LMFDB - Embedded newform 8007.2.a.j.1.62

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			1.62
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)

$f(q)$	$=$	$q+2.72963 q^{2} -1.00000 q^{3} +5.45086 q^{4} -4.14782 q^{5} -2.72963 q^{6} -3.92805 q^{7} +9.41956 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.72963 q^{2} -1.00000 q^{3} +5.45086 q^{4} -4.14782 q^{5} -2.72963 q^{6} -3.92805 q^{7} +9.41956 q^{8} +1.00000 q^{9} -11.3220 q^{10} +0.0630788 q^{11} -5.45086 q^{12} -3.70731 q^{13} -10.7221 q^{14} +4.14782 q^{15} +14.8102 q^{16} +1.00000 q^{17} +2.72963 q^{18} -0.641859 q^{19} -22.6092 q^{20} +3.92805 q^{21} +0.172182 q^{22} -7.23007 q^{23} -9.41956 q^{24} +12.2044 q^{25} -10.1196 q^{26} -1.00000 q^{27} -21.4112 q^{28} -9.14630 q^{29} +11.3220 q^{30} +6.42005 q^{31} +21.5871 q^{32} -0.0630788 q^{33} +2.72963 q^{34} +16.2928 q^{35} +5.45086 q^{36} +7.63521 q^{37} -1.75204 q^{38} +3.70731 q^{39} -39.0707 q^{40} +7.17802 q^{41} +10.7221 q^{42} +12.4297 q^{43} +0.343834 q^{44} -4.14782 q^{45} -19.7354 q^{46} +3.37178 q^{47} -14.8102 q^{48} +8.42957 q^{49} +33.3135 q^{50} -1.00000 q^{51} -20.2080 q^{52} -4.83965 q^{53} -2.72963 q^{54} -0.261640 q^{55} -37.0005 q^{56} +0.641859 q^{57} -24.9660 q^{58} -7.16670 q^{59} +22.6092 q^{60} -0.316579 q^{61} +17.5243 q^{62} -3.92805 q^{63} +29.3044 q^{64} +15.3773 q^{65} -0.172182 q^{66} -2.75590 q^{67} +5.45086 q^{68} +7.23007 q^{69} +44.4734 q^{70} +16.0541 q^{71} +9.41956 q^{72} -7.68491 q^{73} +20.8413 q^{74} -12.2044 q^{75} -3.49868 q^{76} -0.247777 q^{77} +10.1196 q^{78} +8.32825 q^{79} -61.4299 q^{80} +1.00000 q^{81} +19.5933 q^{82} +4.87784 q^{83} +21.4112 q^{84} -4.14782 q^{85} +33.9284 q^{86} +9.14630 q^{87} +0.594175 q^{88} -6.93379 q^{89} -11.3220 q^{90} +14.5625 q^{91} -39.4101 q^{92} -6.42005 q^{93} +9.20370 q^{94} +2.66232 q^{95} -21.5871 q^{96} +5.57115 q^{97} +23.0096 q^{98} +0.0630788 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.72963	1.93014	0.965069	−	0.261997i	$-0.0843810\pi$
$2$	2.72963	1.93014	0.965069	+	0.261997i	$0.0843810\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.45086	2.72543
$5$	−4.14782	−1.85496	−0.927481	−	0.373870i	$-0.878031\pi$
$5$	−4.14782	−1.85496	−0.927481	+	0.373870i	$0.878031\pi$
$6$	−2.72963	−1.11437
$7$	−3.92805	−1.48466	−0.742331	−	0.670033i	$-0.766280\pi$
$7$	−3.92805	−1.48466	−0.742331	+	0.670033i	$0.766280\pi$
$8$	9.41956	3.33032
$9$	1.00000	0.333333
$10$	−11.3220	−3.58033
$11$	0.0630788	0.0190190	0.00950949	−	0.999955i	$-0.496973\pi$
$11$	0.0630788	0.0190190	0.00950949	+	0.999955i	$0.496973\pi$
$12$	−5.45086	−1.57353
$13$	−3.70731	−1.02822	−0.514111	−	0.857724i	$-0.671878\pi$
$13$	−3.70731	−1.02822	−0.514111	+	0.857724i	$0.671878\pi$
$14$	−10.7221	−2.86560
$15$	4.14782	1.07096
$16$	14.8102	3.70254
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.72963	0.643379
$19$	−0.641859	−0.147253	−0.0736263	−	0.997286i	$-0.523457\pi$
$19$	−0.641859	−0.147253	−0.0736263	+	0.997286i	$0.523457\pi$
$20$	−22.6092	−5.05557
$21$	3.92805	0.857170
$22$	0.172182	0.0367092
$23$	−7.23007	−1.50757	−0.753787	−	0.657119i	$-0.771775\pi$
$23$	−7.23007	−1.50757	−0.753787	+	0.657119i	$0.771775\pi$
$24$	−9.41956	−1.92276
$25$	12.2044	2.44088
$26$	−10.1196	−1.98461
$27$	−1.00000	−0.192450
$28$	−21.4112	−4.04635
$29$	−9.14630	−1.69843	−0.849213	−	0.528051i	$-0.822923\pi$
$29$	−9.14630	−1.69843	−0.849213	+	0.528051i	$0.822923\pi$
$30$	11.3220	2.06711
$31$	6.42005	1.15307	0.576537	−	0.817071i	$-0.304404\pi$
$31$	6.42005	1.15307	0.576537	+	0.817071i	$0.304404\pi$
$32$	21.5871	3.81610
$33$	−0.0630788	−0.0109806
$34$	2.72963	0.468127
$35$	16.2928	2.75399
$36$	5.45086	0.908477
$37$	7.63521	1.25522	0.627610	−	0.778528i	$-0.284033\pi$
$37$	7.63521	1.25522	0.627610	+	0.778528i	$0.284033\pi$
$38$	−1.75204	−0.284218
$39$	3.70731	0.593644
$40$	−39.0707	−6.17761
$41$	7.17802	1.12102	0.560509	−	0.828148i	$-0.310606\pi$
$41$	7.17802	1.12102	0.560509	+	0.828148i	$0.310606\pi$
$42$	10.7221	1.65446
$43$	12.4297	1.89551	0.947754	−	0.319002i	$-0.103348\pi$
$43$	12.4297	1.89551	0.947754	+	0.319002i	$0.103348\pi$
$44$	0.343834	0.0518349
$45$	−4.14782	−0.618321
$46$	−19.7354	−2.90983
$47$	3.37178	0.491824	0.245912	−	0.969292i	$-0.420913\pi$
$47$	3.37178	0.491824	0.245912	+	0.969292i	$0.420913\pi$
$48$	−14.8102	−2.13766
$49$	8.42957	1.20422
$50$	33.3135	4.71124
$51$	−1.00000	−0.140028
$52$	−20.2080	−2.80235
$53$	−4.83965	−0.664777	−0.332388	−	0.943143i	$-0.607854\pi$
$53$	−4.83965	−0.664777	−0.332388	+	0.943143i	$0.607854\pi$
$54$	−2.72963	−0.371455
$55$	−0.261640	−0.0352795
$56$	−37.0005	−4.94440
$57$	0.641859	0.0850163
$58$	−24.9660	−3.27819
$59$	−7.16670	−0.933024	−0.466512	−	0.884515i	$-0.654490\pi$
$59$	−7.16670	−0.933024	−0.466512	+	0.884515i	$0.654490\pi$
$60$	22.6092	2.91884
$61$	−0.316579	−0.0405338	−0.0202669	−	0.999795i	$-0.506452\pi$
$61$	−0.316579	−0.0405338	−0.0202669	+	0.999795i	$0.506452\pi$
$62$	17.5243	2.22559
$63$	−3.92805	−0.494888
$64$	29.3044	3.66305
$65$	15.3773	1.90731
$66$	−0.172182	−0.0211941
$67$	−2.75590	−0.336686	−0.168343	−	0.985728i	$-0.553842\pi$
$67$	−2.75590	−0.336686	−0.168343	+	0.985728i	$0.553842\pi$
$68$	5.45086	0.661014
$69$	7.23007	0.870398
$70$	44.4734	5.31559
$71$	16.0541	1.90527	0.952636	−	0.304112i	$-0.0983596\pi$
$71$	16.0541	1.90527	0.952636	+	0.304112i	$0.0983596\pi$
$72$	9.41956	1.11011
$73$	−7.68491	−0.899450	−0.449725	−	0.893167i	$-0.648478\pi$
$73$	−7.68491	−0.899450	−0.449725	+	0.893167i	$0.648478\pi$
$74$	20.8413	2.42275
$75$	−12.2044	−1.40925
$76$	−3.49868	−0.401327
$77$	−0.247777	−0.0282368
$78$	10.1196	1.14582
$79$	8.32825	0.937001	0.468501	−	0.883463i	$-0.344794\pi$
$79$	8.32825	0.937001	0.468501	+	0.883463i	$0.344794\pi$
$80$	−61.4299	−6.86808
$81$	1.00000	0.111111
$82$	19.5933	2.16372
$83$	4.87784	0.535412	0.267706	−	0.963501i	$-0.413734\pi$
$83$	4.87784	0.535412	0.267706	+	0.963501i	$0.413734\pi$
$84$	21.4112	2.33616
$85$	−4.14782	−0.449894
$86$	33.9284	3.65859
$87$	9.14630	0.980586
$88$	0.594175	0.0633393
$89$	−6.93379	−0.734981	−0.367490	−	0.930027i	$-0.619783\pi$
$89$	−6.93379	−0.734981	−0.367490	+	0.930027i	$0.619783\pi$
$90$	−11.3220	−1.19344
$91$	14.5625	1.52656
$92$	−39.4101	−4.10879
$93$	−6.42005	−0.665728
$94$	9.20370	0.949289
$95$	2.66232	0.273148
$96$	−21.5871	−2.20322
$97$	5.57115	0.565665	0.282832	−	0.959169i	$-0.408726\pi$
$97$	5.57115	0.565665	0.282832	+	0.959169i	$0.408726\pi$
$98$	23.0096	2.32432
$99$	0.0630788	0.00633966
$100$	66.5246	6.65246
$101$	−2.77044	−0.275669	−0.137834	−	0.990455i	$-0.544014\pi$
$101$	−2.77044	−0.275669	−0.137834	+	0.990455i	$0.544014\pi$
$102$	−2.72963	−0.270273
$103$	6.54919	0.645311	0.322655	−	0.946516i	$-0.395424\pi$
$103$	6.54919	0.645311	0.322655	+	0.946516i	$0.395424\pi$
$104$	−34.9212	−3.42431
$105$	−16.2928	−1.59002
$106$	−13.2104	−1.28311
$107$	1.07288	0.103719	0.0518596	−	0.998654i	$-0.483485\pi$
$107$	1.07288	0.103719	0.0518596	+	0.998654i	$0.483485\pi$
$108$	−5.45086	−0.524509
$109$	17.4173	1.66827	0.834137	−	0.551557i	$-0.185966\pi$
$109$	17.4173	1.66827	0.834137	+	0.551557i	$0.185966\pi$
$110$	−0.714178	−0.0680942
$111$	−7.63521	−0.724702
$112$	−58.1751	−5.49703
$113$	16.1603	1.52023	0.760115	−	0.649788i	$-0.225142\pi$
$113$	16.1603	1.52023	0.760115	+	0.649788i	$0.225142\pi$
$114$	1.75204	0.164093
$115$	29.9890	2.79649
$116$	−49.8552	−4.62894
$117$	−3.70731	−0.342741
$118$	−19.5624	−1.80087
$119$	−3.92805	−0.360084
$120$	39.0707	3.56665
$121$	−10.9960	−0.999638
$122$	−0.864142	−0.0782357
$123$	−7.17802	−0.647220
$124$	34.9948	3.14263
$125$	−29.8826	−2.67279
$126$	−10.7221	−0.955201
$127$	−22.0374	−1.95551	−0.977753	−	0.209760i	$-0.932732\pi$
$127$	−22.0374	−1.95551	−0.977753	+	0.209760i	$0.932732\pi$
$128$	36.8159	3.25409
$129$	−12.4297	−1.09437
$130$	41.9742	3.68138
$131$	−9.12393	−0.797162	−0.398581	−	0.917133i	$-0.630497\pi$
$131$	−9.12393	−0.797162	−0.398581	+	0.917133i	$0.630497\pi$
$132$	−0.343834	−0.0299269
$133$	2.52125	0.218620
$134$	−7.52257	−0.649851
$135$	4.14782	0.356988
$136$	9.41956	0.807721
$137$	17.7569	1.51707	0.758537	−	0.651630i	$-0.225914\pi$
$137$	17.7569	1.51707	0.758537	+	0.651630i	$0.225914\pi$
$138$	19.7354	1.67999
$139$	14.7128	1.24792	0.623961	−	0.781455i	$-0.285522\pi$
$139$	14.7128	1.24792	0.623961	+	0.781455i	$0.285522\pi$
$140$	88.8100	7.50582
$141$	−3.37178	−0.283955
$142$	43.8217	3.67744
$143$	−0.233853	−0.0195557
$144$	14.8102	1.23418
$145$	37.9372	3.15051
$146$	−20.9769	−1.73606
$147$	−8.42957	−0.695259
$148$	41.6185	3.42102
$149$	5.59091	0.458025	0.229013	−	0.973423i	$-0.426450\pi$
$149$	5.59091	0.458025	0.229013	+	0.973423i	$0.426450\pi$
$150$	−33.3135	−2.72004
$151$	9.16118	0.745527	0.372763	−	0.927926i	$-0.378410\pi$
$151$	9.16118	0.745527	0.372763	+	0.927926i	$0.378410\pi$
$152$	−6.04603	−0.490398
$153$	1.00000	0.0808452
$154$	−0.676338	−0.0545008
$155$	−26.6292	−2.13891
$156$	20.2080	1.61794
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	22.7330	1.80854
$159$	4.83965	0.383809
$160$	−89.5395	−7.07872
$161$	28.4001	2.23824
$162$	2.72963	0.214460
$163$	5.67746	0.444693	0.222347	−	0.974968i	$-0.428628\pi$
$163$	5.67746	0.444693	0.222347	+	0.974968i	$0.428628\pi$
$164$	39.1264	3.05526
$165$	0.261640	0.0203686
$166$	13.3147	1.03342
$167$	10.5362	0.815316	0.407658	−	0.913135i	$-0.366346\pi$
$167$	10.5362	0.815316	0.407658	+	0.913135i	$0.366346\pi$
$168$	37.0005	2.85465
$169$	0.744138	0.0572414
$170$	−11.3220	−0.868358
$171$	−0.641859	−0.0490842
$172$	67.7525	5.16608
$173$	−19.4168	−1.47623	−0.738115	−	0.674675i	$-0.764284\pi$
$173$	−19.4168	−1.47623	−0.738115	+	0.674675i	$0.764284\pi$
$174$	24.9660	1.89267
$175$	−47.9396	−3.62389
$176$	0.934208	0.0704186
$177$	7.16670	0.538682
$178$	−18.9267	−1.41861
$179$	−8.91796	−0.666559	−0.333280	−	0.942828i	$-0.608155\pi$
$179$	−8.91796	−0.666559	−0.333280	+	0.942828i	$0.608155\pi$
$180$	−22.6092	−1.68519
$181$	−16.7653	−1.24615	−0.623076	−	0.782161i	$-0.714117\pi$
$181$	−16.7653	−1.24615	−0.623076	+	0.782161i	$0.714117\pi$
$182$	39.7502	2.94648
$183$	0.316579	0.0234022
$184$	−68.1041	−5.02070
$185$	−31.6695	−2.32839
$186$	−17.5243	−1.28495
$187$	0.0630788	0.00461278
$188$	18.3791	1.34043
$189$	3.92805	0.285723
$190$	7.26713	0.527213
$191$	−11.6978	−0.846421	−0.423211	−	0.906031i	$-0.639097\pi$
$191$	−11.6978	−0.846421	−0.423211	+	0.906031i	$0.639097\pi$
$192$	−29.3044	−2.11486
$193$	19.4276	1.39843	0.699216	−	0.714910i	$-0.253533\pi$
$193$	19.4276	1.39843	0.699216	+	0.714910i	$0.253533\pi$
$194$	15.2072	1.09181
$195$	−15.3773	−1.10119
$196$	45.9484	3.28203
$197$	6.55972	0.467361	0.233680	−	0.972313i	$-0.424923\pi$
$197$	6.55972	0.467361	0.233680	+	0.972313i	$0.424923\pi$
$198$	0.172182	0.0122364
$199$	22.2820	1.57953	0.789765	−	0.613409i	$-0.210202\pi$
$199$	22.2820	1.57953	0.789765	+	0.613409i	$0.210202\pi$
$200$	114.960	8.12892
$201$	2.75590	0.194386
$202$	−7.56226	−0.532079
$203$	35.9271	2.52159
$204$	−5.45086	−0.381637
$205$	−29.7731	−2.07945
$206$	17.8768	1.24554
$207$	−7.23007	−0.502525
$208$	−54.9059	−3.80704
$209$	−0.0404877	−0.00280059
$210$	−44.4734	−3.06895
$211$	−7.05989	−0.486023	−0.243012	−	0.970023i	$-0.578135\pi$
$211$	−7.05989	−0.486023	−0.243012	+	0.970023i	$0.578135\pi$
$212$	−26.3803	−1.81180
$213$	−16.0541	−1.10001
$214$	2.92856	0.200192
$215$	−51.5561	−3.51610
$216$	−9.41956	−0.640920
$217$	−25.2183	−1.71193
$218$	47.5427	3.22000
$219$	7.68491	0.519298
$220$	−1.42616	−0.0961518
$221$	−3.70731	−0.249381
$222$	−20.8413	−1.39877
$223$	3.23763	0.216808	0.108404	−	0.994107i	$-0.465426\pi$
$223$	3.23763	0.216808	0.108404	+	0.994107i	$0.465426\pi$
$224$	−84.7952	−5.66562
$225$	12.2044	0.813628
$226$	44.1115	2.93425
$227$	−4.77404	−0.316864	−0.158432	−	0.987370i	$-0.550644\pi$
$227$	−4.77404	−0.316864	−0.158432	+	0.987370i	$0.550644\pi$
$228$	3.49868	0.231706
$229$	10.8139	0.714604	0.357302	−	0.933989i	$-0.383697\pi$
$229$	10.8139	0.714604	0.357302	+	0.933989i	$0.383697\pi$
$230$	81.8589	5.39762
$231$	0.247777	0.0163025
$232$	−86.1542	−5.65630
$233$	23.7254	1.55430	0.777150	−	0.629315i	$-0.216665\pi$
$233$	23.7254	1.55430	0.777150	+	0.629315i	$0.216665\pi$
$234$	−10.1196	−0.661537
$235$	−13.9855	−0.912316
$236$	−39.0647	−2.54289
$237$	−8.32825	−0.540978
$238$	−10.7221	−0.695011
$239$	11.3094	0.731545	0.365773	−	0.930704i	$-0.380805\pi$
$239$	11.3094	0.731545	0.365773	+	0.930704i	$0.380805\pi$
$240$	61.4299	3.96529
$241$	−18.6398	−1.20070	−0.600348	−	0.799739i	$-0.704971\pi$
$241$	−18.6398	−1.20070	−0.600348	+	0.799739i	$0.704971\pi$
$242$	−30.0150	−1.92944
$243$	−1.00000	−0.0641500
$244$	−1.72563	−0.110472
$245$	−34.9643	−2.23379
$246$	−19.5933	−1.24922
$247$	2.37957	0.151408
$248$	60.4741	3.84011
$249$	−4.87784	−0.309121
$250$	−81.5685	−5.15884
$251$	−17.1930	−1.08521	−0.542606	−	0.839987i	$-0.682562\pi$
$251$	−17.1930	−1.08521	−0.542606	+	0.839987i	$0.682562\pi$
$252$	−21.4112	−1.34878
$253$	−0.456064	−0.0286725
$254$	−60.1540	−3.77439
$255$	4.14782	0.259747
$256$	41.8848	2.61780
$257$	18.6067	1.16066	0.580328	−	0.814383i	$-0.302924\pi$
$257$	18.6067	1.16066	0.580328	+	0.814383i	$0.302924\pi$
$258$	−33.9284	−2.11229
$259$	−29.9915	−1.86358
$260$	83.8193	5.19825
$261$	−9.14630	−0.566142
$262$	−24.9049	−1.53863
$263$	14.2568	0.879110	0.439555	−	0.898216i	$-0.355136\pi$
$263$	14.2568	0.879110	0.439555	+	0.898216i	$0.355136\pi$
$264$	−0.594175	−0.0365689
$265$	20.0740	1.23314
$266$	6.88208	0.421967
$267$	6.93379	0.424341
$268$	−15.0220	−0.917615
$269$	−12.4656	−0.760044	−0.380022	−	0.924977i	$-0.624084\pi$
$269$	−12.4656	−0.760044	−0.380022	+	0.924977i	$0.624084\pi$
$270$	11.3220	0.689035
$271$	−19.9965	−1.21470	−0.607352	−	0.794433i	$-0.707768\pi$
$271$	−19.9965	−1.21470	−0.607352	+	0.794433i	$0.707768\pi$
$272$	14.8102	0.897998
$273$	−14.5625	−0.881362
$274$	48.4697	2.92816
$275$	0.769840	0.0464231
$276$	39.4101	2.37221
$277$	−21.6667	−1.30183	−0.650913	−	0.759152i	$-0.725614\pi$
$277$	−21.6667	−1.30183	−0.650913	+	0.759152i	$0.725614\pi$
$278$	40.1604	2.40866
$279$	6.42005	0.384358
$280$	153.471	9.17167
$281$	−3.31143	−0.197544	−0.0987718	−	0.995110i	$-0.531491\pi$
$281$	−3.31143	−0.197544	−0.0987718	+	0.995110i	$0.531491\pi$
$282$	−9.20370	−0.548072
$283$	6.67587	0.396839	0.198420	−	0.980117i	$-0.436419\pi$
$283$	6.67587	0.396839	0.198420	+	0.980117i	$0.436419\pi$
$284$	87.5088	5.19269
$285$	−2.66232	−0.157702
$286$	−0.638330	−0.0377453
$287$	−28.1956	−1.66433
$288$	21.5871	1.27203
$289$	1.00000	0.0588235
$290$	103.554	6.08093
$291$	−5.57115	−0.326587
$292$	−41.8894	−2.45139
$293$	10.4833	0.612441	0.306221	−	0.951961i	$-0.400935\pi$
$293$	10.4833	0.612441	0.306221	+	0.951961i	$0.400935\pi$
$294$	−23.0096	−1.34195
$295$	29.7262	1.73072
$296$	71.9203	4.18028
$297$	−0.0630788	−0.00366020
$298$	15.2611	0.884051
$299$	26.8041	1.55012
$300$	−66.5246	−3.84080
$301$	−48.8244	−2.81419
$302$	25.0066	1.43897
$303$	2.77044	0.159157
$304$	−9.50604	−0.545209
$305$	1.31311	0.0751886
$306$	2.72963	0.156042
$307$	25.4210	1.45086	0.725428	−	0.688298i	$-0.241642\pi$
$307$	25.4210	1.45086	0.725428	+	0.688298i	$0.241642\pi$
$308$	−1.35060	−0.0769574
$309$	−6.54919	−0.372570
$310$	−72.6878	−4.12839
$311$	−32.6614	−1.85206	−0.926029	−	0.377452i	$-0.876800\pi$
$311$	−32.6614	−1.85206	−0.926029	+	0.377452i	$0.876800\pi$
$312$	34.9212	1.97703
$313$	9.36224	0.529185	0.264593	−	0.964360i	$-0.414763\pi$
$313$	9.36224	0.529185	0.264593	+	0.964360i	$0.414763\pi$
$314$	−2.72963	−0.154042
$315$	16.2928	0.917998
$316$	45.3961	2.55373
$317$	1.04256	0.0585561	0.0292780	−	0.999571i	$-0.490679\pi$
$317$	1.04256	0.0585561	0.0292780	+	0.999571i	$0.490679\pi$
$318$	13.2104	0.740804
$319$	−0.576938	−0.0323023
$320$	−121.549	−6.79482
$321$	−1.07288	−0.0598823
$322$	77.5216	4.32011
$323$	−0.641859	−0.0357140
$324$	5.45086	0.302826
$325$	−45.2456	−2.50977
$326$	15.4973	0.858319
$327$	−17.4173	−0.963178
$328$	67.6138	3.73335
$329$	−13.2445	−0.730193
$330$	0.714178	0.0393142
$331$	−12.4912	−0.686576	−0.343288	−	0.939230i	$-0.611541\pi$
$331$	−12.4912	−0.686576	−0.343288	+	0.939230i	$0.611541\pi$
$332$	26.5884	1.45923
$333$	7.63521	0.418407
$334$	28.7599	1.57367
$335$	11.4310	0.624540
$336$	58.1751	3.17371
$337$	19.9322	1.08578	0.542888	−	0.839805i	$-0.317331\pi$
$337$	19.9322	1.08578	0.542888	+	0.839805i	$0.317331\pi$
$338$	2.03122	0.110484
$339$	−16.1603	−0.877706
$340$	−22.6092	−1.22616
$341$	0.404969	0.0219303
$342$	−1.75204	−0.0947392
$343$	−5.61540	−0.303203
$344$	117.082	6.31265
$345$	−29.9890	−1.61456
$346$	−53.0006	−2.84933
$347$	10.9348	0.587013	0.293506	−	0.955957i	$-0.405178\pi$
$347$	10.9348	0.587013	0.293506	+	0.955957i	$0.405178\pi$
$348$	49.8552	2.67252
$349$	−3.67717	−0.196834	−0.0984171	−	0.995145i	$-0.531378\pi$
$349$	−3.67717	−0.196834	−0.0984171	+	0.995145i	$0.531378\pi$
$350$	−130.857	−6.99461
$351$	3.70731	0.197881
$352$	1.36169	0.0725783
$353$	36.6437	1.95035	0.975174	−	0.221438i	$-0.0710751\pi$
$353$	36.6437	1.95035	0.975174	+	0.221438i	$0.0710751\pi$
$354$	19.5624	1.03973
$355$	−66.5896	−3.53421
$356$	−37.7952	−2.00314
$357$	3.92805	0.207894
$358$	−24.3427	−1.28655
$359$	−5.84963	−0.308732	−0.154366	−	0.988014i	$-0.549333\pi$
$359$	−5.84963	−0.308732	−0.154366	+	0.988014i	$0.549333\pi$
$360$	−39.0707	−2.05920
$361$	−18.5880	−0.978317
$362$	−45.7629	−2.40525
$363$	10.9960	0.577141
$364$	79.3781	4.16054
$365$	31.8756	1.66845
$366$	0.864142	0.0451694
$367$	16.1222	0.841571	0.420785	−	0.907160i	$-0.361755\pi$
$367$	16.1222	0.841571	0.420785	+	0.907160i	$0.361755\pi$
$368$	−107.079	−5.58186
$369$	7.17802	0.373673
$370$	−86.4458	−4.49410
$371$	19.0104	0.986969
$372$	−34.9948	−1.81440
$373$	31.0007	1.60515	0.802577	−	0.596548i	$-0.203461\pi$
$373$	31.0007	1.60515	0.802577	+	0.596548i	$0.203461\pi$
$374$	0.172182	0.00890330
$375$	29.8826	1.54313
$376$	31.7607	1.63793
$377$	33.9082	1.74636
$378$	10.7221	0.551486
$379$	−7.59715	−0.390240	−0.195120	−	0.980779i	$-0.562510\pi$
$379$	−7.59715	−0.390240	−0.195120	+	0.980779i	$0.562510\pi$
$380$	14.5119	0.744446
$381$	22.0374	1.12901
$382$	−31.9306	−1.63371
$383$	20.2666	1.03557	0.517787	−	0.855510i	$-0.326756\pi$
$383$	20.2666	1.03557	0.517787	+	0.855510i	$0.326756\pi$
$384$	−36.8159	−1.87875
$385$	1.02773	0.0523781
$386$	53.0302	2.69917
$387$	12.4297	0.631836
$388$	30.3676	1.54168
$389$	28.2672	1.43320	0.716602	−	0.697482i	$-0.245696\pi$
$389$	28.2672	1.43320	0.716602	+	0.697482i	$0.245696\pi$
$390$	−41.9742	−2.12544
$391$	−7.23007	−0.365640
$392$	79.4028	4.01045
$393$	9.12393	0.460242
$394$	17.9056	0.902070
$395$	−34.5441	−1.73810
$396$	0.343834	0.0172783
$397$	8.78540	0.440926	0.220463	−	0.975395i	$-0.429243\pi$
$397$	8.78540	0.440926	0.220463	+	0.975395i	$0.429243\pi$
$398$	60.8216	3.04871
$399$	−2.52125	−0.126221
$400$	180.750	9.03748
$401$	12.9325	0.645820	0.322910	−	0.946430i	$-0.395339\pi$
$401$	12.9325	0.645820	0.322910	+	0.946430i	$0.395339\pi$
$402$	7.52257	0.375192
$403$	−23.8011	−1.18562
$404$	−15.1013	−0.751316
$405$	−4.14782	−0.206107
$406$	98.0676	4.86701
$407$	0.481620	0.0238730
$408$	−9.41956	−0.466338
$409$	−19.2463	−0.951668	−0.475834	−	0.879535i	$-0.657854\pi$
$409$	−19.2463	−0.951668	−0.475834	+	0.879535i	$0.657854\pi$
$410$	−81.2695	−4.01362
$411$	−17.7569	−0.875883
$412$	35.6987	1.75875
$413$	28.1511	1.38523
$414$	−19.7354	−0.969942
$415$	−20.2324	−0.993170
$416$	−80.0301	−3.92380
$417$	−14.7128	−0.720489
$418$	−0.110516	−0.00540553
$419$	19.8209	0.968316	0.484158	−	0.874981i	$-0.339126\pi$
$419$	19.8209	0.968316	0.484158	+	0.874981i	$0.339126\pi$
$420$	−88.8100	−4.33349
$421$	−0.186414	−0.00908526	−0.00454263	−	0.999990i	$-0.501446\pi$
$421$	−0.186414	−0.00908526	−0.00454263	+	0.999990i	$0.501446\pi$
$422$	−19.2709	−0.938091
$423$	3.37178	0.163941
$424$	−45.5874	−2.21392
$425$	12.2044	0.592001
$426$	−43.8217	−2.12317
$427$	1.24354	0.0601790
$428$	5.84812	0.282679
$429$	0.233853	0.0112905
$430$	−140.729	−6.78655
$431$	−32.2565	−1.55374	−0.776870	−	0.629661i	$-0.783194\pi$
$431$	−32.2565	−1.55374	−0.776870	+	0.629661i	$0.783194\pi$
$432$	−14.8102	−0.712555
$433$	−4.39151	−0.211043	−0.105521	−	0.994417i	$-0.533651\pi$
$433$	−4.39151	−0.211043	−0.105521	+	0.994417i	$0.533651\pi$
$434$	−68.8364	−3.30425
$435$	−37.9372	−1.81895
$436$	94.9392	4.54677
$437$	4.64069	0.221994
$438$	20.9769	1.00232
$439$	19.7218	0.941272	0.470636	−	0.882328i	$-0.344025\pi$
$439$	19.7218	0.941272	0.470636	+	0.882328i	$0.344025\pi$
$440$	−2.46453	−0.117492
$441$	8.42957	0.401408
$442$	−10.1196	−0.481339
$443$	4.39772	0.208942	0.104471	−	0.994528i	$-0.466685\pi$
$443$	4.39772	0.208942	0.104471	+	0.994528i	$0.466685\pi$
$444$	−41.6185	−1.97512
$445$	28.7601	1.36336
$446$	8.83752	0.418468
$447$	−5.59091	−0.264441
$448$	−115.109	−5.43839
$449$	−36.5822	−1.72642	−0.863209	−	0.504846i	$-0.831549\pi$
$449$	−36.5822	−1.72642	−0.863209	+	0.504846i	$0.831549\pi$
$450$	33.3135	1.57041
$451$	0.452781	0.0213206
$452$	88.0874	4.14328
$453$	−9.16118	−0.430430
$454$	−13.0314	−0.611592
$455$	−60.4026	−2.83172
$456$	6.04603	0.283131
$457$	27.1533	1.27018	0.635090	−	0.772438i	$-0.280963\pi$
$457$	27.1533	1.27018	0.635090	+	0.772438i	$0.280963\pi$
$458$	29.5180	1.37928
$459$	−1.00000	−0.0466760
$460$	163.466	7.62165
$461$	20.4535	0.952615	0.476307	−	0.879279i	$-0.341975\pi$
$461$	20.4535	0.952615	0.476307	+	0.879279i	$0.341975\pi$
$462$	0.676338	0.0314661
$463$	−8.18289	−0.380291	−0.190146	−	0.981756i	$-0.560896\pi$
$463$	−8.18289	−0.380291	−0.190146	+	0.981756i	$0.560896\pi$
$464$	−135.458	−6.28849
$465$	26.6292	1.23490
$466$	64.7614	3.00001
$467$	−32.0378	−1.48253	−0.741266	−	0.671212i	$-0.765774\pi$
$467$	−32.0378	−1.48253	−0.741266	+	0.671212i	$0.765774\pi$
$468$	−20.2080	−0.934116
$469$	10.8253	0.499866
$470$	−38.1753	−1.76089
$471$	1.00000	0.0460776
$472$	−67.5072	−3.10727
$473$	0.784049	0.0360506
$474$	−22.7330	−1.04416
$475$	−7.83352	−0.359426
$476$	−21.4112	−0.981383
$477$	−4.83965	−0.221592
$478$	30.8705	1.41198
$479$	−30.2066	−1.38018	−0.690088	−	0.723725i	$-0.742428\pi$
$479$	−30.2066	−1.38018	−0.690088	+	0.723725i	$0.742428\pi$
$480$	89.5395	4.08690
$481$	−28.3061	−1.29065
$482$	−50.8797	−2.31751
$483$	−28.4001	−1.29225
$484$	−59.9378	−2.72444
$485$	−23.1081	−1.04929
$486$	−2.72963	−0.123818
$487$	−17.1540	−0.777323	−0.388661	−	0.921381i	$-0.627062\pi$
$487$	−17.1540	−0.777323	−0.388661	+	0.921381i	$0.627062\pi$
$488$	−2.98203	−0.134990
$489$	−5.67746	−0.256744
$490$	−95.4396	−4.31152
$491$	30.7997	1.38997	0.694987	−	0.719023i	$-0.255410\pi$
$491$	30.7997	1.38997	0.694987	+	0.719023i	$0.255410\pi$
$492$	−39.1264	−1.76395
$493$	−9.14630	−0.411929
$494$	6.49533	0.292239
$495$	−0.261640	−0.0117598
$496$	95.0820	4.26931
$497$	−63.0613	−2.82869
$498$	−13.3147	−0.596645
$499$	1.94182	0.0869278	0.0434639	−	0.999055i	$-0.486161\pi$
$499$	1.94182	0.0869278	0.0434639	+	0.999055i	$0.486161\pi$
$500$	−162.886	−7.28449
$501$	−10.5362	−0.470723
$502$	−46.9305	−2.09461
$503$	1.01098	0.0450772	0.0225386	−	0.999746i	$-0.492825\pi$
$503$	1.01098	0.0450772	0.0225386	+	0.999746i	$0.492825\pi$
$504$	−37.0005	−1.64813
$505$	11.4913	0.511355
$506$	−1.24489	−0.0553419
$507$	−0.744138	−0.0330483
$508$	−120.123	−5.32960
$509$	17.7960	0.788793	0.394396	−	0.918940i	$-0.370954\pi$
$509$	17.7960	0.788793	0.394396	+	0.918940i	$0.370954\pi$
$510$	11.3220	0.501347
$511$	30.1867	1.33538
$512$	40.6980	1.79862
$513$	0.641859	0.0283388
$514$	50.7895	2.24023
$515$	−27.1649	−1.19703
$516$	−67.7525	−2.98264
$517$	0.212688	0.00935400
$518$	−81.8655	−3.59696
$519$	19.4168	0.852302
$520$	144.847	6.35196
$521$	−11.0983	−0.486225	−0.243112	−	0.969998i	$-0.578168\pi$
$521$	−11.0983	−0.486225	−0.243112	+	0.969998i	$0.578168\pi$
$522$	−24.9660	−1.09273
$523$	−11.8859	−0.519732	−0.259866	−	0.965645i	$-0.583678\pi$
$523$	−11.8859	−0.519732	−0.259866	+	0.965645i	$0.583678\pi$
$524$	−49.7333	−2.17261
$525$	47.9396	2.09225
$526$	38.9157	1.69680
$527$	6.42005	0.279662
$528$	−0.934208	−0.0406562
$529$	29.2739	1.27278
$530$	54.7945	2.38012
$531$	−7.16670	−0.311008
$532$	13.7430	0.595835
$533$	−26.6111	−1.15266
$534$	18.9267	0.819037
$535$	−4.45011	−0.192395
$536$	−25.9593	−1.12127
$537$	8.91796	0.384838
$538$	−34.0266	−1.46699
$539$	0.531727	0.0229031
$540$	22.6092	0.972945
$541$	−37.1191	−1.59588	−0.797938	−	0.602740i	$-0.794076\pi$
$541$	−37.1191	−1.59588	−0.797938	+	0.602740i	$0.794076\pi$
$542$	−54.5831	−2.34455
$543$	16.7653	0.719467
$544$	21.5871	0.925540
$545$	−72.2438	−3.09458
$546$	−39.7502	−1.70115
$547$	23.0677	0.986305	0.493153	−	0.869943i	$-0.335844\pi$
$547$	23.0677	0.986305	0.493153	+	0.869943i	$0.335844\pi$
$548$	96.7904	4.13468
$549$	−0.316579	−0.0135113
$550$	2.10138	0.0896030
$551$	5.87063	0.250097
$552$	68.1041	2.89870
$553$	−32.7138	−1.39113
$554$	−59.1420	−2.51270
$555$	31.6695	1.34429
$556$	80.1974	3.40113
$557$	−17.3455	−0.734952	−0.367476	−	0.930033i	$-0.619778\pi$
$557$	−17.3455	−0.734952	−0.367476	+	0.930033i	$0.619778\pi$
$558$	17.5243	0.741864
$559$	−46.0807	−1.94900
$560$	241.300	10.1968
$561$	−0.0630788	−0.00266319
$562$	−9.03897	−0.381286
$563$	−16.5654	−0.698147	−0.349074	−	0.937095i	$-0.613504\pi$
$563$	−16.5654	−0.698147	−0.349074	+	0.937095i	$0.613504\pi$
$564$	−18.3791	−0.773900
$565$	−67.0299	−2.81997
$566$	18.2226	0.765955
$567$	−3.92805	−0.164963
$568$	151.223	6.34517
$569$	−15.3449	−0.643291	−0.321646	−	0.946860i	$-0.604236\pi$
$569$	−15.3449	−0.643291	−0.321646	+	0.946860i	$0.604236\pi$
$570$	−7.26713	−0.304386
$571$	10.6263	0.444697	0.222349	−	0.974967i	$-0.428628\pi$
$571$	10.6263	0.444697	0.222349	+	0.974967i	$0.428628\pi$
$572$	−1.27470	−0.0532978
$573$	11.6978	0.488682
$574$	−76.9635	−3.21239
$575$	−88.2388	−3.67981
$576$	29.3044	1.22102
$577$	−15.2805	−0.636137	−0.318069	−	0.948068i	$-0.603034\pi$
$577$	−15.2805	−0.636137	−0.318069	+	0.948068i	$0.603034\pi$
$578$	2.72963	0.113538
$579$	−19.4276	−0.807385
$580$	206.791	8.58651
$581$	−19.1604	−0.794907
$582$	−15.2072	−0.630357
$583$	−0.305279	−0.0126434
$584$	−72.3885	−2.99546
$585$	15.3773	0.635771
$586$	28.6155	1.18210
$587$	10.3072	0.425423	0.212711	−	0.977115i	$-0.431771\pi$
$587$	10.3072	0.425423	0.212711	+	0.977115i	$0.431771\pi$
$588$	−45.9484	−1.89488
$589$	−4.12076	−0.169793
$590$	81.1414	3.34054
$591$	−6.55972	−0.269831
$592$	113.079	4.64751
$593$	−29.3815	−1.20655	−0.603277	−	0.797532i	$-0.706139\pi$
$593$	−29.3815	−1.20655	−0.603277	+	0.797532i	$0.706139\pi$
$594$	−0.172182	−0.00706470
$595$	16.2928	0.667941
$596$	30.4753	1.24832
$597$	−22.2820	−0.911942
$598$	73.1652	2.99195
$599$	−28.9785	−1.18403	−0.592015	−	0.805927i	$-0.701667\pi$
$599$	−28.9785	−1.18403	−0.592015	+	0.805927i	$0.701667\pi$
$600$	−114.960	−4.69324
$601$	5.77567	0.235595	0.117797	−	0.993038i	$-0.462417\pi$
$601$	5.77567	0.235595	0.117797	+	0.993038i	$0.462417\pi$
$602$	−133.272	−5.43177
$603$	−2.75590	−0.112229
$604$	49.9364	2.03188
$605$	45.6095	1.85429
$606$	7.56226	0.307196
$607$	22.0810	0.896240	0.448120	−	0.893973i	$-0.352094\pi$
$607$	22.0810	0.896240	0.448120	+	0.893973i	$0.352094\pi$
$608$	−13.8559	−0.561930
$609$	−35.9271	−1.45584
$610$	3.58431	0.145124
$611$	−12.5002	−0.505705
$612$	5.45086	0.220338
$613$	−2.13895	−0.0863914	−0.0431957	−	0.999067i	$-0.513754\pi$
$613$	−2.13895	−0.0863914	−0.0431957	+	0.999067i	$0.513754\pi$
$614$	69.3900	2.80035
$615$	29.7731	1.20057
$616$	−2.33395	−0.0940374
$617$	13.4880	0.543006	0.271503	−	0.962438i	$-0.412479\pi$
$617$	13.4880	0.543006	0.271503	+	0.962438i	$0.412479\pi$
$618$	−17.8768	−0.719112
$619$	18.2801	0.734741	0.367370	−	0.930075i	$-0.380258\pi$
$619$	18.2801	0.734741	0.367370	+	0.930075i	$0.380258\pi$
$620$	−145.152	−5.82945
$621$	7.23007	0.290133
$622$	−89.1534	−3.57473
$623$	27.2363	1.09120
$624$	54.9059	2.19799
$625$	62.9258	2.51703
$626$	25.5554	1.02140
$627$	0.0404877	0.00161692
$628$	−5.45086	−0.217513
$629$	7.63521	0.304436
$630$	44.4734	1.77186
$631$	10.8376	0.431438	0.215719	−	0.976456i	$-0.430791\pi$
$631$	10.8376	0.431438	0.215719	+	0.976456i	$0.430791\pi$
$632$	78.4485	3.12051
$633$	7.05989	0.280606
$634$	2.84580	0.113021
$635$	91.4073	3.62739
$636$	26.3803	1.04605
$637$	−31.2510	−1.23821
$638$	−1.57482	−0.0623479
$639$	16.0541	0.635091
$640$	−152.706	−6.03622
$641$	14.0005	0.552986	0.276493	−	0.961016i	$-0.410828\pi$
$641$	14.0005	0.552986	0.276493	+	0.961016i	$0.410828\pi$
$642$	−2.92856	−0.115581
$643$	−7.54396	−0.297505	−0.148752	−	0.988874i	$-0.547526\pi$
$643$	−7.54396	−0.297505	−0.148752	+	0.988874i	$0.547526\pi$
$644$	154.805	6.10017
$645$	51.5561	2.03002
$646$	−1.75204	−0.0689329
$647$	−10.2858	−0.404378	−0.202189	−	0.979347i	$-0.564806\pi$
$647$	−10.2858	−0.404378	−0.202189	+	0.979347i	$0.564806\pi$
$648$	9.41956	0.370035
$649$	−0.452067	−0.0177452
$650$	−123.503	−4.84420
$651$	25.2183	0.988382
$652$	30.9471	1.21198
$653$	1.84062	0.0720289	0.0360145	−	0.999351i	$-0.488534\pi$
$653$	1.84062	0.0720289	0.0360145	+	0.999351i	$0.488534\pi$
$654$	−47.5427	−1.85907
$655$	37.8444	1.47870
$656$	106.308	4.15062
$657$	−7.68491	−0.299817
$658$	−36.1526	−1.40937
$659$	−23.1310	−0.901057	−0.450528	−	0.892762i	$-0.648764\pi$
$659$	−23.1310	−0.901057	−0.450528	+	0.892762i	$0.648764\pi$
$660$	1.42616	0.0555133
$661$	13.9045	0.540824	0.270412	−	0.962745i	$-0.412840\pi$
$661$	13.9045	0.540824	0.270412	+	0.962745i	$0.412840\pi$
$662$	−34.0962	−1.32519
$663$	3.70731	0.143980
$664$	45.9471	1.78309
$665$	−10.4577	−0.405532
$666$	20.8413	0.807583
$667$	66.1284	2.56050
$668$	57.4314	2.22209
$669$	−3.23763	−0.125174
$670$	31.2023	1.20545
$671$	−0.0199694	−0.000770911 0
$672$	84.7952	3.27105
$673$	1.88717	0.0727450	0.0363725	−	0.999338i	$-0.488420\pi$
$673$	1.88717	0.0727450	0.0363725	+	0.999338i	$0.488420\pi$
$674$	54.4075	2.09570
$675$	−12.2044	−0.469748
$676$	4.05619	0.156007
$677$	19.3699	0.744447	0.372224	−	0.928143i	$-0.378595\pi$
$677$	19.3699	0.744447	0.372224	+	0.928143i	$0.378595\pi$
$678$	−44.1115	−1.69409
$679$	−21.8838	−0.839822
$680$	−39.0707	−1.49829
$681$	4.77404	0.182942
$682$	1.10541	0.0423285
$683$	−25.6895	−0.982983	−0.491491	−	0.870882i	$-0.663548\pi$
$683$	−25.6895	−0.982983	−0.491491	+	0.870882i	$0.663548\pi$
$684$	−3.49868	−0.133776
$685$	−73.6525	−2.81412
$686$	−15.3279	−0.585224
$687$	−10.8139	−0.412577
$688$	184.086	7.01820
$689$	17.9421	0.683538
$690$	−81.8589	−3.11631
$691$	−18.8186	−0.715894	−0.357947	−	0.933742i	$-0.616523\pi$
$691$	−18.8186	−0.715894	−0.357947	+	0.933742i	$0.616523\pi$
$692$	−105.838	−4.02336
$693$	−0.247777	−0.00941226
$694$	29.8480	1.13302
$695$	−61.0260	−2.31485
$696$	86.1542	3.26567
$697$	7.17802	0.271887
$698$	−10.0373	−0.379917
$699$	−23.7254	−0.897376
$700$	−261.312	−9.87666
$701$	−4.80306	−0.181409	−0.0907046	−	0.995878i	$-0.528912\pi$
$701$	−4.80306	−0.181409	−0.0907046	+	0.995878i	$0.528912\pi$
$702$	10.1196	0.381939
$703$	−4.90072	−0.184834
$704$	1.84849	0.0696675
$705$	13.9855	0.526726
$706$	100.024	3.76444
$707$	10.8824	0.409275
$708$	39.0647	1.46814
$709$	15.1202	0.567853	0.283926	−	0.958846i	$-0.408363\pi$
$709$	15.1202	0.567853	0.283926	+	0.958846i	$0.408363\pi$
$710$	−181.765	−6.82151
$711$	8.32825	0.312334
$712$	−65.3133	−2.44772
$713$	−46.4174	−1.73835
$714$	10.7221	0.401265
$715$	0.969979	0.0362752
$716$	−48.6106	−1.81666
$717$	−11.3094	−0.422358
$718$	−15.9673	−0.595894
$719$	−2.57567	−0.0960562	−0.0480281	−	0.998846i	$-0.515294\pi$
$719$	−2.57567	−0.0960562	−0.0480281	+	0.998846i	$0.515294\pi$
$720$	−61.4299	−2.28936
$721$	−25.7255	−0.958069
$722$	−50.7383	−1.88829
$723$	18.6398	0.693222
$724$	−91.3852	−3.39630
$725$	−111.625	−4.14566
$726$	30.0150	1.11396
$727$	46.2740	1.71621	0.858103	−	0.513477i	$-0.171643\pi$
$727$	46.2740	1.71621	0.858103	+	0.513477i	$0.171643\pi$
$728$	137.172	5.08394
$729$	1.00000	0.0370370
$730$	87.0086	3.22033
$731$	12.4297	0.459728
$732$	1.72563	0.0637810
$733$	11.9307	0.440671	0.220336	−	0.975424i	$-0.429285\pi$
$733$	11.9307	0.440671	0.220336	+	0.975424i	$0.429285\pi$
$734$	44.0075	1.62435
$735$	34.9643	1.28968
$736$	−156.076	−5.75305
$737$	−0.173839	−0.00640343
$738$	19.5933	0.721240
$739$	−4.08403	−0.150234	−0.0751168	−	0.997175i	$-0.523933\pi$
$739$	−4.08403	−0.150234	−0.0751168	+	0.997175i	$0.523933\pi$
$740$	−172.626	−6.34585
$741$	−2.37957	−0.0874156
$742$	51.8912	1.90499
$743$	−24.9510	−0.915364	−0.457682	−	0.889116i	$-0.651320\pi$
$743$	−24.9510	−0.915364	−0.457682	+	0.889116i	$0.651320\pi$
$744$	−60.4741	−2.21709
$745$	−23.1901	−0.849619
$746$	84.6203	3.09817
$747$	4.87784	0.178471
$748$	0.343834	0.0125718
$749$	−4.21432	−0.153988
$750$	81.5685	2.97846
$751$	−23.6816	−0.864153	−0.432077	−	0.901837i	$-0.642219\pi$
$751$	−23.6816	−0.864153	−0.432077	+	0.901837i	$0.642219\pi$
$752$	49.9366	1.82100
$753$	17.1930	0.626548
$754$	92.5566	3.37071
$755$	−37.9990	−1.38292
$756$	21.4112	0.778720
$757$	−35.5066	−1.29051	−0.645255	−	0.763968i	$-0.723249\pi$
$757$	−35.5066	−1.29051	−0.645255	+	0.763968i	$0.723249\pi$
$758$	−20.7374	−0.753216
$759$	0.456064	0.0165541
$760$	25.0779	0.909669
$761$	−41.4324	−1.50192	−0.750962	−	0.660345i	$-0.770410\pi$
$761$	−41.4324	−1.50192	−0.750962	+	0.660345i	$0.770410\pi$
$762$	60.1540	2.17915
$763$	−68.4160	−2.47682
$764$	−63.7630	−2.30686
$765$	−4.14782	−0.149965
$766$	55.3202	1.99880
$767$	26.5692	0.959357
$768$	−41.8848	−1.51139
$769$	−26.0162	−0.938169	−0.469085	−	0.883153i	$-0.655416\pi$
$769$	−26.0162	−0.938169	−0.469085	+	0.883153i	$0.655416\pi$
$770$	2.80533	0.101097
$771$	−18.6067	−0.670106
$772$	105.897	3.81133
$773$	−6.28144	−0.225928	−0.112964	−	0.993599i	$-0.536034\pi$
$773$	−6.28144	−0.225928	−0.112964	+	0.993599i	$0.536034\pi$
$774$	33.9284	1.21953
$775$	78.3530	2.81452
$776$	52.4778	1.88384
$777$	29.9915	1.07594
$778$	77.1590	2.76628
$779$	−4.60727	−0.165073
$780$	−83.8193	−3.00121
$781$	1.01267	0.0362363
$782$	−19.7354	−0.705736
$783$	9.14630	0.326862
$784$	124.843	4.45869
$785$	4.14782	0.148042
$786$	24.9049	0.888329
$787$	29.3060	1.04464	0.522322	−	0.852748i	$-0.325066\pi$
$787$	29.3060	1.04464	0.522322	+	0.852748i	$0.325066\pi$
$788$	35.7561	1.27376
$789$	−14.2568	−0.507554
$790$	−94.2924	−3.35477
$791$	−63.4783	−2.25703
$792$	0.594175	0.0211131
$793$	1.17366	0.0416777
$794$	23.9809	0.851049
$795$	−20.0740	−0.711951
$796$	121.456	4.30490
$797$	22.3796	0.792727	0.396364	−	0.918094i	$-0.370272\pi$
$797$	22.3796	0.792727	0.396364	+	0.918094i	$0.370272\pi$
$798$	−6.88208	−0.243623
$799$	3.37178	0.119285
$800$	263.458	9.31465
$801$	−6.93379	−0.244994
$802$	35.3010	1.24652
$803$	−0.484755	−0.0171066
$804$	15.0220	0.529785
$805$	−117.798	−4.15185
$806$	−64.9681	−2.28840
$807$	12.4656	0.438812
$808$	−26.0963	−0.918065
$809$	38.0513	1.33781	0.668907	−	0.743346i	$-0.266763\pi$
$809$	38.0513	1.33781	0.668907	+	0.743346i	$0.266763\pi$
$810$	−11.3220	−0.397815
$811$	−26.4186	−0.927682	−0.463841	−	0.885918i	$-0.653529\pi$
$811$	−26.4186	−0.927682	−0.463841	+	0.885918i	$0.653529\pi$
$812$	195.834	6.87242
$813$	19.9965	0.701310
$814$	1.31464	0.0460782
$815$	−23.5491	−0.824889
$816$	−14.8102	−0.518460
$817$	−7.97810	−0.279118
$818$	−52.5352	−1.83685
$819$	14.5625	0.508855
$820$	−162.289	−5.66739
$821$	25.3571	0.884969	0.442485	−	0.896776i	$-0.354097\pi$
$821$	25.3571	0.884969	0.442485	+	0.896776i	$0.354097\pi$
$822$	−48.4697	−1.69058
$823$	−0.688866	−0.0240124	−0.0120062	−	0.999928i	$-0.503822\pi$
$823$	−0.688866	−0.0240124	−0.0120062	+	0.999928i	$0.503822\pi$
$824$	61.6905	2.14909
$825$	−0.769840	−0.0268024
$826$	76.8421	2.67368
$827$	53.5585	1.86241	0.931206	−	0.364494i	$-0.118758\pi$
$827$	53.5585	1.86241	0.931206	+	0.364494i	$0.118758\pi$
$828$	−39.4101	−1.36960
$829$	39.2914	1.36465	0.682324	−	0.731050i	$-0.260969\pi$
$829$	39.2914	1.36465	0.682324	+	0.731050i	$0.260969\pi$
$830$	−55.2269	−1.91695
$831$	21.6667	0.751609
$832$	−108.640	−3.76643
$833$	8.42957	0.292067
$834$	−40.1604	−1.39064
$835$	−43.7023	−1.51238
$836$	−0.220693	−0.00763282
$837$	−6.42005	−0.221909
$838$	54.1038	1.86898
$839$	32.7204	1.12963	0.564817	−	0.825216i	$-0.308947\pi$
$839$	32.7204	1.12963	0.564817	+	0.825216i	$0.308947\pi$
$840$	−153.471	−5.29527
$841$	54.6548	1.88465
$842$	−0.508840	−0.0175358
$843$	3.31143	0.114052
$844$	−38.4825	−1.32462
$845$	−3.08655	−0.106181
$846$	9.20370	0.316430
$847$	43.1929	1.48413
$848$	−71.6760	−2.46136
$849$	−6.67587	−0.229115
$850$	33.3135	1.14264
$851$	−55.2031	−1.89234
$852$	−87.5088	−2.99800
$853$	−1.45069	−0.0496706	−0.0248353	−	0.999692i	$-0.507906\pi$
$853$	−1.45069	−0.0496706	−0.0248353	+	0.999692i	$0.507906\pi$
$854$	3.39439	0.116154
$855$	2.66232	0.0910493
$856$	10.1061	0.345418
$857$	−47.1759	−1.61150	−0.805748	−	0.592258i	$-0.798237\pi$
$857$	−47.1759	−1.61150	−0.805748	+	0.592258i	$0.798237\pi$
$858$	0.638330	0.0217922
$859$	33.0964	1.12923	0.564617	−	0.825353i	$-0.309024\pi$
$859$	33.0964	1.12923	0.564617	+	0.825353i	$0.309024\pi$
$860$	−281.025	−9.58288
$861$	28.1956	0.960904
$862$	−88.0481	−2.99893
$863$	−29.2110	−0.994354	−0.497177	−	0.867649i	$-0.665630\pi$
$863$	−29.2110	−0.994354	−0.497177	+	0.867649i	$0.665630\pi$
$864$	−21.5871	−0.734408
$865$	80.5373	2.73835
$866$	−11.9872	−0.407341
$867$	−1.00000	−0.0339618
$868$	−137.461	−4.66574
$869$	0.525336	0.0178208
$870$	−103.554	−3.51082
$871$	10.2170	0.346188
$872$	164.063	5.55588
$873$	5.57115	0.188555
$874$	12.6673	0.428479
$875$	117.380	3.96818
$876$	41.8894	1.41531
$877$	−7.80243	−0.263469	−0.131735	−	0.991285i	$-0.542055\pi$
$877$	−7.80243	−0.263469	−0.131735	+	0.991285i	$0.542055\pi$
$878$	53.8332	1.81678
$879$	−10.4833	−0.353593
$880$	−3.87493	−0.130624
$881$	26.0101	0.876302	0.438151	−	0.898901i	$-0.355634\pi$
$881$	26.0101	0.876302	0.438151	+	0.898901i	$0.355634\pi$
$882$	23.0096	0.774772
$883$	−37.7604	−1.27074	−0.635369	−	0.772209i	$-0.719152\pi$
$883$	−37.7604	−1.27074	−0.635369	+	0.772209i	$0.719152\pi$
$884$	−20.2080	−0.679669
$885$	−29.7262	−0.999235
$886$	12.0041	0.403287
$887$	59.0884	1.98399	0.991997	−	0.126258i	$-0.0402967\pi$
$887$	59.0884	1.98399	0.991997	+	0.126258i	$0.0402967\pi$
$888$	−71.9203	−2.41349
$889$	86.5641	2.90327
$890$	78.5044	2.63147
$891$	0.0630788	0.00211322
$892$	17.6479	0.590894
$893$	−2.16421	−0.0724224
$894$	−15.2611	−0.510407
$895$	36.9901	1.23644
$896$	−144.614	−4.83123
$897$	−26.8041	−0.894963
$898$	−99.8556	−3.33223
$899$	−58.7197	−1.95841
$900$	66.5246	2.21749
$901$	−4.83965	−0.161232
$902$	1.23592	0.0411517
$903$	48.8244	1.62477
$904$	152.223	5.06285
$905$	69.5394	2.31157
$906$	−25.0066	−0.830789
$907$	−34.2461	−1.13712	−0.568561	−	0.822641i	$-0.692500\pi$
$907$	−34.2461	−1.13712	−0.568561	+	0.822641i	$0.692500\pi$
$908$	−26.0227	−0.863592
$909$	−2.77044	−0.0918896
$910$	−164.877	−5.46560
$911$	−21.6593	−0.717606	−0.358803	−	0.933413i	$-0.616815\pi$
$911$	−21.6593	−0.717606	−0.358803	+	0.933413i	$0.616815\pi$
$912$	9.50604	0.314776
$913$	0.307688	0.0101830
$914$	74.1185	2.45162
$915$	−1.31311	−0.0434102
$916$	58.9452	1.94760
$917$	35.8392	1.18352
$918$	−2.72963	−0.0900911
$919$	−4.74579	−0.156549	−0.0782747	−	0.996932i	$-0.524941\pi$
$919$	−4.74579	−0.156549	−0.0782747	+	0.996932i	$0.524941\pi$
$920$	282.484	9.31321
$921$	−25.4210	−0.837652
$922$	55.8304	1.83868
$923$	−59.5176	−1.95904
$924$	1.35060	0.0444313
$925$	93.1833	3.06385
$926$	−22.3362	−0.734015
$927$	6.54919	0.215104
$928$	−197.442	−6.48136
$929$	43.5304	1.42819	0.714093	−	0.700051i	$-0.246839\pi$
$929$	43.5304	1.42819	0.714093	+	0.700051i	$0.246839\pi$
$930$	72.6878	2.38353
$931$	−5.41059	−0.177325
$932$	129.324	4.23614
$933$	32.6614	1.06929
$934$	−87.4512	−2.86149
$935$	−0.261640	−0.00855653
$936$	−34.9212	−1.14144
$937$	−5.74388	−0.187644	−0.0938222	−	0.995589i	$-0.529909\pi$
$937$	−5.74388	−0.187644	−0.0938222	+	0.995589i	$0.529909\pi$
$938$	29.5490	0.964810
$939$	−9.36224	−0.305525
$940$	−76.2332	−2.48645
$941$	−16.8669	−0.549844	−0.274922	−	0.961467i	$-0.588652\pi$
$941$	−16.8669	−0.549844	−0.274922	+	0.961467i	$0.588652\pi$
$942$	2.72963	0.0889360
$943$	−51.8976	−1.69002
$944$	−106.140	−3.45456
$945$	−16.2928	−0.530006
$946$	2.14016	0.0695827
$947$	37.4578	1.21721	0.608607	−	0.793472i	$-0.291729\pi$
$947$	37.4578	1.21721	0.608607	+	0.793472i	$0.291729\pi$
$948$	−45.3961	−1.47440
$949$	28.4903	0.924835
$950$	−21.3826	−0.693742
$951$	−1.04256	−0.0338074
$952$	−37.0005	−1.19919
$953$	28.1283	0.911165	0.455583	−	0.890193i	$-0.349431\pi$
$953$	28.1283	0.911165	0.455583	+	0.890193i	$0.349431\pi$
$954$	−13.2104	−0.427704
$955$	48.5203	1.57008
$956$	61.6460	1.99378
$957$	0.576938	0.0186497
$958$	−82.4528	−2.66393
$959$	−69.7500	−2.25234
$960$	121.549	3.92299
$961$	10.2170	0.329581
$962$	−77.2650	−2.49112
$963$	1.07288	0.0345730
$964$	−101.603	−3.27241
$965$	−80.5824	−2.59404
$966$	−77.5216	−2.49422
$967$	−8.23502	−0.264820	−0.132410	−	0.991195i	$-0.542272\pi$
$967$	−8.23502	−0.264820	−0.132410	+	0.991195i	$0.542272\pi$
$968$	−103.578	−3.32911
$969$	0.641859	0.0206195
$970$	−63.0766	−2.02527
$971$	33.3465	1.07014	0.535070	−	0.844808i	$-0.320285\pi$
$971$	33.3465	1.07014	0.535070	+	0.844808i	$0.320285\pi$
$972$	−5.45086	−0.174836
$973$	−57.7926	−1.85274
$974$	−46.8241	−1.50034
$975$	45.2456	1.44902
$976$	−4.68859	−0.150078
$977$	−22.6696	−0.725265	−0.362633	−	0.931932i	$-0.618122\pi$
$977$	−22.6696	−0.725265	−0.362633	+	0.931932i	$0.618122\pi$
$978$	−15.4973	−0.495551
$979$	−0.437375	−0.0139786
$980$	−190.586	−6.08804
$981$	17.4173	0.556091
$982$	84.0718	2.68284
$983$	−24.5626	−0.783425	−0.391713	−	0.920088i	$-0.628117\pi$
$983$	−24.5626	−0.783425	−0.391713	+	0.920088i	$0.628117\pi$
$984$	−67.6138	−2.15545
$985$	−27.2085	−0.866936
$986$	−24.9660	−0.795079
$987$	13.2445	0.421577
$988$	12.9707	0.412653
$989$	−89.8675	−2.85762
$990$	−0.714178	−0.0226981
$991$	−18.4806	−0.587055	−0.293528	−	0.955951i	$-0.594829\pi$
$991$	−18.4806	−0.587055	−0.293528	+	0.955951i	$0.594829\pi$
$992$	138.590	4.40025
$993$	12.4912	0.396395
$994$	−172.134	−5.45976
$995$	−92.4218	−2.92997
$996$	−26.5884	−0.842487
$997$	−10.9802	−0.347747	−0.173874	−	0.984768i	$-0.555628\pi$
$997$	−10.9802	−0.347747	−0.173874	+	0.984768i	$0.555628\pi$
$998$	5.30044	0.167783
$999$	−7.63521	−0.241567

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.62	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.62	✓	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)

\(f(q)\)	\(=\)	\(q+2.72963 q^{2} -1.00000 q^{3} +5.45086 q^{4} -4.14782 q^{5} -2.72963 q^{6} -3.92805 q^{7} +9.41956 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.72963 q^{2} -1.00000 q^{3} +5.45086 q^{4} -4.14782 q^{5} -2.72963 q^{6} -3.92805 q^{7} +9.41956 q^{8} +1.00000 q^{9} -11.3220 q^{10} +0.0630788 q^{11} -5.45086 q^{12} -3.70731 q^{13} -10.7221 q^{14} +4.14782 q^{15} +14.8102 q^{16} +1.00000 q^{17} +2.72963 q^{18} -0.641859 q^{19} -22.6092 q^{20} +3.92805 q^{21} +0.172182 q^{22} -7.23007 q^{23} -9.41956 q^{24} +12.2044 q^{25} -10.1196 q^{26} -1.00000 q^{27} -21.4112 q^{28} -9.14630 q^{29} +11.3220 q^{30} +6.42005 q^{31} +21.5871 q^{32} -0.0630788 q^{33} +2.72963 q^{34} +16.2928 q^{35} +5.45086 q^{36} +7.63521 q^{37} -1.75204 q^{38} +3.70731 q^{39} -39.0707 q^{40} +7.17802 q^{41} +10.7221 q^{42} +12.4297 q^{43} +0.343834 q^{44} -4.14782 q^{45} -19.7354 q^{46} +3.37178 q^{47} -14.8102 q^{48} +8.42957 q^{49} +33.3135 q^{50} -1.00000 q^{51} -20.2080 q^{52} -4.83965 q^{53} -2.72963 q^{54} -0.261640 q^{55} -37.0005 q^{56} +0.641859 q^{57} -24.9660 q^{58} -7.16670 q^{59} +22.6092 q^{60} -0.316579 q^{61} +17.5243 q^{62} -3.92805 q^{63} +29.3044 q^{64} +15.3773 q^{65} -0.172182 q^{66} -2.75590 q^{67} +5.45086 q^{68} +7.23007 q^{69} +44.4734 q^{70} +16.0541 q^{71} +9.41956 q^{72} -7.68491 q^{73} +20.8413 q^{74} -12.2044 q^{75} -3.49868 q^{76} -0.247777 q^{77} +10.1196 q^{78} +8.32825 q^{79} -61.4299 q^{80} +1.00000 q^{81} +19.5933 q^{82} +4.87784 q^{83} +21.4112 q^{84} -4.14782 q^{85} +33.9284 q^{86} +9.14630 q^{87} +0.594175 q^{88} -6.93379 q^{89} -11.3220 q^{90} +14.5625 q^{91} -39.4101 q^{92} -6.42005 q^{93} +9.20370 q^{94} +2.66232 q^{95} -21.5871 q^{96} +5.57115 q^{97} +23.0096 q^{98} +0.0630788 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 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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