029
$469$	32.4683	1.49925
$470$	−0.943109	−0.0435024
$471$	1.00000	0.0460776
$472$	−6.71116	−0.308906
$473$	−13.8143	−0.635180
$474$	33.4607	1.53690
$475$	20.3526	0.933840
$476$	10.2227	0.468558
$477$	7.98981	0.365828
$478$	4.52969	0.207183
$479$	25.1840	1.15069	0.575344	−	0.817912i	$-0.304868\pi$
$479$	25.1840	1.15069	0.575344	+	0.817912i	$0.304868\pi$
$480$	−0.267777	−0.0122223
$481$	−1.78751	−0.0815036
$482$	−30.2305	−1.37696
$483$	6.95222	0.316337
$484$	−18.1991	−0.827231
$485$	−0.437382	−0.0198605
$486$	−2.12676	−0.0964717
$487$	−15.8824	−0.719700	−0.359850	−	0.933010i	$-0.617172\pi$
$487$	−15.8824	−0.719700	−0.359850	+	0.933010i	$0.617172\pi$
$488$	16.0823	0.728010
$489$	−10.8532	−0.490801
$490$	0.676629	0.0305670
$491$	20.2380	0.913328	0.456664	−	0.889639i	$-0.349044\pi$
$491$	20.2380	0.913328	0.456664	+	0.889639i	$0.349044\pi$
$492$	11.7408	0.529316
$493$	−0.704078	−0.0317101
$494$	7.29829	0.328366
$495$	−0.0657533	−0.00295539
$496$	−12.9805	−0.582843
$497$	30.7364	1.37872
$498$	21.5506	0.965707
$499$	18.6303	0.834008	0.417004	−	0.908905i	$-0.363080\pi$
$499$	18.6303	0.834008	0.417004	+	0.908905i	$0.363080\pi$
$500$	0.852421	0.0381214
$501$	20.6878	0.924264
$502$	38.6964	1.72710
$503$	21.3105	0.950189	0.475095	−	0.879935i	$-0.342414\pi$
$503$	21.3105	0.950189	0.475095	+	0.879935i	$0.342414\pi$
$504$	−4.50750	−0.200780
$505$	−0.533558	−0.0237430
$506$	−7.10162	−0.315706
$507$	−12.2896	−0.545800
$508$	47.5138	2.10809
$509$	−14.1565	−0.627476	−0.313738	−	0.949510i	$-0.601581\pi$
$509$	−14.1565	−0.627476	−0.313738	+	0.949510i	$0.601581\pi$
$510$	0.0718600	0.00318201
$511$	25.4642	1.12647
$512$	−27.2039	−1.20226
$513$	−4.07144	−0.179759
$514$	23.5900	1.04051
$515$	−0.465587	−0.0205162
$516$	−17.9107	−0.788475
$517$	−25.5401	−1.12325
$518$	18.2745	0.802936
$519$	4.18027	0.183493
$520$	0.0316830	0.00138939
$521$	−30.4820	−1.33544	−0.667720	−	0.744413i	$-0.732730\pi$
$521$	−30.4820	−1.33544	−0.667720	+	0.744413i	$0.732730\pi$
$522$	1.49740	0.0655395
$523$	25.5696	1.11808	0.559041	−	0.829140i	$-0.311170\pi$
$523$	25.5696	1.11808	0.559041	+	0.829140i	$0.311170\pi$
$524$	6.69357	0.292410
$525$	−20.2537	−0.883942
$526$	38.6161	1.68374
$527$	4.84318	0.210972
$528$	−5.21568	−0.226983
$529$	−20.0557	−0.871987
$530$	0.574148	0.0249394
$531$	6.03247	0.261787
$532$	−41.6213	−1.80451
$533$	3.92209	0.169884
$534$	−30.4736	−1.31872
$535$	−0.205294	−0.00887564
$536$	−8.91516	−0.385076
$537$	3.03705	0.131058
$538$	2.84510	0.122661
$539$	18.3236	0.789255
$540$	−0.0852518	−0.00366865
$541$	−1.78066	−0.0765566	−0.0382783	−	0.999267i	$-0.512187\pi$
$541$	−1.78066	−0.0765566	−0.0382783	+	0.999267i	$0.512187\pi$
$542$	4.90619	0.210739
$543$	−0.370034	−0.0158797
$544$	7.92508	0.339785
$545$	−0.576035	−0.0246746
$546$	−7.26282	−0.310820
$547$	−27.1310	−1.16004	−0.580019	−	0.814603i	$-0.696955\pi$
$547$	−27.1310	−1.16004	−0.580019	+	0.814603i	$0.696955\pi$
$548$	53.9604	2.30508
$549$	−14.4559	−0.616962
$550$	20.6889	0.882178
$551$	2.86661	0.122122
$552$	−1.90895	−0.0812501
$553$	−63.7456	−2.71074
$554$	44.7761	1.90236
$555$	0.0716579	0.00304171
$556$	−7.21447	−0.305962
$557$	−1.42701	−0.0604643	−0.0302322	−	0.999543i	$-0.509625\pi$
$557$	−1.42701	−0.0604643	−0.0302322	+	0.999543i	$0.509625\pi$
$558$	−10.3003	−0.436045
$559$	−5.98320	−0.253062
$560$	0.366913	0.0155049
$561$	1.94603	0.0821613
$562$	−39.6334	−1.67184
$563$	−31.2105	−1.31537	−0.657683	−	0.753295i	$-0.728463\pi$
$563$	−31.2105	−1.31537	−0.657683	+	0.753295i	$0.728463\pi$
$564$	−33.1138	−1.39434
$565$	−0.0452528	−0.00190380
$566$	−35.8728	−1.50785
$567$	4.05166	0.170154
$568$	−8.43962	−0.354118
$569$	−27.5356	−1.15435	−0.577176	−	0.816619i	$-0.695846\pi$
$569$	−27.5356	−1.15435	−0.577176	+	0.816619i	$0.695846\pi$
$570$	−0.292574	−0.0122546
$571$	−21.7369	−0.909662	−0.454831	−	0.890578i	$-0.650300\pi$
$571$	−21.7369	−0.909662	−0.454831	+	0.890578i	$0.650300\pi$
$572$	4.13845	0.173037
$573$	14.8900	0.622038
$574$	−40.0972	−1.67362
$575$	−8.57752	−0.357707
$576$	−11.4944	−0.478933
$577$	32.1949	1.34029	0.670145	−	0.742231i	$-0.266232\pi$
$577$	32.1949	1.34029	0.670145	+	0.742231i	$0.266232\pi$
$578$	−2.12676	−0.0884615
$579$	−10.4219	−0.433120
$580$	0.0600239	0.00249236
$581$	−41.0558	−1.70328
$582$	−27.5303	−1.14117
$583$	15.5484	0.643948
$584$	−6.99198	−0.289330
$585$	−0.0284789	−0.00117746
$586$	−4.86279	−0.200880
$587$	−23.9186	−0.987225	−0.493612	−	0.869682i	$-0.664324\pi$
$587$	−23.9186	−0.987225	−0.493612	+	0.869682i	$0.664324\pi$
$588$	23.7573	0.979736
$589$	−19.7187	−0.812496
$590$	0.433493	0.0178466
$591$	−13.2484	−0.544967
$592$	5.68403	0.233612
$593$	−33.9651	−1.39478	−0.697389	−	0.716692i	$-0.745655\pi$
$593$	−33.9651	−1.39478	−0.697389	+	0.716692i	$0.745655\pi$
$594$	−4.13873	−0.169814
$595$	−0.136899	−0.00561233
$596$	30.5373	1.25086
$597$	2.21865	0.0908034
$598$	−3.07584	−0.125780
$599$	15.5589	0.635718	0.317859	−	0.948138i	$-0.397036\pi$
$599$	15.5589	0.635718	0.317859	+	0.948138i	$0.397036\pi$
$600$	5.56126	0.227038
$601$	38.3787	1.56550	0.782750	−	0.622336i	$-0.213816\pi$
$601$	38.3787	1.56550	0.782750	+	0.622336i	$0.213816\pi$
$602$	61.1687	2.49305
$603$	8.01358	0.326338
$604$	15.2575	0.620818
$605$	0.243716	0.00990846
$606$	−33.5839	−1.36425
$607$	13.1999	0.535769	0.267884	−	0.963451i	$-0.413675\pi$
$607$	13.1999	0.535769	0.267884	+	0.963451i	$0.413675\pi$
$608$	−32.2665	−1.30858
$609$	−2.85268	−0.115596
$610$	−1.03880	−0.0420598
$611$	−11.0619	−0.447516
$612$	2.52310	0.101990
$613$	−24.9920	−1.00942	−0.504709	−	0.863290i	$-0.668400\pi$
$613$	−24.9920	−1.00942	−0.504709	+	0.863290i	$0.668400\pi$
$614$	50.3657	2.03259
$615$	−0.157229	−0.00634007
$616$	−8.77171	−0.353422
$617$	24.2512	0.976318	0.488159	−	0.872755i	$-0.337669\pi$
$617$	24.2512	0.976318	0.488159	+	0.872755i	$0.337669\pi$
$618$	−29.3056	−1.17884
$619$	−20.2448	−0.813707	−0.406854	−	0.913493i	$-0.633374\pi$
$619$	−20.2448	−0.813707	−0.406854	+	0.913493i	$0.633374\pi$
$620$	−0.412890	−0.0165820
$621$	1.71590	0.0688565
$622$	17.1031	0.685771
$623$	58.0548	2.32592
$624$	−2.25900	−0.0904324
$625$	24.9829	0.999315
$626$	33.1264	1.32400
$627$	−7.92314	−0.316420
$628$	2.52310	0.100683
$629$	−2.12078	−0.0845609
$630$	0.291152	0.0115998
$631$	−23.2661	−0.926207	−0.463104	−	0.886304i	$-0.653264\pi$
$631$	−23.2661	−0.926207	−0.463104	+	0.886304i	$0.653264\pi$
$632$	17.5033	0.696244
$633$	0.354591	0.0140937
$634$	28.8450	1.14558
$635$	−0.636289	−0.0252504
$636$	20.1591	0.799360
$637$	7.93630	0.314447
$638$	2.91398	0.115366
$639$	7.58612	0.300102
$640$	−0.290434	−0.0114804
$641$	−1.97200	−0.0778893	−0.0389447	−	0.999241i	$-0.512400\pi$
$641$	−1.97200	−0.0778893	−0.0389447	+	0.999241i	$0.512400\pi$
$642$	−12.9219	−0.509986
$643$	−19.9177	−0.785477	−0.392739	−	0.919650i	$-0.628472\pi$
$643$	−19.9177	−0.785477	−0.392739	+	0.919650i	$0.628472\pi$
$644$	17.5412	0.691218
$645$	0.239854	0.00944426
$646$	8.65898	0.340683
$647$	−13.3801	−0.526025	−0.263013	−	0.964792i	$-0.584716\pi$
$647$	−13.3801	−0.526025	−0.263013	+	0.964792i	$0.584716\pi$
$648$	−1.11251	−0.0437034
$649$	11.7393	0.460810
$650$	8.96073	0.351469
$651$	19.6229	0.769082
$652$	−27.3838	−1.07243
$653$	28.8149	1.12761	0.563807	−	0.825906i	$-0.309336\pi$
$653$	28.8149	1.12761	0.563807	+	0.825906i	$0.309336\pi$
$654$	−36.2575	−1.41778
$655$	−0.0896380	−0.00350245
$656$	−12.4717	−0.486937
$657$	6.28488	0.245197
$658$	113.090	4.40872
$659$	−10.1076	−0.393737	−0.196869	−	0.980430i	$-0.563077\pi$
$659$	−10.1076	−0.393737	−0.196869	+	0.980430i	$0.563077\pi$
$660$	−0.165902	−0.00645774
$661$	−50.1893	−1.95214	−0.976068	−	0.217466i	$-0.930221\pi$
$661$	−50.1893	−1.95214	−0.976068	+	0.217466i	$0.930221\pi$
$662$	−27.2686	−1.05983
$663$	0.842858	0.0327339
$664$	11.2731	0.437482
$665$	0.557379	0.0216142
$666$	4.51038	0.174774
$667$	−1.20812	−0.0467787
$668$	52.1975	2.01958
$669$	5.86293	0.226674
$670$	0.575855	0.0222472
$671$	−28.1315	−1.08601
$672$	32.1097	1.23866
$673$	−50.3815	−1.94207	−0.971033	−	0.238946i	$-0.923198\pi$
$673$	−50.3815	−1.94207	−0.971033	+	0.238946i	$0.923198\pi$
$674$	3.94057	0.151785
$675$	−4.99886	−0.192406
$676$	−31.0079	−1.19261
$677$	−0.407429	−0.0156588	−0.00782938	−	0.999969i	$-0.502492\pi$
$677$	−0.407429	−0.0156588	−0.00782938	+	0.999969i	$0.502492\pi$
$678$	−2.84836	−0.109390
$679$	52.4475	2.01275
$680$	0.0375899	0.00144151
$681$	2.02617	0.0776431
$682$	−20.0446	−0.767547
$683$	28.5357	1.09189	0.545944	−	0.837822i	$-0.316171\pi$
$683$	28.5357	1.09189	0.545944	+	0.837822i	$0.316171\pi$
$684$	−10.2727	−0.392785
$685$	−0.722620	−0.0276099
$686$	−20.8178	−0.794828
$687$	17.4044	0.664019
$688$	19.0257	0.725348
$689$	6.73428	0.256556
$690$	0.123304	0.00469411
$691$	15.9906	0.608310	0.304155	−	0.952623i	$-0.401626\pi$
$691$	15.9906	0.608310	0.304155	+	0.952623i	$0.401626\pi$
$692$	10.5472	0.400946
$693$	7.88463	0.299512
$694$	−33.9840	−1.29002
$695$	0.0966138	0.00366477
$696$	0.783291	0.0296906
$697$	4.65332	0.176257
$698$	−3.44237	−0.130296
$699$	9.90283	0.374559
$700$	−51.1020	−1.93147
$701$	−23.7423	−0.896734	−0.448367	−	0.893850i	$-0.647994\pi$
$701$	−23.7423	−0.896734	−0.448367	+	0.893850i	$0.647994\pi$
$702$	−1.79256	−0.0676557
$703$	8.63462	0.325661
$704$	−22.3684	−0.843041
$705$	0.443449	0.0167013
$706$	−52.1214	−1.96162
$707$	63.9802	2.40622
$708$	15.2205	0.572022
$709$	40.9275	1.53706	0.768531	−	0.639812i	$-0.220988\pi$
$709$	40.9275	1.53706	0.768531	+	0.639812i	$0.220988\pi$
$710$	0.545139	0.0204587
$711$	−15.7332	−0.590042
$712$	−15.9407	−0.597404
$713$	8.31039	0.311227
$714$	−8.61690	−0.322479
$715$	−0.0554208	−0.00207262
$716$	7.66278	0.286372
$717$	−2.12986	−0.0795410
$718$	17.6096	0.657184
$719$	−31.6061	−1.17871	−0.589354	−	0.807875i	$-0.700618\pi$
$719$	−31.6061	−1.17871	−0.589354	+	0.807875i	$0.700618\pi$
$720$	0.0905588	0.00337493
$721$	55.8296	2.07920
$722$	5.15387	0.191807
$723$	14.2144	0.528638
$724$	−0.933633	−0.0346982
$725$	3.51958	0.130714
$726$	15.3403	0.569331
$727$	−36.9396	−1.37001	−0.685007	−	0.728536i	$-0.740201\pi$
$727$	−36.9396	−1.37001	−0.685007	+	0.728536i	$0.740201\pi$
$728$	−3.79918	−0.140807
$729$	1.00000	0.0370370
$730$	0.451632	0.0167156
$731$	−7.09870	−0.262555
$732$	−36.4736	−1.34810
$733$	32.5940	1.20389	0.601943	−	0.798539i	$-0.294393\pi$
$733$	32.5940	1.20389	0.601943	+	0.798539i	$0.294393\pi$
$734$	−70.2437	−2.59274
$735$	−0.318150	−0.0117351
$736$	13.5986	0.501251
$737$	15.5946	0.574436
$738$	−9.89648	−0.364295
$739$	21.7689	0.800782	0.400391	−	0.916344i	$-0.368874\pi$
$739$	21.7689	0.800782	0.400391	+	0.916344i	$0.368874\pi$
$740$	0.180800	0.00664634
$741$	−3.43165	−0.126065
$742$	−68.8474	−2.52747
$743$	5.70501	0.209296	0.104648	−	0.994509i	$-0.466628\pi$
$743$	5.70501	0.209296	0.104648	+	0.994509i	$0.466628\pi$
$744$	−5.38807	−0.197536
$745$	−0.408946	−0.0149826
$746$	63.2377	2.31530
$747$	−10.1331	−0.370750
$748$	4.91002	0.179528
$749$	24.6173	0.899496
$750$	−0.718518	−0.0262366
$751$	24.6809	0.900620	0.450310	−	0.892872i	$-0.351313\pi$
$751$	24.6809	0.900620	0.450310	+	0.892872i	$0.351313\pi$
$752$	35.1752	1.28271
$753$	−18.1950	−0.663063
$754$	1.26210	0.0459629
$755$	−0.204323	−0.00743608
$756$	10.2227	0.371797
$757$	8.86664	0.322263	0.161132	−	0.986933i	$-0.448486\pi$
$757$	8.86664	0.322263	0.161132	+	0.986933i	$0.448486\pi$
$758$	−55.9882	−2.03358
$759$	3.33918	0.121204
$760$	−0.153045	−0.00555154
$761$	−31.0567	−1.12580	−0.562902	−	0.826523i	$-0.690315\pi$
$761$	−31.0567	−1.12580	−0.562902	+	0.826523i	$0.690315\pi$
$762$	−40.0501	−1.45086
$763$	69.0737	2.50063
$764$	37.5689	1.35920
$765$	−0.0337885	−0.00122163
$766$	76.2714	2.75580
$767$	5.08452	0.183591
$768$	4.70795	0.169884
$769$	10.5870	0.381776	0.190888	−	0.981612i	$-0.438863\pi$
$769$	10.5870	0.381776	0.190888	+	0.981612i	$0.438863\pi$
$770$	0.566590	0.0204185
$771$	−11.0920	−0.399469
$772$	−26.2955	−0.946396
$773$	17.3353	0.623506	0.311753	−	0.950163i	$-0.399084\pi$
$773$	17.3353	0.623506	0.311753	+	0.950163i	$0.399084\pi$
$774$	15.0972	0.542658
$775$	−24.2104	−0.869662
$776$	−14.4011	−0.516968
$777$	−8.59266	−0.308260
$778$	50.2127	1.80021
$779$	−18.9457	−0.678801
$780$	−0.0718552	−0.00257283
$781$	14.7628	0.528255
$782$	−3.64930	−0.130499
$783$	−0.704078	−0.0251617
$784$	−25.2363	−0.901295
$785$	−0.0337885	−0.00120596
$786$	−5.64211	−0.201247
$787$	−33.2246	−1.18433	−0.592164	−	0.805818i	$-0.701726\pi$
$787$	−33.2246	−1.18433	−0.592164	+	0.805818i	$0.701726\pi$
$788$	−33.4271	−1.19079
$789$	−18.1573	−0.646416
$790$	−1.13059	−0.0402245
$791$	5.42637	0.192939
$792$	−2.16497	−0.0769288
$793$	−12.1843	−0.432676
$794$	20.3811	0.723299
$795$	−0.269964	−0.00957463
$796$	5.59788	0.198412
$797$	47.1629	1.67059	0.835297	−	0.549799i	$-0.185296\pi$
$797$	47.1629	1.67059	0.835297	+	0.549799i	$0.185296\pi$
$798$	35.0832	1.24193
$799$	−13.1243	−0.464303
$800$	−39.6164	−1.40065
$801$	14.3287	0.506278
$802$	−35.1625	−1.24163
$803$	12.2306	0.431607
$804$	20.2191	0.713071
$805$	−0.234905	−0.00827932
$806$	−8.68167	−0.305799
$807$	−1.33776	−0.0470915
$808$	−17.5677	−0.618030
$809$	32.2709	1.13458	0.567292	−	0.823517i	$-0.307991\pi$
$809$	32.2709	1.13458	0.567292	+	0.823517i	$0.307991\pi$
$810$	0.0718600	0.00252490
$811$	31.9485	1.12186	0.560932	−	0.827862i	$-0.310443\pi$
$811$	31.9485	1.12186	0.560932	+	0.827862i	$0.310443\pi$
$812$	−7.19760	−0.252586
$813$	−2.30689	−0.0809060
$814$	8.77731	0.307645
$815$	0.366715	0.0128455
$816$	−2.68017	−0.0938246
$817$	28.9019	1.01115
$818$	−28.3994	−0.992961
$819$	3.41497	0.119329
$820$	−0.396704	−0.0138535
$821$	−47.9663	−1.67404	−0.837018	−	0.547175i	$-0.815703\pi$
$821$	−47.9663	−1.67404	−0.837018	+	0.547175i	$0.815703\pi$
$822$	−45.4840	−1.58644
$823$	−8.85169	−0.308551	−0.154275	−	0.988028i	$-0.549304\pi$
$823$	−8.85169	−0.308551	−0.154275	+	0.988028i	$0.549304\pi$
$824$	−15.3297	−0.534036
$825$	−9.72791	−0.338682
$826$	−51.9812	−1.80866
$827$	40.5852	1.41129	0.705643	−	0.708568i	$-0.250658\pi$
$827$	40.5852	1.41129	0.705643	+	0.708568i	$0.250658\pi$
$828$	4.32938	0.150456
$829$	10.2092	0.354580	0.177290	−	0.984159i	$-0.443267\pi$
$829$	10.2092	0.354580	0.177290	+	0.984159i	$0.443267\pi$
$830$	−0.728164	−0.0252749
$831$	−21.0537	−0.730345
$832$	−9.68815	−0.335876
$833$	9.41593	0.326243
$834$	6.08119	0.210574
$835$	−0.699011	−0.0241903
$836$	−19.9909	−0.691399
$837$	4.84318	0.167405
$838$	−38.1227	−1.31693
$839$	−32.9083	−1.13612	−0.568061	−	0.822987i	$-0.692306\pi$
$839$	−32.9083	−1.13612	−0.568061	+	0.822987i	$0.692306\pi$
$840$	0.152302	0.00525490
$841$	−28.5043	−0.982906
$842$	−42.3917	−1.46091
$843$	18.6356	0.641845
$844$	0.894669	0.0307958
$845$	0.415247	0.0142849
$846$	27.9121	0.959638
$847$	−29.2245	−1.00417
$848$	−21.4140	−0.735361
$849$	16.8674	0.578887
$850$	10.6314	0.364653
$851$	−3.63903	−0.124744
$852$	19.1406	0.655744
$853$	43.6815	1.49563	0.747814	−	0.663909i	$-0.231104\pi$
$853$	43.6815	1.49563	0.747814	+	0.663909i	$0.231104\pi$
$854$	124.565	4.26252
$855$	0.137568	0.00470473
$856$	−6.75943	−0.231033
$857$	55.7611	1.90476	0.952382	−	0.304907i	$-0.0986254\pi$
$857$	55.7611	1.90476	0.952382	+	0.304907i	$0.0986254\pi$
$858$	−3.48836	−0.119091
$859$	−49.4966	−1.68880	−0.844402	−	0.535710i	$-0.820044\pi$
$859$	−49.4966	−1.68880	−0.844402	+	0.535710i	$0.820044\pi$
$860$	0.605177	0.0206363
$861$	18.8537	0.642531
$862$	5.68320	0.193571
$863$	11.5504	0.393181	0.196591	−	0.980486i	$-0.437013\pi$
$863$	11.5504	0.393181	0.196591	+	0.980486i	$0.437013\pi$
$864$	7.92508	0.269617
$865$	−0.141245	−0.00480248
$866$	67.3110	2.28732
$867$	1.00000	0.0339618
$868$	49.5105	1.68050
$869$	−30.6173	−1.03862
$870$	−0.0505950	−0.00171533
$871$	6.75431	0.228861
$872$	−18.9663	−0.642280
$873$	12.9447	0.438112
$874$	14.8579	0.502576
$875$	1.36884	0.0462752
$876$	15.8574	0.535772
$877$	4.74448	0.160210	0.0801048	−	0.996786i	$-0.474474\pi$
$877$	4.74448	0.160210	0.0801048	+	0.996786i	$0.474474\pi$
$878$	9.70656	0.327580
$879$	2.28648	0.0771211
$880$	0.176230	0.00594071
$881$	−4.93399	−0.166230	−0.0831152	−	0.996540i	$-0.526487\pi$
$881$	−4.93399	−0.166230	−0.0831152	+	0.996540i	$0.526487\pi$
$882$	−20.0254	−0.674290
$883$	−8.42249	−0.283439	−0.141720	−	0.989907i	$-0.545263\pi$
$883$	−8.42249	−0.283439	−0.141720	+	0.989907i	$0.545263\pi$
$884$	2.12662	0.0715258
$885$	−0.203828	−0.00685161
$886$	41.4272	1.39177
$887$	−0.151894	−0.00510012	−0.00255006	−	0.999997i	$-0.500812\pi$
$887$	−0.151894	−0.00510012	−0.00255006	+	0.999997i	$0.500812\pi$
$888$	2.35938	0.0791755
$889$	76.2989	2.55898
$890$	1.02966	0.0345142
$891$	1.94603	0.0651943
$892$	14.7928	0.495298
$893$	53.4347	1.78812
$894$	−25.7404	−0.860886
$895$	−0.102617	−0.00343012
$896$	34.8266	1.16347
$897$	1.44626	0.0482891
$898$	−47.9785	−1.60106
$899$	−3.40997	−0.113729
$900$	−12.6126	−0.420421
$901$	7.98981	0.266179
$902$	−19.2588	−0.641248
$903$	−28.7615	−0.957122
$904$	−1.48998	−0.0495558
$905$	0.0125029	0.000415610 0
$906$	−12.8608	−0.427270
$907$	14.5863	0.484329	0.242164	−	0.970235i	$-0.422143\pi$
$907$	14.5863	0.484329	0.242164	+	0.970235i	$0.422143\pi$
$908$	5.11223	0.169655
$909$	15.7911	0.523758
$910$	0.245400	0.00813493
$911$	38.8939	1.28861	0.644306	−	0.764768i	$-0.277146\pi$
$911$	38.8939	1.28861	0.644306	+	0.764768i	$0.277146\pi$
$912$	10.9121	0.361337
$913$	−19.7193	−0.652613
$914$	8.06115	0.266639
$915$	0.488443	0.0161474
$916$	43.9130	1.45093
$917$	10.7487	0.354953
$918$	−2.12676	−0.0701935
$919$	23.1276	0.762910	0.381455	−	0.924387i	$-0.375423\pi$
$919$	23.1276	0.762910	0.381455	+	0.924387i	$0.375423\pi$
$920$	0.0645004	0.00212652
$921$	−23.6819	−0.780345
$922$	−54.3929	−1.79133
$923$	6.39403	0.210462
$924$	19.8937	0.654455
$925$	10.6015	0.348574
$926$	−23.6399	−0.776857
$927$	13.7794	0.452576
$928$	−5.57987	−0.183168
$929$	−15.9742	−0.524095	−0.262048	−	0.965055i	$-0.584398\pi$
$929$	−15.9742	−0.524095	−0.262048	+	0.965055i	$0.584398\pi$
$930$	0.348031	0.0114124
$931$	−38.3364	−1.25643
$932$	24.9858	0.818438
$933$	−8.04185	−0.263278
$934$	29.8782	0.977644
$935$	−0.0657533	−0.00215036
$936$	−0.937686	−0.0306492
$937$	48.7159	1.59148	0.795739	−	0.605640i	$-0.207083\pi$
$937$	48.7159	1.59148	0.795739	+	0.605640i	$0.207083\pi$
$938$	−69.0521	−2.25463
$939$	−15.5760	−0.508304
$940$	1.11887	0.0364934
$941$	−31.0717	−1.01291	−0.506454	−	0.862267i	$-0.669044\pi$
$941$	−31.0717	−1.01291	−0.506454	+	0.862267i	$0.669044\pi$
$942$	−2.12676	−0.0692935
$943$	7.98461	0.260015
$944$	−16.1680	−0.526224
$945$	−0.136899	−0.00445334
$946$	29.3796	0.955212
$947$	−7.30124	−0.237258	−0.118629	−	0.992939i	$-0.537850\pi$
$947$	−7.30124	−0.237258	−0.118629	+	0.992939i	$0.537850\pi$
$948$	−39.6965	−1.28928
$949$	5.29727	0.171957
$950$	−43.2850	−1.40435
$951$	−13.5629	−0.439807
$952$	−4.50750	−0.146089
$953$	−47.4011	−1.53547	−0.767736	−	0.640766i	$-0.778617\pi$
$953$	−47.4011	−1.53547	−0.767736	+	0.640766i	$0.778617\pi$
$954$	−16.9924	−0.550149
$955$	−0.503111	−0.0162803
$956$	−5.37384	−0.173802
$957$	−1.37015	−0.0442908
$958$	−53.5603	−1.73046
$959$	86.6510	2.79811
$960$	0.388378	0.0125349
$961$	−7.54362	−0.243342
$962$	3.80161	0.122569
$963$	6.07586	0.195792
$964$	35.8643	1.15511
$965$	0.352141	0.0113358
$966$	−14.7857	−0.475722
$967$	−7.64664	−0.245899	−0.122950	−	0.992413i	$-0.539235\pi$
$967$	−7.64664	−0.245899	−0.122950	+	0.992413i	$0.539235\pi$
$968$	8.02449	0.257917
$969$	−4.07144	−0.130794
$970$	0.930207	0.0298671
$971$	−4.43657	−0.142376	−0.0711882	−	0.997463i	$-0.522679\pi$
$971$	−4.43657	−0.142376	−0.0711882	+	0.997463i	$0.522679\pi$
$972$	2.52310	0.0809285
$973$	−11.5852	−0.371404
$974$	33.7780	1.08232
$975$	−4.21333	−0.134935
$976$	38.7442	1.24017
$977$	31.6788	1.01350	0.506748	−	0.862094i	$-0.330848\pi$
$977$	31.6788	1.01350	0.506748	+	0.862094i	$0.330848\pi$
$978$	23.0822	0.738088
$979$	27.8840	0.891175
$980$	−0.802725	−0.0256421
$981$	17.0482	0.544309
$982$	−43.0413	−1.37350
$983$	−44.2059	−1.40995	−0.704974	−	0.709233i	$-0.749041\pi$
$983$	−44.2059	−1.40995	−0.704974	+	0.709233i	$0.749041\pi$
$984$	−5.17685	−0.165032
$985$	0.447645	0.0142631
$986$	1.49740	0.0476870
$987$	−53.1750	−1.69258
$988$	−8.65840	−0.275460
$989$	−12.1806	−0.387321
$990$	0.139841	0.00444445
$991$	58.6845	1.86417	0.932087	−	0.362235i	$-0.117986\pi$
$991$	58.6845	1.86417	0.932087	+	0.362235i	$0.117986\pi$
$992$	38.3826	1.21865
$993$	12.8217	0.406884
$994$	−65.3688	−2.07337
$995$	−0.0749650	−0.00237655
$996$	−25.5668	−0.810115
$997$	−56.3815	−1.78562	−0.892810	−	0.450434i	$-0.851269\pi$
$997$	−56.3815	−1.78562	−0.892810	+	0.450434i	$0.851269\pi$
$998$	−39.6222	−1.25422
$999$	−2.12078	−0.0670984

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.i.1.9	✓	63

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.i.1.9	✓	63	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)

\(f(q)\)	\(=\)	\(q-2.12676 q^{2} +1.00000 q^{3} +2.52310 q^{4} -0.0337885 q^{5} -2.12676 q^{6} +4.05166 q^{7} -1.11251 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.12676 q^{2} +1.00000 q^{3} +2.52310 q^{4} -0.0337885 q^{5} -2.12676 q^{6} +4.05166 q^{7} -1.11251 q^{8} +1.00000 q^{9} +0.0718600 q^{10} +1.94603 q^{11} +2.52310 q^{12} +0.842858 q^{13} -8.61690 q^{14} -0.0337885 q^{15} -2.68017 q^{16} +1.00000 q^{17} -2.12676 q^{18} -4.07144 q^{19} -0.0852518 q^{20} +4.05166 q^{21} -4.13873 q^{22} +1.71590 q^{23} -1.11251 q^{24} -4.99886 q^{25} -1.79256 q^{26} +1.00000 q^{27} +10.2227 q^{28} -0.704078 q^{29} +0.0718600 q^{30} +4.84318 q^{31} +7.92508 q^{32} +1.94603 q^{33} -2.12676 q^{34} -0.136899 q^{35} +2.52310 q^{36} -2.12078 q^{37} +8.65898 q^{38} +0.842858 q^{39} +0.0375899 q^{40} +4.65332 q^{41} -8.61690 q^{42} -7.09870 q^{43} +4.91002 q^{44} -0.0337885 q^{45} -3.64930 q^{46} -13.1243 q^{47} -2.68017 q^{48} +9.41593 q^{49} +10.6314 q^{50} +1.00000 q^{51} +2.12662 q^{52} +7.98981 q^{53} -2.12676 q^{54} -0.0657533 q^{55} -4.50750 q^{56} -4.07144 q^{57} +1.49740 q^{58} +6.03247 q^{59} -0.0852518 q^{60} -14.4559 q^{61} -10.3003 q^{62} +4.05166 q^{63} -11.4944 q^{64} -0.0284789 q^{65} -4.13873 q^{66} +8.01358 q^{67} +2.52310 q^{68} +1.71590 q^{69} +0.291152 q^{70} +7.58612 q^{71} -1.11251 q^{72} +6.28488 q^{73} +4.51038 q^{74} -4.99886 q^{75} -10.2727 q^{76} +7.88463 q^{77} -1.79256 q^{78} -15.7332 q^{79} +0.0905588 q^{80} +1.00000 q^{81} -9.89648 q^{82} -10.1331 q^{83} +10.2227 q^{84} -0.0337885 q^{85} +15.0972 q^{86} -0.704078 q^{87} -2.16497 q^{88} +14.3287 q^{89} +0.0718600 q^{90} +3.41497 q^{91} +4.32938 q^{92} +4.84318 q^{93} +27.9121 q^{94} +0.137568 q^{95} +7.92508 q^{96} +12.9447 q^{97} -20.0254 q^{98} +1.94603 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * q^99

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