LMFDB - Embedded newform 8007.2.a.g.1.19

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:	$56$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.15978 q^{2} -1.00000 q^{3} -0.654916 q^{4} -0.00396327 q^{5} +1.15978 q^{6} +3.25506 q^{7} +3.07911 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.15978 q^{2} -1.00000 q^{3} -0.654916 q^{4} -0.00396327 q^{5} +1.15978 q^{6} +3.25506 q^{7} +3.07911 q^{8} +1.00000 q^{9} +0.00459651 q^{10} -3.30448 q^{11} +0.654916 q^{12} -3.21522 q^{13} -3.77514 q^{14} +0.00396327 q^{15} -2.26125 q^{16} -1.00000 q^{17} -1.15978 q^{18} -6.76736 q^{19} +0.00259561 q^{20} -3.25506 q^{21} +3.83246 q^{22} +5.73943 q^{23} -3.07911 q^{24} -4.99998 q^{25} +3.72895 q^{26} -1.00000 q^{27} -2.13179 q^{28} -7.08433 q^{29} -0.00459651 q^{30} +1.78690 q^{31} -3.53567 q^{32} +3.30448 q^{33} +1.15978 q^{34} -0.0129007 q^{35} -0.654916 q^{36} -4.03845 q^{37} +7.84863 q^{38} +3.21522 q^{39} -0.0122034 q^{40} -9.11345 q^{41} +3.77514 q^{42} -1.87011 q^{43} +2.16415 q^{44} -0.00396327 q^{45} -6.65646 q^{46} -2.26637 q^{47} +2.26125 q^{48} +3.59539 q^{49} +5.79887 q^{50} +1.00000 q^{51} +2.10570 q^{52} -6.29550 q^{53} +1.15978 q^{54} +0.0130965 q^{55} +10.0227 q^{56} +6.76736 q^{57} +8.21625 q^{58} +11.5523 q^{59} -0.00259561 q^{60} -2.66832 q^{61} -2.07240 q^{62} +3.25506 q^{63} +8.62310 q^{64} +0.0127428 q^{65} -3.83246 q^{66} -3.39566 q^{67} +0.654916 q^{68} -5.73943 q^{69} +0.0149619 q^{70} +5.09193 q^{71} +3.07911 q^{72} -2.53864 q^{73} +4.68371 q^{74} +4.99998 q^{75} +4.43205 q^{76} -10.7563 q^{77} -3.72895 q^{78} +12.0610 q^{79} +0.00896196 q^{80} +1.00000 q^{81} +10.5696 q^{82} +8.95769 q^{83} +2.13179 q^{84} +0.00396327 q^{85} +2.16892 q^{86} +7.08433 q^{87} -10.1749 q^{88} +2.66196 q^{89} +0.00459651 q^{90} -10.4657 q^{91} -3.75884 q^{92} -1.78690 q^{93} +2.62848 q^{94} +0.0268209 q^{95} +3.53567 q^{96} +16.6487 q^{97} -4.16985 q^{98} -3.30448 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) $ 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.15978	−0.820087	−0.410043	−	0.912066i	$-0.634486\pi$
$2$	−1.15978	−0.820087	−0.410043	+	0.912066i	$0.634486\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.654916	−0.327458
$5$	−0.00396327	−0.00177243	−0.000886214	−	1.00000i	$-0.500282\pi$
$5$	−0.00396327	−0.00177243	−0.000886214		1.00000i	$0.500282\pi$
$6$	1.15978	0.473477
$7$	3.25506	1.23030	0.615148	−	0.788412i	$-0.289096\pi$
$7$	3.25506	1.23030	0.615148	+	0.788412i	$0.289096\pi$
$8$	3.07911	1.08863
$9$	1.00000	0.333333
$10$	0.00459651	0.00145355
$11$	−3.30448	−0.996338	−0.498169	−	0.867080i	$-0.665994\pi$
$11$	−3.30448	−0.996338	−0.498169	+	0.867080i	$0.665994\pi$
$12$	0.654916	0.189058
$13$	−3.21522	−0.891743	−0.445871	−	0.895097i	$-0.647106\pi$
$13$	−3.21522	−0.891743	−0.445871	+	0.895097i	$0.647106\pi$
$14$	−3.77514	−1.00895
$15$	0.00396327	0.00102331
$16$	−2.26125	−0.565314
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.15978	−0.273362
$19$	−6.76736	−1.55254	−0.776269	−	0.630402i	$-0.782890\pi$
$19$	−6.76736	−1.55254	−0.776269	+	0.630402i	$0.782890\pi$
$20$	0.00259561	0.000580396 0
$21$	−3.25506	−0.710311
$22$	3.83246	0.817083
$23$	5.73943	1.19675	0.598376	−	0.801215i	$-0.295813\pi$
$23$	5.73943	1.19675	0.598376	+	0.801215i	$0.295813\pi$
$24$	−3.07911	−0.628521
$25$	−4.99998	−0.999997
$26$	3.72895	0.731306
$27$	−1.00000	−0.192450
$28$	−2.13179	−0.402870
$29$	−7.08433	−1.31553	−0.657764	−	0.753224i	$-0.728498\pi$
$29$	−7.08433	−1.31553	−0.657764	+	0.753224i	$0.728498\pi$
$30$	−0.00459651	−0.000839205 0
$31$	1.78690	0.320936	0.160468	−	0.987041i	$-0.448700\pi$
$31$	1.78690	0.320936	0.160468	+	0.987041i	$0.448700\pi$
$32$	−3.53567	−0.625024
$33$	3.30448	0.575236
$34$	1.15978	0.198900
$35$	−0.0129007	−0.00218061
$36$	−0.654916	−0.109153
$37$	−4.03845	−0.663917	−0.331959	−	0.943294i	$-0.607709\pi$
$37$	−4.03845	−0.663917	−0.331959	+	0.943294i	$0.607709\pi$
$38$	7.84863	1.27322
$39$	3.21522	0.514848
$40$	−0.0122034	−0.00192952
$41$	−9.11345	−1.42328	−0.711641	−	0.702543i	$-0.752048\pi$
$41$	−9.11345	−1.42328	−0.711641	+	0.702543i	$0.752048\pi$
$42$	3.77514	0.582517
$43$	−1.87011	−0.285190	−0.142595	−	0.989781i	$-0.545545\pi$
$43$	−1.87011	−0.285190	−0.142595	+	0.989781i	$0.545545\pi$
$44$	2.16415	0.326259
$45$	−0.00396327	−0.000590810 0
$46$	−6.65646	−0.981441
$47$	−2.26637	−0.330583	−0.165292	−	0.986245i	$-0.552857\pi$
$47$	−2.26637	−0.330583	−0.165292	+	0.986245i	$0.552857\pi$
$48$	2.26125	0.326384
$49$	3.59539	0.513627
$50$	5.79887	0.820084
$51$	1.00000	0.140028
$52$	2.10570	0.292008
$53$	−6.29550	−0.864753	−0.432377	−	0.901693i	$-0.642325\pi$
$53$	−6.29550	−0.864753	−0.432377	+	0.901693i	$0.642325\pi$
$54$	1.15978	0.157826
$55$	0.0130965	0.00176594
$56$	10.0227	1.33934
$57$	6.76736	0.896358
$58$	8.21625	1.07885
$59$	11.5523	1.50398	0.751990	−	0.659175i	$-0.229094\pi$
$59$	11.5523	1.50398	0.751990	+	0.659175i	$0.229094\pi$
$60$	−0.00259561	−0.000335092 0
$61$	−2.66832	−0.341643	−0.170821	−	0.985302i	$-0.554642\pi$
$61$	−2.66832	−0.341643	−0.170821	+	0.985302i	$0.554642\pi$
$62$	−2.07240	−0.263196
$63$	3.25506	0.410098
$64$	8.62310	1.07789
$65$	0.0127428	0.00158055
$66$	−3.83246	−0.471743
$67$	−3.39566	−0.414845	−0.207423	−	0.978251i	$-0.566508\pi$
$67$	−3.39566	−0.414845	−0.207423	+	0.978251i	$0.566508\pi$
$68$	0.654916	0.0794202
$69$	−5.73943	−0.690946
$70$	0.0149619	0.00178829
$71$	5.09193	0.604301	0.302150	−	0.953260i	$-0.402296\pi$
$71$	5.09193	0.604301	0.302150	+	0.953260i	$0.402296\pi$
$72$	3.07911	0.362877
$73$	−2.53864	−0.297125	−0.148563	−	0.988903i	$-0.547465\pi$
$73$	−2.53864	−0.297125	−0.148563	+	0.988903i	$0.547465\pi$
$74$	4.68371	0.544470
$75$	4.99998	0.577348
$76$	4.43205	0.508391
$77$	−10.7563	−1.22579
$78$	−3.72895	−0.422220
$79$	12.0610	1.35697	0.678486	−	0.734614i	$-0.262637\pi$
$79$	12.0610	1.35697	0.678486	+	0.734614i	$0.262637\pi$
$80$	0.00896196	0.00100198
$81$	1.00000	0.111111
$82$	10.5696	1.16721
$83$	8.95769	0.983234	0.491617	−	0.870812i	$-0.336406\pi$
$83$	8.95769	0.983234	0.491617	+	0.870812i	$0.336406\pi$
$84$	2.13179	0.232597
$85$	0.00396327	0.000429877 0
$86$	2.16892	0.233880
$87$	7.08433	0.759520
$88$	−10.1749	−1.08464
$89$	2.66196	0.282167	0.141084	−	0.989998i	$-0.454941\pi$
$89$	2.66196	0.282167	0.141084	+	0.989998i	$0.454941\pi$
$90$	0.00459651	0.000484515 0
$91$	−10.4657	−1.09711
$92$	−3.75884	−0.391886
$93$	−1.78690	−0.185293
$94$	2.62848	0.271107
$95$	0.0268209	0.00275176
$96$	3.53567	0.360858
$97$	16.6487	1.69042	0.845211	−	0.534433i	$-0.179475\pi$
$97$	16.6487	1.69042	0.845211	+	0.534433i	$0.179475\pi$
$98$	−4.16985	−0.421218
$99$	−3.30448	−0.332113
$100$	3.27457	0.327457
$101$	−5.45881	−0.543172	−0.271586	−	0.962414i	$-0.587548\pi$
$101$	−5.45881	−0.543172	−0.271586	+	0.962414i	$0.587548\pi$
$102$	−1.15978	−0.114835
$103$	5.20658	0.513019	0.256510	−	0.966542i	$-0.417427\pi$
$103$	5.20658	0.513019	0.256510	+	0.966542i	$0.417427\pi$
$104$	−9.90003	−0.970778
$105$	0.0129007	0.00125898
$106$	7.30138	0.709173
$107$	−11.7363	−1.13460	−0.567298	−	0.823513i	$-0.692011\pi$
$107$	−11.7363	−1.13460	−0.567298	+	0.823513i	$0.692011\pi$
$108$	0.654916	0.0630193
$109$	0.492676	0.0471898	0.0235949	−	0.999722i	$-0.492489\pi$
$109$	0.492676	0.0471898	0.0235949	+	0.999722i	$0.492489\pi$
$110$	−0.0151891	−0.00144822
$111$	4.03845	0.383313
$112$	−7.36051	−0.695503
$113$	3.41962	0.321691	0.160845	−	0.986980i	$-0.448578\pi$
$113$	3.41962	0.321691	0.160845	+	0.986980i	$0.448578\pi$
$114$	−7.84863	−0.735091
$115$	−0.0227469	−0.00212116
$116$	4.63964	0.430780
$117$	−3.21522	−0.297248
$118$	−13.3981	−1.23339
$119$	−3.25506	−0.298390
$120$	0.0122034	0.00111401
$121$	−0.0804200	−0.00731091
$122$	3.09465	0.280177
$123$	9.11345	0.821732
$124$	−1.17027	−0.105093
$125$	0.0396327	0.00354485
$126$	−3.77514	−0.336316
$127$	12.0447	1.06880	0.534399	−	0.845232i	$-0.320538\pi$
$127$	12.0447	1.06880	0.534399	+	0.845232i	$0.320538\pi$
$128$	−2.92954	−0.258937
$129$	1.87011	0.164654
$130$	−0.0147788	−0.00129619
$131$	−14.1655	−1.23764	−0.618821	−	0.785532i	$-0.712389\pi$
$131$	−14.1655	−1.23764	−0.618821	+	0.785532i	$0.712389\pi$
$132$	−2.16415	−0.188366
$133$	−22.0281	−1.91008
$134$	3.93821	0.340209
$135$	0.00396327	0.000341104 0
$136$	−3.07911	−0.264032
$137$	6.92072	0.591277	0.295638	−	0.955300i	$-0.404468\pi$
$137$	6.92072	0.591277	0.295638	+	0.955300i	$0.404468\pi$
$138$	6.65646	0.566635
$139$	17.6256	1.49499	0.747493	−	0.664269i	$-0.231257\pi$
$139$	17.6256	1.49499	0.747493	+	0.664269i	$0.231257\pi$
$140$	0.00844885	0.000714058 0
$141$	2.26637	0.190862
$142$	−5.90551	−0.495579
$143$	10.6246	0.888477
$144$	−2.26125	−0.188438
$145$	0.0280771	0.00233168
$146$	2.94426	0.243669
$147$	−3.59539	−0.296542
$148$	2.64485	0.217405
$149$	−6.50671	−0.533050	−0.266525	−	0.963828i	$-0.585876\pi$
$149$	−6.50671	−0.533050	−0.266525	+	0.963828i	$0.585876\pi$
$150$	−5.79887	−0.473476
$151$	17.4455	1.41969	0.709847	−	0.704356i	$-0.248764\pi$
$151$	17.4455	1.41969	0.709847	+	0.704356i	$0.248764\pi$
$152$	−20.8374	−1.69014
$153$	−1.00000	−0.0808452
$154$	12.4749	1.00525
$155$	−0.00708196	−0.000568837 0
$156$	−2.10570	−0.168591
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−13.9881	−1.11283
$159$	6.29550	0.499266
$160$	0.0140128	0.00110781
$161$	18.6821	1.47236
$162$	−1.15978	−0.0911207
$163$	4.71834	0.369569	0.184784	−	0.982779i	$-0.440841\pi$
$163$	4.71834	0.369569	0.184784	+	0.982779i	$0.440841\pi$
$164$	5.96854	0.466065
$165$	−0.0130965	−0.00101956
$166$	−10.3889	−0.806337
$167$	5.51629	0.426864	0.213432	−	0.976958i	$-0.431536\pi$
$167$	5.51629	0.426864	0.213432	+	0.976958i	$0.431536\pi$
$168$	−10.0227	−0.773267
$169$	−2.66233	−0.204795
$170$	−0.00459651	−0.000352537 0
$171$	−6.76736	−0.517513
$172$	1.22477	0.0933876
$173$	−2.55515	−0.194264	−0.0971322	−	0.995271i	$-0.530967\pi$
$173$	−2.55515	−0.194264	−0.0971322	+	0.995271i	$0.530967\pi$
$174$	−8.21625	−0.622872
$175$	−16.2752	−1.23029
$176$	7.47227	0.563243
$177$	−11.5523	−0.868323
$178$	−3.08728	−0.231401
$179$	−25.7232	−1.92264	−0.961319	−	0.275436i	$-0.911178\pi$
$179$	−25.7232	−1.92264	−0.961319	+	0.275436i	$0.911178\pi$
$180$	0.00259561	0.000193465 0
$181$	17.7789	1.32149	0.660747	−	0.750609i	$-0.270240\pi$
$181$	17.7789	1.32149	0.660747	+	0.750609i	$0.270240\pi$
$182$	12.1379	0.899723
$183$	2.66832	0.197248
$184$	17.6723	1.30282
$185$	0.0160055	0.00117675
$186$	2.07240	0.151956
$187$	3.30448	0.241647
$188$	1.48428	0.108252
$189$	−3.25506	−0.236770
$190$	−0.0311062	−0.00225668
$191$	11.7761	0.852086	0.426043	−	0.904703i	$-0.359907\pi$
$191$	11.7761	0.852086	0.426043	+	0.904703i	$0.359907\pi$
$192$	−8.62310	−0.622319
$193$	−3.94271	−0.283803	−0.141901	−	0.989881i	$-0.545322\pi$
$193$	−3.94271	−0.283803	−0.141901	+	0.989881i	$0.545322\pi$
$194$	−19.3088	−1.38629
$195$	−0.0127428	−0.000912531 0
$196$	−2.35467	−0.168191
$197$	−18.3470	−1.30717	−0.653586	−	0.756852i	$-0.726736\pi$
$197$	−18.3470	−1.30717	−0.653586	+	0.756852i	$0.726736\pi$
$198$	3.83246	0.272361
$199$	2.82963	0.200587	0.100294	−	0.994958i	$-0.468022\pi$
$199$	2.82963	0.200587	0.100294	+	0.994958i	$0.468022\pi$
$200$	−15.3955	−1.08863
$201$	3.39566	0.239511
$202$	6.33101	0.445448
$203$	−23.0599	−1.61849
$204$	−0.654916	−0.0458533
$205$	0.0361191	0.00252267
$206$	−6.03847	−0.420720
$207$	5.73943	0.398918
$208$	7.27044	0.504114
$209$	22.3626	1.54685
$210$	−0.0149619	−0.00103247
$211$	−9.43502	−0.649533	−0.324767	−	0.945794i	$-0.605286\pi$
$211$	−9.43502	−0.649533	−0.324767	+	0.945794i	$0.605286\pi$
$212$	4.12302	0.283170
$213$	−5.09193	−0.348893
$214$	13.6116	0.930467
$215$	0.00741177	0.000505479 0
$216$	−3.07911	−0.209507
$217$	5.81645	0.394846
$218$	−0.571395	−0.0386998
$219$	2.53864	0.171545
$220$	−0.00857713	−0.000578270 0
$221$	3.21522	0.216279
$222$	−4.68371	−0.314350
$223$	−20.7588	−1.39011	−0.695057	−	0.718954i	$-0.744621\pi$
$223$	−20.7588	−1.39011	−0.695057	+	0.718954i	$0.744621\pi$
$224$	−11.5088	−0.768965
$225$	−4.99998	−0.333332
$226$	−3.96600	−0.263814
$227$	9.19516	0.610304	0.305152	−	0.952304i	$-0.401293\pi$
$227$	9.19516	0.610304	0.305152	+	0.952304i	$0.401293\pi$
$228$	−4.43205	−0.293519
$229$	−0.278614	−0.0184113	−0.00920567	−	0.999958i	$-0.502930\pi$
$229$	−0.278614	−0.0184113	−0.00920567	+	0.999958i	$0.502930\pi$
$230$	0.0263813	0.00173953
$231$	10.7563	0.707710
$232$	−21.8135	−1.43212
$233$	−24.0505	−1.57560	−0.787800	−	0.615931i	$-0.788780\pi$
$233$	−24.0505	−1.57560	−0.787800	+	0.615931i	$0.788780\pi$
$234$	3.72895	0.243769
$235$	0.00898222	0.000585936 0
$236$	−7.56578	−0.492490
$237$	−12.0610	−0.783448
$238$	3.77514	0.244706
$239$	1.35012	0.0873319	0.0436660	−	0.999046i	$-0.486096\pi$
$239$	1.35012	0.0873319	0.0436660	+	0.999046i	$0.486096\pi$
$240$	−0.00896196	−0.000578492 0
$241$	13.8473	0.891986	0.445993	−	0.895037i	$-0.352851\pi$
$241$	13.8473	0.891986	0.445993	+	0.895037i	$0.352851\pi$
$242$	0.0932693	0.00599558
$243$	−1.00000	−0.0641500
$244$	1.74752	0.111874
$245$	−0.0142495	−0.000910366 0
$246$	−10.5696	−0.673892
$247$	21.7586	1.38446
$248$	5.50206	0.349381
$249$	−8.95769	−0.567670
$250$	−0.0459651	−0.00290709
$251$	−0.0436837	−0.00275729	−0.00137865	−	0.999999i	$-0.500439\pi$
$251$	−0.0436837	−0.00275729	−0.00137865	+	0.999999i	$0.500439\pi$
$252$	−2.13179	−0.134290
$253$	−18.9658	−1.19237
$254$	−13.9692	−0.876508
$255$	−0.00396327	−0.000248190 0
$256$	−13.8486	−0.865537
$257$	−6.45198	−0.402464	−0.201232	−	0.979544i	$-0.564494\pi$
$257$	−6.45198	−0.402464	−0.201232	+	0.979544i	$0.564494\pi$
$258$	−2.16892	−0.135031
$259$	−13.1454	−0.816814
$260$	−0.00834546	−0.000517564 0
$261$	−7.08433	−0.438509
$262$	16.4288	1.01497
$263$	3.89711	0.240306	0.120153	−	0.992755i	$-0.461661\pi$
$263$	3.89711	0.240306	0.120153	+	0.992755i	$0.461661\pi$
$264$	10.1749	0.626219
$265$	0.0249508	0.00153271
$266$	25.5477	1.56643
$267$	−2.66196	−0.162909
$268$	2.22387	0.135844
$269$	8.33075	0.507935	0.253967	−	0.967213i	$-0.418264\pi$
$269$	8.33075	0.507935	0.253967	+	0.967213i	$0.418264\pi$
$270$	−0.00459651	−0.000279735 0
$271$	10.4230	0.633155	0.316577	−	0.948567i	$-0.397466\pi$
$271$	10.4230	0.633155	0.316577	+	0.948567i	$0.397466\pi$
$272$	2.26125	0.137109
$273$	10.4657	0.633415
$274$	−8.02649	−0.484898
$275$	16.5223	0.996335
$276$	3.75884	0.226256
$277$	−24.9332	−1.49809	−0.749047	−	0.662517i	$-0.769488\pi$
$277$	−24.9332	−1.49809	−0.749047	+	0.662517i	$0.769488\pi$
$278$	−20.4418	−1.22602
$279$	1.78690	0.106979
$280$	−0.0397226	−0.00237388
$281$	17.8411	1.06431	0.532157	−	0.846646i	$-0.321382\pi$
$281$	17.8411	1.06431	0.532157	+	0.846646i	$0.321382\pi$
$282$	−2.62848	−0.156524
$283$	−7.63987	−0.454143	−0.227072	−	0.973878i	$-0.572915\pi$
$283$	−7.63987	−0.454143	−0.227072	+	0.973878i	$0.572915\pi$
$284$	−3.33478	−0.197883
$285$	−0.0268209	−0.00158873
$286$	−12.3222	−0.728628
$287$	−29.6648	−1.75106
$288$	−3.53567	−0.208341
$289$	1.00000	0.0588235
$290$	−0.0325632	−0.00191218
$291$	−16.6487	−0.975965
$292$	1.66260	0.0972960
$293$	34.0379	1.98852	0.994258	−	0.107006i	$-0.0341264\pi$
$293$	34.0379	1.98852	0.994258	+	0.107006i	$0.0341264\pi$
$294$	4.16985	0.243190
$295$	−0.0457849	−0.00266570
$296$	−12.4348	−0.722761
$297$	3.30448	0.191745
$298$	7.54633	0.437147
$299$	−18.4535	−1.06720
$300$	−3.27457	−0.189057
$301$	−6.08733	−0.350868
$302$	−20.2329	−1.16427
$303$	5.45881	0.313600
$304$	15.3027	0.877671
$305$	0.0105753	0.000605538 0
$306$	1.15978	0.0663001
$307$	26.3201	1.50217	0.751083	−	0.660208i	$-0.229532\pi$
$307$	26.3201	1.50217	0.751083	+	0.660208i	$0.229532\pi$
$308$	7.04444	0.401394
$309$	−5.20658	−0.296192
$310$	0.00821350	0.000466495 0
$311$	−25.0014	−1.41770	−0.708848	−	0.705361i	$-0.750785\pi$
$311$	−25.0014	−1.41770	−0.708848	+	0.705361i	$0.750785\pi$
$312$	9.90003	0.560479
$313$	−8.07270	−0.456296	−0.228148	−	0.973626i	$-0.573267\pi$
$313$	−8.07270	−0.456296	−0.228148	+	0.973626i	$0.573267\pi$
$314$	−1.15978	−0.0654500
$315$	−0.0129007	−0.000726870 0
$316$	−7.89895	−0.444351
$317$	1.16145	0.0652335	0.0326168	−	0.999468i	$-0.489616\pi$
$317$	1.16145	0.0652335	0.0326168	+	0.999468i	$0.489616\pi$
$318$	−7.30138	−0.409441
$319$	23.4100	1.31071
$320$	−0.0341757	−0.00191048
$321$	11.7363	0.655059
$322$	−21.6671	−1.20746
$323$	6.76736	0.376546
$324$	−0.654916	−0.0363842
$325$	16.0761	0.891740
$326$	−5.47222	−0.303078
$327$	−0.492676	−0.0272451
$328$	−28.0613	−1.54943
$329$	−7.37715	−0.406715
$330$	0.0151891	0.000836131 0
$331$	11.4650	0.630174	0.315087	−	0.949063i	$-0.397966\pi$
$331$	11.4650	0.630174	0.315087	+	0.949063i	$0.397966\pi$
$332$	−5.86653	−0.321968
$333$	−4.03845	−0.221306
$334$	−6.39768	−0.350065
$335$	0.0134579	0.000735284 0
$336$	7.36051	0.401549
$337$	5.70724	0.310893	0.155446	−	0.987844i	$-0.450318\pi$
$337$	5.70724	0.310893	0.155446	+	0.987844i	$0.450318\pi$
$338$	3.08772	0.167950
$339$	−3.41962	−0.185728
$340$	−0.00259561	−0.000140767 0
$341$	−5.90476	−0.319761
$342$	7.84863	0.424405
$343$	−11.0822	−0.598383
$344$	−5.75829	−0.310466
$345$	0.0227469	0.00122465
$346$	2.96341	0.159314
$347$	−29.6989	−1.59432	−0.797161	−	0.603766i	$-0.793666\pi$
$347$	−29.6989	−1.59432	−0.797161	+	0.603766i	$0.793666\pi$
$348$	−4.63964	−0.248711
$349$	−6.02223	−0.322363	−0.161181	−	0.986925i	$-0.551530\pi$
$349$	−6.02223	−0.322363	−0.161181	+	0.986925i	$0.551530\pi$
$350$	18.8756	1.00895
$351$	3.21522	0.171616
$352$	11.6836	0.622735
$353$	−19.5863	−1.04247	−0.521236	−	0.853413i	$-0.674529\pi$
$353$	−19.5863	−1.04247	−0.521236	+	0.853413i	$0.674529\pi$
$354$	13.3981	0.712100
$355$	−0.0201807	−0.00107108
$356$	−1.74336	−0.0923978
$357$	3.25506	0.172276
$358$	29.8331	1.57673
$359$	6.67072	0.352067	0.176034	−	0.984384i	$-0.443673\pi$
$359$	6.67072	0.352067	0.176034	+	0.984384i	$0.443673\pi$
$360$	−0.0122034	−0.000643173 0
$361$	26.7971	1.41037
$362$	−20.6195	−1.08374
$363$	0.0804200	0.00422096
$364$	6.85417	0.359256
$365$	0.0100613	0.000526634 0
$366$	−3.09465	−0.161760
$367$	25.8511	1.34942	0.674709	−	0.738084i	$-0.264269\pi$
$367$	25.8511	1.34942	0.674709	+	0.738084i	$0.264269\pi$
$368$	−12.9783	−0.676541
$369$	−9.11345	−0.474427
$370$	−0.0185628	−0.000965034 0
$371$	−20.4922	−1.06390
$372$	1.17027	0.0606755
$373$	5.02038	0.259945	0.129973	−	0.991518i	$-0.458511\pi$
$373$	5.02038	0.259945	0.129973	+	0.991518i	$0.458511\pi$
$374$	−3.83246	−0.198172
$375$	−0.0396327	−0.00204662
$376$	−6.97839	−0.359883
$377$	22.7777	1.17311
$378$	3.77514	0.194172
$379$	11.3522	0.583121	0.291561	−	0.956552i	$-0.405825\pi$
$379$	11.3522	0.583121	0.291561	+	0.956552i	$0.405825\pi$
$380$	−0.0175654	−0.000901086 0
$381$	−12.0447	−0.617071
$382$	−13.6576	−0.698784
$383$	−26.6331	−1.36089	−0.680444	−	0.732801i	$-0.738213\pi$
$383$	−26.6331	−1.36089	−0.680444	+	0.732801i	$0.738213\pi$
$384$	2.92954	0.149497
$385$	0.0426300	0.00217263
$386$	4.57267	0.232743
$387$	−1.87011	−0.0950632
$388$	−10.9035	−0.553542
$389$	13.0193	0.660102	0.330051	−	0.943963i	$-0.392934\pi$
$389$	13.0193	0.660102	0.330051	+	0.943963i	$0.392934\pi$
$390$	0.0147788	0.000748355 0
$391$	−5.73943	−0.290255
$392$	11.0706	0.559149
$393$	14.1655	0.714553
$394$	21.2785	1.07199
$395$	−0.0478011	−0.00240514
$396$	2.16415	0.108753
$397$	20.1938	1.01350	0.506748	−	0.862094i	$-0.330847\pi$
$397$	20.1938	1.01350	0.506748	+	0.862094i	$0.330847\pi$
$398$	−3.28174	−0.164499
$399$	22.0281	1.10279
$400$	11.3062	0.565312
$401$	11.1786	0.558234	0.279117	−	0.960257i	$-0.409958\pi$
$401$	11.1786	0.558234	0.279117	+	0.960257i	$0.409958\pi$
$402$	−3.93821	−0.196420
$403$	−5.74527	−0.286193
$404$	3.57506	0.177866
$405$	−0.00396327	−0.000196937 0
$406$	26.7444	1.32730
$407$	13.3450	0.661486
$408$	3.07911	0.152439
$409$	17.8837	0.884290	0.442145	−	0.896944i	$-0.354218\pi$
$409$	17.8837	0.884290	0.442145	+	0.896944i	$0.354218\pi$
$410$	−0.0418901	−0.00206880
$411$	−6.92072	−0.341374
$412$	−3.40987	−0.167992
$413$	37.6033	1.85034
$414$	−6.65646	−0.327147
$415$	−0.0355017	−0.00174271
$416$	11.3680	0.557361
$417$	−17.6256	−0.863131
$418$	−25.9356	−1.26855
$419$	23.0041	1.12382	0.561911	−	0.827198i	$-0.310066\pi$
$419$	23.0041	1.12382	0.561911	+	0.827198i	$0.310066\pi$
$420$	−0.00844885	−0.000412262 0
$421$	29.0271	1.41469	0.707347	−	0.706866i	$-0.249892\pi$
$421$	29.0271	1.41469	0.707347	+	0.706866i	$0.249892\pi$
$422$	10.9425	0.532674
$423$	−2.26637	−0.110194
$424$	−19.3845	−0.941397
$425$	4.99998	0.242535
$426$	5.90551	0.286123
$427$	−8.68551	−0.420321
$428$	7.68632	0.371532
$429$	−10.6246	−0.512962
$430$	−0.00859601	−0.000414536 0
$431$	34.1351	1.64423	0.822115	−	0.569321i	$-0.192794\pi$
$431$	34.1351	1.64423	0.822115	+	0.569321i	$0.192794\pi$
$432$	2.26125	0.108795
$433$	9.46701	0.454955	0.227478	−	0.973783i	$-0.426952\pi$
$433$	9.46701	0.454955	0.227478	+	0.973783i	$0.426952\pi$
$434$	−6.74579	−0.323808
$435$	−0.0280771	−0.00134620
$436$	−0.322662	−0.0154527
$437$	−38.8407	−1.85800
$438$	−2.94426	−0.140682
$439$	−4.53664	−0.216522	−0.108261	−	0.994123i	$-0.534528\pi$
$439$	−4.53664	−0.216522	−0.108261	+	0.994123i	$0.534528\pi$
$440$	0.0403257	0.00192245
$441$	3.59539	0.171209
$442$	−3.72895	−0.177368
$443$	37.7504	1.79357	0.896787	−	0.442463i	$-0.145895\pi$
$443$	37.7504	1.79357	0.896787	+	0.442463i	$0.145895\pi$
$444$	−2.64485	−0.125519
$445$	−0.0105501	−0.000500121 0
$446$	24.0756	1.14001
$447$	6.50671	0.307757
$448$	28.0687	1.32612
$449$	25.9018	1.22238	0.611191	−	0.791483i	$-0.290691\pi$
$449$	25.9018	1.22238	0.611191	+	0.791483i	$0.290691\pi$
$450$	5.79887	0.273361
$451$	30.1152	1.41807
$452$	−2.23956	−0.105340
$453$	−17.4455	−0.819661
$454$	−10.6643	−0.500502
$455$	0.0414785	0.00194454
$456$	20.8374	0.975803
$457$	−20.4798	−0.958006	−0.479003	−	0.877813i	$-0.659002\pi$
$457$	−20.4798	−0.958006	−0.479003	+	0.877813i	$0.659002\pi$
$458$	0.323131	0.0150989
$459$	1.00000	0.0466760
$460$	0.0148973	0.000694590 0
$461$	−5.10929	−0.237964	−0.118982	−	0.992896i	$-0.537963\pi$
$461$	−5.10929	−0.237964	−0.118982	+	0.992896i	$0.537963\pi$
$462$	−12.4749	−0.580384
$463$	−3.65259	−0.169750	−0.0848752	−	0.996392i	$-0.527049\pi$
$463$	−3.65259	−0.169750	−0.0848752	+	0.996392i	$0.527049\pi$
$464$	16.0195	0.743686
$465$	0.00708196	0.000328418 0
$466$	27.8932	1.29213
$467$	−29.0032	−1.34211	−0.671054	−	0.741408i	$-0.734158\pi$
$467$	−29.0032	−1.34211	−0.671054	+	0.741408i	$0.734158\pi$
$468$	2.10570	0.0973360
$469$	−11.0530	−0.510382
$470$	−0.0104174	−0.000480518 0
$471$	−1.00000	−0.0460776
$472$	35.5708	1.63728
$473$	6.17975	0.284145
$474$	13.9881	0.642495
$475$	33.8367	1.55253
$476$	2.13179	0.0977103
$477$	−6.29550	−0.288251
$478$	−1.56584	−0.0716198
$479$	0.570867	0.0260836	0.0130418	−	0.999915i	$-0.495849\pi$
$479$	0.570867	0.0260836	0.0130418	+	0.999915i	$0.495849\pi$
$480$	−0.0140128	−0.000639595 0
$481$	12.9845	0.592043
$482$	−16.0598	−0.731506
$483$	−18.6821	−0.850067
$484$	0.0526683	0.00239401
$485$	−0.0659834	−0.00299615
$486$	1.15978	0.0526086
$487$	14.3124	0.648559	0.324279	−	0.945961i	$-0.394878\pi$
$487$	14.3124	0.648559	0.324279	+	0.945961i	$0.394878\pi$
$488$	−8.21604	−0.371923
$489$	−4.71834	−0.213371
$490$	0.0165262	0.000746579 0
$491$	−3.61981	−0.163360	−0.0816799	−	0.996659i	$-0.526029\pi$
$491$	−3.61981	−0.163360	−0.0816799	+	0.996659i	$0.526029\pi$
$492$	−5.96854	−0.269083
$493$	7.08433	0.319062
$494$	−25.2351	−1.13538
$495$	0.0130965	0.000588646 0
$496$	−4.04063	−0.181430
$497$	16.5745	0.743468
$498$	10.3889	0.465539
$499$	3.72651	0.166822	0.0834108	−	0.996515i	$-0.473419\pi$
$499$	3.72651	0.166822	0.0834108	+	0.996515i	$0.473419\pi$
$500$	−0.0259560	−0.00116079
$501$	−5.51629	−0.246450
$502$	0.0506634	0.00226122
$503$	−3.85200	−0.171752	−0.0858761	−	0.996306i	$-0.527369\pi$
$503$	−3.85200	−0.171752	−0.0858761	+	0.996306i	$0.527369\pi$
$504$	10.0227	0.446446
$505$	0.0216347	0.000962733 0
$506$	21.9961	0.977847
$507$	2.66233	0.118238
$508$	−7.88829	−0.349986
$509$	−10.3708	−0.459678	−0.229839	−	0.973229i	$-0.573820\pi$
$509$	−10.3708	−0.459678	−0.229839	+	0.973229i	$0.573820\pi$
$510$	0.00459651	0.000203537 0
$511$	−8.26341	−0.365552
$512$	21.9204	0.968752
$513$	6.76736	0.298786
$514$	7.48286	0.330055
$515$	−0.0206351	−0.000909290 0
$516$	−1.22477	−0.0539174
$517$	7.48916	0.329373
$518$	15.2457	0.669859
$519$	2.55515	0.112159
$520$	0.0392365	0.00172064
$521$	33.8804	1.48433	0.742164	−	0.670219i	$-0.233800\pi$
$521$	33.8804	1.48433	0.742164	+	0.670219i	$0.233800\pi$
$522$	8.21625	0.359616
$523$	−1.32734	−0.0580405	−0.0290203	−	0.999579i	$-0.509239\pi$
$523$	−1.32734	−0.0580405	−0.0290203	+	0.999579i	$0.509239\pi$
$524$	9.27719	0.405276
$525$	16.2752	0.710309
$526$	−4.51978	−0.197072
$527$	−1.78690	−0.0778385
$528$	−7.47227	−0.325189
$529$	9.94100	0.432218
$530$	−0.0289373	−0.00125696
$531$	11.5523	0.501327
$532$	14.4266	0.625471
$533$	29.3018	1.26920
$534$	3.08728	0.133600
$535$	0.0465143	0.00201099
$536$	−10.4556	−0.451613
$537$	25.7232	1.11004
$538$	−9.66182	−0.416551
$539$	−11.8809	−0.511746
$540$	−0.00259561	−0.000111697 0
$541$	13.8672	0.596197	0.298099	−	0.954535i	$-0.403648\pi$
$541$	13.8672	0.596197	0.298099	+	0.954535i	$0.403648\pi$
$542$	−12.0884	−0.519242
$543$	−17.7789	−0.762965
$544$	3.53567	0.151591
$545$	−0.00195261	−8.36406e−5 0
$546$	−12.1379	−0.519455
$547$	−13.3022	−0.568763	−0.284381	−	0.958711i	$-0.591788\pi$
$547$	−13.3022	−0.568763	−0.284381	+	0.958711i	$0.591788\pi$
$548$	−4.53249	−0.193618
$549$	−2.66832	−0.113881
$550$	−19.1622	−0.817081
$551$	47.9422	2.04241
$552$	−17.6723	−0.752184
$553$	39.2593	1.66948
$554$	28.9170	1.22857
$555$	−0.0160055	−0.000679395 0
$556$	−11.5433	−0.489545
$557$	0.461504	0.0195545	0.00977727	−	0.999952i	$-0.496888\pi$
$557$	0.461504	0.0195545	0.00977727	+	0.999952i	$0.496888\pi$
$558$	−2.07240	−0.0877318
$559$	6.01284	0.254316
$560$	0.0291717	0.00123273
$561$	−3.30448	−0.139515
$562$	−20.6918	−0.872829
$563$	−16.6465	−0.701567	−0.350784	−	0.936457i	$-0.614085\pi$
$563$	−16.6465	−0.701567	−0.350784	+	0.936457i	$0.614085\pi$
$564$	−1.48428	−0.0624994
$565$	−0.0135529	−0.000570174 0
$566$	8.86055	0.372437
$567$	3.25506	0.136699
$568$	15.6786	0.657860
$569$	−20.3524	−0.853219	−0.426610	−	0.904436i	$-0.640292\pi$
$569$	−20.3524	−0.853219	−0.426610	+	0.904436i	$0.640292\pi$
$570$	0.0311062	0.00130290
$571$	19.7795	0.827745	0.413873	−	0.910335i	$-0.364176\pi$
$571$	19.7795	0.827745	0.413873	+	0.910335i	$0.364176\pi$
$572$	−6.95824	−0.290939
$573$	−11.7761	−0.491952
$574$	34.4046	1.43602
$575$	−28.6970	−1.19675
$576$	8.62310	0.359296
$577$	6.71287	0.279461	0.139730	−	0.990190i	$-0.455376\pi$
$577$	6.71287	0.279461	0.139730	+	0.990190i	$0.455376\pi$
$578$	−1.15978	−0.0482404
$579$	3.94271	0.163854
$580$	−0.0183882	−0.000763527 0
$581$	29.1578	1.20967
$582$	19.3088	0.800376
$583$	20.8033	0.861586
$584$	−7.81676	−0.323460
$585$	0.0127428	0.000526850 0
$586$	−39.4764	−1.63076
$587$	−0.754242	−0.0311309	−0.0155655	−	0.999879i	$-0.504955\pi$
$587$	−0.754242	−0.0311309	−0.0155655	+	0.999879i	$0.504955\pi$
$588$	2.35467	0.0971051
$589$	−12.0926	−0.498266
$590$	0.0531003	0.00218610
$591$	18.3470	0.754696
$592$	9.13197	0.375321
$593$	9.03484	0.371017	0.185508	−	0.982643i	$-0.440607\pi$
$593$	9.03484	0.371017	0.185508	+	0.982643i	$0.440607\pi$
$594$	−3.83246	−0.157248
$595$	0.0129007	0.000528876 0
$596$	4.26135	0.174551
$597$	−2.82963	−0.115809
$598$	21.4020	0.875193
$599$	5.05599	0.206582	0.103291	−	0.994651i	$-0.467063\pi$
$599$	5.05599	0.206582	0.103291	+	0.994651i	$0.467063\pi$
$600$	15.3955	0.628519
$601$	−3.37237	−0.137562	−0.0687810	−	0.997632i	$-0.521911\pi$
$601$	−3.37237	−0.137562	−0.0687810	+	0.997632i	$0.521911\pi$
$602$	7.05994	0.287742
$603$	−3.39566	−0.138282
$604$	−11.4253	−0.464890
$605$	0.000318726 0	1.29581e−5 0
$606$	−6.33101	−0.257180
$607$	−36.0497	−1.46321	−0.731605	−	0.681728i	$-0.761229\pi$
$607$	−36.0497	−1.46321	−0.731605	+	0.681728i	$0.761229\pi$
$608$	23.9271	0.970374
$609$	23.0599	0.934434
$610$	−0.0122649	−0.000496593 0
$611$	7.28687	0.294795
$612$	0.654916	0.0264734
$613$	41.0128	1.65649	0.828245	−	0.560367i	$-0.189340\pi$
$613$	41.0128	1.65649	0.828245	+	0.560367i	$0.189340\pi$
$614$	−30.5254	−1.23191
$615$	−0.0361191	−0.00145646
$616$	−33.1197	−1.33443
$617$	24.7581	0.996725	0.498362	−	0.866969i	$-0.333935\pi$
$617$	24.7581	0.996725	0.498362	+	0.866969i	$0.333935\pi$
$618$	6.03847	0.242903
$619$	−30.1542	−1.21200	−0.605999	−	0.795465i	$-0.707226\pi$
$619$	−30.1542	−1.21200	−0.605999	+	0.795465i	$0.707226\pi$
$620$	0.00463809	0.000186270 0
$621$	−5.73943	−0.230315
$622$	28.9960	1.16263
$623$	8.66482	0.347149
$624$	−7.27044	−0.291050
$625$	24.9998	0.999991
$626$	9.36254	0.374202
$627$	−22.3626	−0.893075
$628$	−0.654916	−0.0261340
$629$	4.03845	0.161024
$630$	0.0149619	0.000596097 0
$631$	41.2254	1.64116	0.820579	−	0.571533i	$-0.193651\pi$
$631$	41.2254	1.64116	0.820579	+	0.571533i	$0.193651\pi$
$632$	37.1372	1.47724
$633$	9.43502	0.375008
$634$	−1.34702	−0.0534971
$635$	−0.0477366	−0.00189437
$636$	−4.12302	−0.163488
$637$	−11.5600	−0.458023
$638$	−27.1504	−1.07490
$639$	5.09193	0.201434
$640$	0.0116106	0.000458947 0
$641$	−14.5378	−0.574209	−0.287105	−	0.957899i	$-0.592693\pi$
$641$	−14.5378	−0.574209	−0.287105	+	0.957899i	$0.592693\pi$
$642$	−13.6116	−0.537205
$643$	31.0033	1.22265	0.611325	−	0.791380i	$-0.290637\pi$
$643$	31.0033	1.22265	0.611325	+	0.791380i	$0.290637\pi$
$644$	−12.2352	−0.482136
$645$	−0.00741177	−0.000291838 0
$646$	−7.84863	−0.308800
$647$	34.4680	1.35508	0.677539	−	0.735487i	$-0.263046\pi$
$647$	34.4680	1.35508	0.677539	+	0.735487i	$0.263046\pi$
$648$	3.07911	0.120959
$649$	−38.1743	−1.49847
$650$	−18.6447	−0.731304
$651$	−5.81645	−0.227965
$652$	−3.09011	−0.121018
$653$	19.6843	0.770305	0.385152	−	0.922853i	$-0.374149\pi$
$653$	19.6843	0.770305	0.385152	+	0.922853i	$0.374149\pi$
$654$	0.571395	0.0223433
$655$	0.0561416	0.00219363
$656$	20.6078	0.804601
$657$	−2.53864	−0.0990418
$658$	8.55585	0.333542
$659$	−1.72636	−0.0672493	−0.0336246	−	0.999435i	$-0.510705\pi$
$659$	−1.72636	−0.0672493	−0.0336246	+	0.999435i	$0.510705\pi$
$660$	0.00857713	0.000333864 0
$661$	14.9396	0.581082	0.290541	−	0.956863i	$-0.406165\pi$
$661$	14.9396	0.581082	0.290541	+	0.956863i	$0.406165\pi$
$662$	−13.2969	−0.516797
$663$	−3.21522	−0.124869
$664$	27.5817	1.07038
$665$	0.0873034	0.00338548
$666$	4.68371	0.181490
$667$	−40.6600	−1.57436
$668$	−3.61271	−0.139780
$669$	20.7588	0.802583
$670$	−0.0156082	−0.000602996 0
$671$	8.81739	0.340392
$672$	11.5088	0.443962
$673$	−14.6191	−0.563524	−0.281762	−	0.959484i	$-0.590919\pi$
$673$	−14.6191	−0.563524	−0.281762	+	0.959484i	$0.590919\pi$
$674$	−6.61913	−0.254959
$675$	4.99998	0.192449
$676$	1.74360	0.0670617
$677$	21.4200	0.823236	0.411618	−	0.911356i	$-0.364964\pi$
$677$	21.4200	0.823236	0.411618	+	0.911356i	$0.364964\pi$
$678$	3.96600	0.152313
$679$	54.1925	2.07972
$680$	0.0122034	0.000467977 0
$681$	−9.19516	−0.352359
$682$	6.84821	0.262232
$683$	20.4461	0.782347	0.391173	−	0.920317i	$-0.372069\pi$
$683$	20.4461	0.782347	0.391173	+	0.920317i	$0.372069\pi$
$684$	4.43205	0.169464
$685$	−0.0274287	−0.00104800
$686$	12.8529	0.490726
$687$	0.278614	0.0106298
$688$	4.22880	0.161222
$689$	20.2414	0.771137
$690$	−0.0263813	−0.00100432
$691$	−24.8895	−0.946841	−0.473420	−	0.880837i	$-0.656981\pi$
$691$	−24.8895	−0.946841	−0.473420	+	0.880837i	$0.656981\pi$
$692$	1.67341	0.0636134
$693$	−10.7563	−0.408597
$694$	34.4442	1.30748
$695$	−0.0698552	−0.00264976
$696$	21.8135	0.826837
$697$	9.11345	0.345197
$698$	6.98445	0.264365
$699$	24.0505	0.909673
$700$	10.6589	0.402869
$701$	−9.90852	−0.374240	−0.187120	−	0.982337i	$-0.559915\pi$
$701$	−9.90852	−0.374240	−0.187120	+	0.982337i	$0.559915\pi$
$702$	−3.72895	−0.140740
$703$	27.3296	1.03076
$704$	−28.4949	−1.07394
$705$	−0.00898222	−0.000338290 0
$706$	22.7157	0.854917
$707$	−17.7687	−0.668262
$708$	7.56578	0.284339
$709$	−18.9483	−0.711619	−0.355810	−	0.934558i	$-0.615795\pi$
$709$	−18.9483	−0.711619	−0.355810	+	0.934558i	$0.615795\pi$
$710$	0.0234051	0.000878379 0
$711$	12.0610	0.452324
$712$	8.19647	0.307176
$713$	10.2558	0.384081
$714$	−3.77514	−0.141281
$715$	−0.0421083	−0.00157476
$716$	16.8465	0.629583
$717$	−1.35012	−0.0504211
$718$	−7.73655	−0.288726
$719$	−37.9793	−1.41639	−0.708195	−	0.706017i	$-0.750490\pi$
$719$	−37.9793	−1.41639	−0.708195	+	0.706017i	$0.750490\pi$
$720$	0.00896196	0.000333993 0
$721$	16.9477	0.631165
$722$	−31.0787	−1.15663
$723$	−13.8473	−0.514988
$724$	−11.6437	−0.432733
$725$	35.4216	1.31552
$726$	−0.0932693	−0.00346155
$727$	−18.7719	−0.696212	−0.348106	−	0.937455i	$-0.613175\pi$
$727$	−18.7719	−0.696212	−0.348106	+	0.937455i	$0.613175\pi$
$728$	−32.2252	−1.19434
$729$	1.00000	0.0370370
$730$	−0.0116689	−0.000431885 0
$731$	1.87011	0.0691687
$732$	−1.74752	−0.0645903
$733$	51.7596	1.91178	0.955892	−	0.293720i	$-0.0948932\pi$
$733$	51.7596	1.91178	0.955892	+	0.293720i	$0.0948932\pi$
$734$	−29.9816	−1.10664
$735$	0.0142495	0.000525600 0
$736$	−20.2927	−0.748000
$737$	11.2209	0.413326
$738$	10.5696	0.389072
$739$	11.4111	0.419764	0.209882	−	0.977727i	$-0.432692\pi$
$739$	11.4111	0.419764	0.209882	+	0.977727i	$0.432692\pi$
$740$	−0.0104822	−0.000385335 0
$741$	−21.7586	−0.799321
$742$	23.7664	0.872492
$743$	−31.7142	−1.16348	−0.581741	−	0.813374i	$-0.697628\pi$
$743$	−31.7142	−1.16348	−0.581741	+	0.813374i	$0.697628\pi$
$744$	−5.50206	−0.201715
$745$	0.0257878	0.000944794 0
$746$	−5.82252	−0.213178
$747$	8.95769	0.327745
$748$	−2.16415	−0.0791293
$749$	−38.2025	−1.39589
$750$	0.0459651	0.00167841
$751$	−25.9154	−0.945666	−0.472833	−	0.881152i	$-0.656769\pi$
$751$	−25.9154	−0.945666	−0.472833	+	0.881152i	$0.656769\pi$
$752$	5.12483	0.186883
$753$	0.0436837	0.00159192
$754$	−26.4171	−0.962054
$755$	−0.0691412	−0.00251631
$756$	2.13179	0.0775323
$757$	21.8524	0.794238	0.397119	−	0.917767i	$-0.370010\pi$
$757$	21.8524	0.794238	0.397119	+	0.917767i	$0.370010\pi$
$758$	−13.1660	−0.478210
$759$	18.9658	0.688415
$760$	0.0825844	0.00299565
$761$	20.1864	0.731758	0.365879	−	0.930663i	$-0.380768\pi$
$761$	20.1864	0.731758	0.365879	+	0.930663i	$0.380768\pi$
$762$	13.9692	0.506052
$763$	1.60369	0.0580574
$764$	−7.71233	−0.279022
$765$	0.00396327	0.000143292 0
$766$	30.8885	1.11605
$767$	−37.1432	−1.34116
$768$	13.8486	0.499718
$769$	−40.7627	−1.46994	−0.734970	−	0.678100i	$-0.762804\pi$
$769$	−40.7627	−1.46994	−0.734970	+	0.678100i	$0.762804\pi$
$770$	−0.0494413	−0.00178174
$771$	6.45198	0.232362
$772$	2.58215	0.0929334
$773$	11.0428	0.397181	0.198591	−	0.980083i	$-0.436364\pi$
$773$	11.0428	0.397181	0.198591	+	0.980083i	$0.436364\pi$
$774$	2.16892	0.0779601
$775$	−8.93446	−0.320935
$776$	51.2633	1.84024
$777$	13.1454	0.471588
$778$	−15.0994	−0.541341
$779$	61.6740	2.20970
$780$	0.00834546	0.000298816 0
$781$	−16.8262	−0.602088
$782$	6.65646	0.238034
$783$	7.08433	0.253173
$784$	−8.13008	−0.290360
$785$	−0.00396327	−0.000141455 0
$786$	−16.4288	−0.585996
$787$	−5.94302	−0.211846	−0.105923	−	0.994374i	$-0.533780\pi$
$787$	−5.94302	−0.211846	−0.105923	+	0.994374i	$0.533780\pi$
$788$	12.0158	0.428044
$789$	−3.89711	−0.138741
$790$	0.0554387	0.00197242
$791$	11.1311	0.395775
$792$	−10.1749	−0.361548
$793$	8.57923	0.304657
$794$	−23.4203	−0.831155
$795$	−0.0249508	−0.000884913 0
$796$	−1.85317	−0.0656838
$797$	−41.2355	−1.46064	−0.730319	−	0.683106i	$-0.760628\pi$
$797$	−41.2355	−1.46064	−0.730319	+	0.683106i	$0.760628\pi$
$798$	−25.5477	−0.904379
$799$	2.26637	0.0801783
$800$	17.6783	0.625022
$801$	2.66196	0.0940557
$802$	−12.9647	−0.457801
$803$	8.38888	0.296037
$804$	−2.22387	−0.0784298
$805$	−0.0740424	−0.00260965
$806$	6.66324	0.234703
$807$	−8.33075	−0.293256
$808$	−16.8083	−0.591313
$809$	−45.1373	−1.58694	−0.793471	−	0.608607i	$-0.791728\pi$
$809$	−45.1373	−1.58694	−0.793471	+	0.608607i	$0.791728\pi$
$810$	0.00459651	0.000161505 0
$811$	24.9875	0.877430	0.438715	−	0.898626i	$-0.355434\pi$
$811$	24.9875	0.877430	0.438715	+	0.898626i	$0.355434\pi$
$812$	15.1023	0.529986
$813$	−10.4230	−0.365552
$814$	−15.4772	−0.542476
$815$	−0.0187001	−0.000655034 0
$816$	−2.26125	−0.0791597
$817$	12.6557	0.442768
$818$	−20.7411	−0.725195
$819$	−10.4657	−0.365702
$820$	−0.0236550	−0.000826067 0
$821$	−14.0389	−0.489961	−0.244980	−	0.969528i	$-0.578781\pi$
$821$	−14.0389	−0.489961	−0.244980	+	0.969528i	$0.578781\pi$
$822$	8.02649	0.279956
$823$	−0.684923	−0.0238749	−0.0119375	−	0.999929i	$-0.503800\pi$
$823$	−0.684923	−0.0238749	−0.0119375	+	0.999929i	$0.503800\pi$
$824$	16.0316	0.558489
$825$	−16.5223	−0.575234
$826$	−43.6115	−1.51744
$827$	−9.97082	−0.346719	−0.173360	−	0.984859i	$-0.555462\pi$
$827$	−9.97082	−0.346719	−0.173360	+	0.984859i	$0.555462\pi$
$828$	−3.75884	−0.130629
$829$	47.4025	1.64636	0.823178	−	0.567784i	$-0.192199\pi$
$829$	47.4025	1.64636	0.823178	+	0.567784i	$0.192199\pi$
$830$	0.0411741	0.00142918
$831$	24.9332	0.864925
$832$	−27.7252	−0.961198
$833$	−3.59539	−0.124573
$834$	20.4418	0.707842
$835$	−0.0218626	−0.000756586 0
$836$	−14.6456	−0.506529
$837$	−1.78690	−0.0617642
$838$	−26.6796	−0.921632
$839$	−29.8008	−1.02884	−0.514420	−	0.857539i	$-0.671993\pi$
$839$	−29.8008	−1.02884	−0.514420	+	0.857539i	$0.671993\pi$
$840$	0.0397226	0.00137056
$841$	21.1878	0.730613
$842$	−33.6650	−1.16017
$843$	−17.8411	−0.614482
$844$	6.17914	0.212695
$845$	0.0105516	0.000362984 0
$846$	2.62848	0.0903690
$847$	−0.261772	−0.00899458
$848$	14.2357	0.488857
$849$	7.63987	0.262200
$850$	−5.79887	−0.198900
$851$	−23.1784	−0.794545
$852$	3.33478	0.114248
$853$	−27.5948	−0.944828	−0.472414	−	0.881377i	$-0.656617\pi$
$853$	−27.5948	−0.944828	−0.472414	+	0.881377i	$0.656617\pi$
$854$	10.0733	0.344700
$855$	0.0268209	0.000917254 0
$856$	−36.1375	−1.23516
$857$	−47.0436	−1.60698	−0.803490	−	0.595319i	$-0.797026\pi$
$857$	−47.0436	−1.60698	−0.803490	+	0.595319i	$0.797026\pi$
$858$	12.3222	0.420674
$859$	23.0067	0.784977	0.392488	−	0.919757i	$-0.371614\pi$
$859$	23.0067	0.784977	0.392488	+	0.919757i	$0.371614\pi$
$860$	−0.00485408	−0.000165523 0
$861$	29.6648	1.01097
$862$	−39.5891	−1.34841
$863$	−31.3418	−1.06689	−0.533444	−	0.845835i	$-0.679102\pi$
$863$	−31.3418	−1.06689	−0.533444	+	0.845835i	$0.679102\pi$
$864$	3.53567	0.120286
$865$	0.0101268	0.000344320 0
$866$	−10.9796	−0.373103
$867$	−1.00000	−0.0339618
$868$	−3.80928	−0.129296
$869$	−39.8554	−1.35200
$870$	0.0325632	0.00110400
$871$	10.9178	0.369935
$872$	1.51701	0.0513723
$873$	16.6487	0.563474
$874$	45.0466	1.52372
$875$	0.129006	0.00436121
$876$	−1.66260	−0.0561739
$877$	−16.1135	−0.544114	−0.272057	−	0.962281i	$-0.587704\pi$
$877$	−16.1135	−0.544114	−0.272057	+	0.962281i	$0.587704\pi$
$878$	5.26150	0.177567
$879$	−34.0379	−1.14807
$880$	−0.0296146	−0.000998309 0
$881$	−18.2775	−0.615784	−0.307892	−	0.951421i	$-0.599623\pi$
$881$	−18.2775	−0.615784	−0.307892	+	0.951421i	$0.599623\pi$
$882$	−4.16985	−0.140406
$883$	27.2868	0.918273	0.459136	−	0.888366i	$-0.348159\pi$
$883$	27.2868	0.918273	0.459136	+	0.888366i	$0.348159\pi$
$884$	−2.10570	−0.0708224
$885$	0.0457849	0.00153904
$886$	−43.7820	−1.47089
$887$	11.2918	0.379141	0.189570	−	0.981867i	$-0.439290\pi$
$887$	11.2918	0.379141	0.189570	+	0.981867i	$0.439290\pi$
$888$	12.4348	0.417286
$889$	39.2063	1.31494
$890$	0.0122357	0.000410143 0
$891$	−3.30448	−0.110704
$892$	13.5953	0.455204
$893$	15.3373	0.513243
$894$	−7.54633	−0.252387
$895$	0.101948	0.00340774
$896$	−9.53581	−0.318569
$897$	18.4535	0.616146
$898$	−30.0404	−1.00246
$899$	−12.6590	−0.422200
$900$	3.27457	0.109152
$901$	6.29550	0.209733
$902$	−34.9269	−1.16294
$903$	6.08733	0.202573
$904$	10.5294	0.350203
$905$	−0.0704625	−0.00234225
$906$	20.2329	0.672193
$907$	−47.7504	−1.58553	−0.792764	−	0.609529i	$-0.791359\pi$
$907$	−47.7504	−1.58553	−0.792764	+	0.609529i	$0.791359\pi$
$908$	−6.02206	−0.199849
$909$	−5.45881	−0.181057
$910$	−0.0481059	−0.00159469
$911$	−28.1079	−0.931256	−0.465628	−	0.884980i	$-0.654172\pi$
$911$	−28.1079	−0.931256	−0.465628	+	0.884980i	$0.654172\pi$
$912$	−15.3027	−0.506723
$913$	−29.6005	−0.979633
$914$	23.7521	0.785648
$915$	−0.0105753	−0.000349607 0
$916$	0.182469	0.00602894
$917$	−46.1094	−1.52267
$918$	−1.15978	−0.0382784
$919$	16.0257	0.528639	0.264319	−	0.964435i	$-0.414853\pi$
$919$	16.0257	0.528639	0.264319	+	0.964435i	$0.414853\pi$
$920$	−0.0700403	−0.00230916
$921$	−26.3201	−0.867276
$922$	5.92564	0.195151
$923$	−16.3717	−0.538881
$924$	−7.04444	−0.231745
$925$	20.1922	0.663915
$926$	4.23620	0.139210
$927$	5.20658	0.171006
$928$	25.0479	0.822237
$929$	−3.60957	−0.118426	−0.0592131	−	0.998245i	$-0.518859\pi$
$929$	−3.60957	−0.118426	−0.0592131	+	0.998245i	$0.518859\pi$
$930$	−0.00821350	−0.000269331 0
$931$	−24.3313	−0.797425
$932$	15.7510	0.515943
$933$	25.0014	0.818508
$934$	33.6373	1.10065
$935$	−0.0130965	−0.000428303 0
$936$	−9.90003	−0.323593
$937$	10.9590	0.358015	0.179007	−	0.983848i	$-0.442711\pi$
$937$	10.9590	0.358015	0.179007	+	0.983848i	$0.442711\pi$
$938$	12.8191	0.418558
$939$	8.07270	0.263443
$940$	−0.00588260	−0.000191869 0
$941$	−6.35988	−0.207326	−0.103663	−	0.994612i	$-0.533056\pi$
$941$	−6.35988	−0.207326	−0.103663	+	0.994612i	$0.533056\pi$
$942$	1.15978	0.0377876
$943$	−52.3060	−1.70332
$944$	−26.1227	−0.850220
$945$	0.0129007	0.000419659 0
$946$	−7.16714	−0.233024
$947$	9.40887	0.305747	0.152874	−	0.988246i	$-0.451147\pi$
$947$	9.40887	0.305747	0.152874	+	0.988246i	$0.451147\pi$
$948$	7.89895	0.256546
$949$	8.16230	0.264959
$950$	−39.2430	−1.27321
$951$	−1.16145	−0.0376626
$952$	−10.0227	−0.324837
$953$	−34.3740	−1.11348	−0.556742	−	0.830685i	$-0.687949\pi$
$953$	−34.3740	−1.11348	−0.556742	+	0.830685i	$0.687949\pi$
$954$	7.30138	0.236391
$955$	−0.0466717	−0.00151026
$956$	−0.884214	−0.0285975
$957$	−23.4100	−0.756739
$958$	−0.662079	−0.0213908
$959$	22.5273	0.727445
$960$	0.0341757	0.00110302
$961$	−27.8070	−0.897000
$962$	−15.0592	−0.485527
$963$	−11.7363	−0.378199
$964$	−9.06884	−0.292088
$965$	0.0156260	0.000503020 0
$966$	21.6671	0.697129
$967$	17.0327	0.547735	0.273867	−	0.961767i	$-0.411697\pi$
$967$	17.0327	0.547735	0.273867	+	0.961767i	$0.411697\pi$
$968$	−0.247622	−0.00795888
$969$	−6.76736	−0.217399
$970$	0.0765261	0.00245710
$971$	35.5250	1.14005	0.570025	−	0.821627i	$-0.306933\pi$
$971$	35.5250	1.14005	0.570025	+	0.821627i	$0.306933\pi$
$972$	0.654916	0.0210064
$973$	57.3724	1.83928
$974$	−16.5993	−0.531875
$975$	−16.0761	−0.514846
$976$	6.03374	0.193135
$977$	6.81349	0.217983	0.108991	−	0.994043i	$-0.465238\pi$
$977$	6.81349	0.217983	0.108991	+	0.994043i	$0.465238\pi$
$978$	5.47222	0.174982
$979$	−8.79639	−0.281134
$980$	0.00933221	0.000298107 0
$981$	0.492676	0.0157299
$982$	4.19817	0.133969
$983$	−20.9151	−0.667088	−0.333544	−	0.942734i	$-0.608245\pi$
$983$	−20.9151	−0.667088	−0.333544	+	0.942734i	$0.608245\pi$
$984$	28.0613	0.894563
$985$	0.0727143	0.00231687
$986$	−8.21625	−0.261659
$987$	7.37715	0.234817
$988$	−14.2500	−0.453354
$989$	−10.7334	−0.341302
$990$	−0.0151891	−0.000482741 0
$991$	35.9424	1.14175	0.570874	−	0.821037i	$-0.306604\pi$
$991$	35.9424	1.14175	0.570874	+	0.821037i	$0.306604\pi$
$992$	−6.31788	−0.200593
$993$	−11.4650	−0.363831
$994$	−19.2227	−0.609709
$995$	−0.0112146	−0.000355526 0
$996$	5.86653	0.185888
$997$	31.0714	0.984042	0.492021	−	0.870583i	$-0.336258\pi$
$997$	31.0714	0.984042	0.492021	+	0.870583i	$0.336258\pi$
$998$	−4.32192	−0.136808
$999$	4.03845	0.127771

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.g.1.19	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.g.1.19	✓	56	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-1.15978 q^{2} -1.00000 q^{3} -0.654916 q^{4} -0.00396327 q^{5} +1.15978 q^{6} +3.25506 q^{7} +3.07911 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.15978 q^{2} -1.00000 q^{3} -0.654916 q^{4} -0.00396327 q^{5} +1.15978 q^{6} +3.25506 q^{7} +3.07911 q^{8} +1.00000 q^{9} +0.00459651 q^{10} -3.30448 q^{11} +0.654916 q^{12} -3.21522 q^{13} -3.77514 q^{14} +0.00396327 q^{15} -2.26125 q^{16} -1.00000 q^{17} -1.15978 q^{18} -6.76736 q^{19} +0.00259561 q^{20} -3.25506 q^{21} +3.83246 q^{22} +5.73943 q^{23} -3.07911 q^{24} -4.99998 q^{25} +3.72895 q^{26} -1.00000 q^{27} -2.13179 q^{28} -7.08433 q^{29} -0.00459651 q^{30} +1.78690 q^{31} -3.53567 q^{32} +3.30448 q^{33} +1.15978 q^{34} -0.0129007 q^{35} -0.654916 q^{36} -4.03845 q^{37} +7.84863 q^{38} +3.21522 q^{39} -0.0122034 q^{40} -9.11345 q^{41} +3.77514 q^{42} -1.87011 q^{43} +2.16415 q^{44} -0.00396327 q^{45} -6.65646 q^{46} -2.26637 q^{47} +2.26125 q^{48} +3.59539 q^{49} +5.79887 q^{50} +1.00000 q^{51} +2.10570 q^{52} -6.29550 q^{53} +1.15978 q^{54} +0.0130965 q^{55} +10.0227 q^{56} +6.76736 q^{57} +8.21625 q^{58} +11.5523 q^{59} -0.00259561 q^{60} -2.66832 q^{61} -2.07240 q^{62} +3.25506 q^{63} +8.62310 q^{64} +0.0127428 q^{65} -3.83246 q^{66} -3.39566 q^{67} +0.654916 q^{68} -5.73943 q^{69} +0.0149619 q^{70} +5.09193 q^{71} +3.07911 q^{72} -2.53864 q^{73} +4.68371 q^{74} +4.99998 q^{75} +4.43205 q^{76} -10.7563 q^{77} -3.72895 q^{78} +12.0610 q^{79} +0.00896196 q^{80} +1.00000 q^{81} +10.5696 q^{82} +8.95769 q^{83} +2.13179 q^{84} +0.00396327 q^{85} +2.16892 q^{86} +7.08433 q^{87} -10.1749 q^{88} +2.66196 q^{89} +0.00459651 q^{90} -10.4657 q^{91} -3.75884 q^{92} -1.78690 q^{93} +2.62848 q^{94} +0.0268209 q^{95} +3.53567 q^{96} +16.6487 q^{97} -4.16985 q^{98} -3.30448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * q^98 - 7 * q^99

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