LMFDB - Embedded newform 8007.2.a.i.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$63$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-1.99602 q^{2} +1.00000 q^{3} +1.98408 q^{4} +2.66347 q^{5} -1.99602 q^{6} -1.66715 q^{7} +0.0317759 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.99602 q^{2} +1.00000 q^{3} +1.98408 q^{4} +2.66347 q^{5} -1.99602 q^{6} -1.66715 q^{7} +0.0317759 q^{8} +1.00000 q^{9} -5.31632 q^{10} +4.22930 q^{11} +1.98408 q^{12} +1.68928 q^{13} +3.32765 q^{14} +2.66347 q^{15} -4.03159 q^{16} +1.00000 q^{17} -1.99602 q^{18} +7.43829 q^{19} +5.28453 q^{20} -1.66715 q^{21} -8.44174 q^{22} -2.12952 q^{23} +0.0317759 q^{24} +2.09406 q^{25} -3.37182 q^{26} +1.00000 q^{27} -3.30775 q^{28} -5.33652 q^{29} -5.31632 q^{30} +4.86248 q^{31} +7.98356 q^{32} +4.22930 q^{33} -1.99602 q^{34} -4.44039 q^{35} +1.98408 q^{36} -4.87500 q^{37} -14.8469 q^{38} +1.68928 q^{39} +0.0846342 q^{40} -7.08513 q^{41} +3.32765 q^{42} +12.6492 q^{43} +8.39126 q^{44} +2.66347 q^{45} +4.25055 q^{46} -0.139627 q^{47} -4.03159 q^{48} -4.22062 q^{49} -4.17977 q^{50} +1.00000 q^{51} +3.35166 q^{52} +6.95402 q^{53} -1.99602 q^{54} +11.2646 q^{55} -0.0529752 q^{56} +7.43829 q^{57} +10.6518 q^{58} +14.5108 q^{59} +5.28453 q^{60} +0.0641631 q^{61} -9.70559 q^{62} -1.66715 q^{63} -7.87214 q^{64} +4.49933 q^{65} -8.44174 q^{66} -9.60638 q^{67} +1.98408 q^{68} -2.12952 q^{69} +8.86309 q^{70} -1.43635 q^{71} +0.0317759 q^{72} +10.3575 q^{73} +9.73058 q^{74} +2.09406 q^{75} +14.7582 q^{76} -7.05086 q^{77} -3.37182 q^{78} +7.94830 q^{79} -10.7380 q^{80} +1.00000 q^{81} +14.1420 q^{82} -10.3132 q^{83} -3.30775 q^{84} +2.66347 q^{85} -25.2480 q^{86} -5.33652 q^{87} +0.134390 q^{88} +13.2549 q^{89} -5.31632 q^{90} -2.81627 q^{91} -4.22513 q^{92} +4.86248 q^{93} +0.278698 q^{94} +19.8116 q^{95} +7.98356 q^{96} +14.9790 q^{97} +8.42443 q^{98} +4.22930 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) $ 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.99602	−1.41140	−0.705698	−	0.708512i	$-0.749367\pi$
$2$	−1.99602	−1.41140	−0.705698	+	0.708512i	$0.749367\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.98408	0.992040
$5$	2.66347	1.19114	0.595569	−	0.803304i	$-0.296926\pi$
$5$	2.66347	1.19114	0.595569	+	0.803304i	$0.296926\pi$
$6$	−1.99602	−0.814870
$7$	−1.66715	−0.630122	−0.315061	−	0.949071i	$-0.602025\pi$
$7$	−1.66715	−0.630122	−0.315061	+	0.949071i	$0.602025\pi$
$8$	0.0317759	0.0112345
$9$	1.00000	0.333333
$10$	−5.31632	−1.68117
$11$	4.22930	1.27518	0.637590	−	0.770376i	$-0.279931\pi$
$11$	4.22930	1.27518	0.637590	+	0.770376i	$0.279931\pi$
$12$	1.98408	0.572755
$13$	1.68928	0.468521	0.234261	−	0.972174i	$-0.424733\pi$
$13$	1.68928	0.468521	0.234261	+	0.972174i	$0.424733\pi$
$14$	3.32765	0.889352
$15$	2.66347	0.687704
$16$	−4.03159	−1.00790
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.99602	−0.470466
$19$	7.43829	1.70646	0.853230	−	0.521535i	$-0.174640\pi$
$19$	7.43829	1.70646	0.853230	+	0.521535i	$0.174640\pi$
$20$	5.28453	1.18166
$21$	−1.66715	−0.363801
$22$	−8.44174	−1.79979
$23$	−2.12952	−0.444035	−0.222017	−	0.975043i	$-0.571264\pi$
$23$	−2.12952	−0.444035	−0.222017	+	0.975043i	$0.571264\pi$
$24$	0.0317759	0.00648624
$25$	2.09406	0.418811
$26$	−3.37182	−0.661269
$27$	1.00000	0.192450
$28$	−3.30775	−0.625107
$29$	−5.33652	−0.990967	−0.495484	−	0.868617i	$-0.665009\pi$
$29$	−5.33652	−0.990967	−0.495484	+	0.868617i	$0.665009\pi$
$30$	−5.31632	−0.970623
$31$	4.86248	0.873327	0.436664	−	0.899625i	$-0.356160\pi$
$31$	4.86248	0.873327	0.436664	+	0.899625i	$0.356160\pi$
$32$	7.98356	1.41131
$33$	4.22930	0.736226
$34$	−1.99602	−0.342314
$35$	−4.44039	−0.750563
$36$	1.98408	0.330680
$37$	−4.87500	−0.801445	−0.400723	−	0.916199i	$-0.631241\pi$
$37$	−4.87500	−0.801445	−0.400723	+	0.916199i	$0.631241\pi$
$38$	−14.8469	−2.40849
$39$	1.68928	0.270501
$40$	0.0846342	0.0133818
$41$	−7.08513	−1.10651	−0.553256	−	0.833011i	$-0.686615\pi$
$41$	−7.08513	−1.10651	−0.553256	+	0.833011i	$0.686615\pi$
$42$	3.32765	0.513468
$43$	12.6492	1.92899	0.964493	−	0.264107i	$-0.0850772\pi$
$43$	12.6492	1.92899	0.964493	+	0.264107i	$0.0850772\pi$
$44$	8.39126	1.26503
$45$	2.66347	0.397046
$46$	4.25055	0.626709
$47$	−0.139627	−0.0203667	−0.0101834	−	0.999948i	$-0.503242\pi$
$47$	−0.139627	−0.0203667	−0.0101834	+	0.999948i	$0.503242\pi$
$48$	−4.03159	−0.581909
$49$	−4.22062	−0.602946
$50$	−4.17977	−0.591109
$51$	1.00000	0.140028
$52$	3.35166	0.464792
$53$	6.95402	0.955209	0.477604	−	0.878575i	$-0.341505\pi$
$53$	6.95402	0.955209	0.477604	+	0.878575i	$0.341505\pi$
$54$	−1.99602	−0.271623
$55$	11.2646	1.51892
$56$	−0.0529752	−0.00707910
$57$	7.43829	0.985225
$58$	10.6518	1.39865
$59$	14.5108	1.88914	0.944572	−	0.328305i	$-0.106477\pi$
$59$	14.5108	1.88914	0.944572	+	0.328305i	$0.106477\pi$
$60$	5.28453	0.682230
$61$	0.0641631	0.00821524	0.00410762	−	0.999992i	$-0.498693\pi$
$61$	0.0641631	0.00821524	0.00410762	+	0.999992i	$0.498693\pi$
$62$	−9.70559	−1.23261
$63$	−1.66715	−0.210041
$64$	−7.87214	−0.984017
$65$	4.49933	0.558074
$66$	−8.44174	−1.03911
$67$	−9.60638	−1.17361	−0.586803	−	0.809730i	$-0.699614\pi$
$67$	−9.60638	−1.17361	−0.586803	+	0.809730i	$0.699614\pi$
$68$	1.98408	0.240605
$69$	−2.12952	−0.256364
$70$	8.86309	1.05934
$71$	−1.43635	−0.170463	−0.0852316	−	0.996361i	$-0.527163\pi$
$71$	−1.43635	−0.170463	−0.0852316	+	0.996361i	$0.527163\pi$
$72$	0.0317759	0.00374483
$73$	10.3575	1.21225	0.606124	−	0.795370i	$-0.292723\pi$
$73$	10.3575	1.21225	0.606124	+	0.795370i	$0.292723\pi$
$74$	9.73058	1.13116
$75$	2.09406	0.241801
$76$	14.7582	1.69288
$77$	−7.05086	−0.803520
$78$	−3.37182	−0.381784
$79$	7.94830	0.894253	0.447127	−	0.894471i	$-0.352447\pi$
$79$	7.94830	0.894253	0.447127	+	0.894471i	$0.352447\pi$
$80$	−10.7380	−1.20054
$81$	1.00000	0.111111
$82$	14.1420	1.56173
$83$	−10.3132	−1.13202	−0.566011	−	0.824398i	$-0.691514\pi$
$83$	−10.3132	−1.13202	−0.566011	+	0.824398i	$0.691514\pi$
$84$	−3.30775	−0.360905
$85$	2.66347	0.288894
$86$	−25.2480	−2.72257
$87$	−5.33652	−0.572135
$88$	0.134390	0.0143260
$89$	13.2549	1.40501	0.702507	−	0.711677i	$-0.252064\pi$
$89$	13.2549	1.40501	0.702507	+	0.711677i	$0.252064\pi$
$90$	−5.31632	−0.560390
$91$	−2.81627	−0.295226
$92$	−4.22513	−0.440501
$93$	4.86248	0.504216
$94$	0.278698	0.0287455
$95$	19.8116	2.03263
$96$	7.98356	0.814819
$97$	14.9790	1.52089	0.760446	−	0.649401i	$-0.224980\pi$
$97$	14.9790	1.52089	0.760446	+	0.649401i	$0.224980\pi$
$98$	8.42443	0.850996
$99$	4.22930	0.425060
$100$	4.15478	0.415478
$101$	−16.7993	−1.67159	−0.835797	−	0.549039i	$-0.814994\pi$
$101$	−16.7993	−1.67159	−0.835797	+	0.549039i	$0.814994\pi$
$102$	−1.99602	−0.197635
$103$	−13.0844	−1.28925	−0.644624	−	0.764500i	$-0.722986\pi$
$103$	−13.0844	−1.28925	−0.644624	+	0.764500i	$0.722986\pi$
$104$	0.0536784	0.00526360
$105$	−4.44039	−0.433338
$106$	−13.8803	−1.34818
$107$	0.753252	0.0728196	0.0364098	−	0.999337i	$-0.488408\pi$
$107$	0.753252	0.0728196	0.0364098	+	0.999337i	$0.488408\pi$
$108$	1.98408	0.190918
$109$	−2.83093	−0.271154	−0.135577	−	0.990767i	$-0.543289\pi$
$109$	−2.83093	−0.271154	−0.135577	+	0.990767i	$0.543289\pi$
$110$	−22.4843	−2.14379
$111$	−4.87500	−0.462715
$112$	6.72125	0.635098
$113$	18.1092	1.70357	0.851784	−	0.523894i	$-0.175521\pi$
$113$	18.1092	1.70357	0.851784	+	0.523894i	$0.175521\pi$
$114$	−14.8469	−1.39054
$115$	−5.67190	−0.528907
$116$	−10.5881	−0.983079
$117$	1.68928	0.156174
$118$	−28.9638	−2.66633
$119$	−1.66715	−0.152827
$120$	0.0846342	0.00772601
$121$	6.88694	0.626085
$122$	−0.128071	−0.0115950
$123$	−7.08513	−0.638845
$124$	9.64755	0.866376
$125$	−7.73988	−0.692276
$126$	3.32765	0.296451
$127$	−13.0098	−1.15443	−0.577216	−	0.816592i	$-0.695861\pi$
$127$	−13.0098	−1.15443	−0.577216	+	0.816592i	$0.695861\pi$
$128$	−0.254200	−0.0224683
$129$	12.6492	1.11370
$130$	−8.98074	−0.787663
$131$	−9.51008	−0.830900	−0.415450	−	0.909616i	$-0.636376\pi$
$131$	−9.51008	−0.830900	−0.415450	+	0.909616i	$0.636376\pi$
$132$	8.39126	0.730366
$133$	−12.4007	−1.07528
$134$	19.1745	1.65642
$135$	2.66347	0.229235
$136$	0.0317759	0.00272476
$137$	16.6168	1.41967	0.709834	−	0.704369i	$-0.248770\pi$
$137$	16.6168	1.41967	0.709834	+	0.704369i	$0.248770\pi$
$138$	4.25055	0.361831
$139$	13.8690	1.17636	0.588178	−	0.808731i	$-0.299845\pi$
$139$	13.8690	1.17636	0.588178	+	0.808731i	$0.299845\pi$
$140$	−8.81009	−0.744589
$141$	−0.139627	−0.0117587
$142$	2.86697	0.240591
$143$	7.14445	0.597449
$144$	−4.03159	−0.335965
$145$	−14.2137	−1.18038
$146$	−20.6736	−1.71096
$147$	−4.22062	−0.348111
$148$	−9.67239	−0.795066
$149$	−17.7565	−1.45467	−0.727336	−	0.686282i	$-0.759242\pi$
$149$	−17.7565	−1.45467	−0.727336	+	0.686282i	$0.759242\pi$
$150$	−4.17977	−0.341277
$151$	8.34133	0.678808	0.339404	−	0.940641i	$-0.389775\pi$
$151$	8.34133	0.678808	0.339404	+	0.940641i	$0.389775\pi$
$152$	0.236359	0.0191712
$153$	1.00000	0.0808452
$154$	14.0736	1.13408
$155$	12.9511	1.04025
$156$	3.35166	0.268348
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−15.8649	−1.26215
$159$	6.95402	0.551490
$160$	21.2639	1.68106
$161$	3.55022	0.279796
$162$	−1.99602	−0.156822
$163$	−4.98971	−0.390824	−0.195412	−	0.980721i	$-0.562604\pi$
$163$	−4.98971	−0.390824	−0.195412	+	0.980721i	$0.562604\pi$
$164$	−14.0575	−1.09770
$165$	11.2646	0.876947
$166$	20.5853	1.59773
$167$	12.7646	0.987754	0.493877	−	0.869532i	$-0.335579\pi$
$167$	12.7646	0.987754	0.493877	+	0.869532i	$0.335579\pi$
$168$	−0.0529752	−0.00408712
$169$	−10.1463	−0.780488
$170$	−5.31632	−0.407743
$171$	7.43829	0.568820
$172$	25.0971	1.91363
$173$	15.1980	1.15548	0.577741	−	0.816220i	$-0.303935\pi$
$173$	15.1980	1.15548	0.577741	+	0.816220i	$0.303935\pi$
$174$	10.6518	0.807510
$175$	−3.49110	−0.263902
$176$	−17.0508	−1.28525
$177$	14.5108	1.09070
$178$	−26.4569	−1.98303
$179$	10.1054	0.755311	0.377656	−	0.925946i	$-0.376730\pi$
$179$	10.1054	0.755311	0.377656	+	0.925946i	$0.376730\pi$
$180$	5.28453	0.393886
$181$	−11.1983	−0.832364	−0.416182	−	0.909281i	$-0.636632\pi$
$181$	−11.1983	−0.832364	−0.416182	+	0.909281i	$0.636632\pi$
$182$	5.62132	0.416680
$183$	0.0641631	0.00474307
$184$	−0.0676674	−0.00498851
$185$	−12.9844	−0.954632
$186$	−9.70559	−0.711648
$187$	4.22930	0.309277
$188$	−0.277031	−0.0202046
$189$	−1.66715	−0.121267
$190$	−39.5443	−2.86885
$191$	−1.20852	−0.0874456	−0.0437228	−	0.999044i	$-0.513922\pi$
$191$	−1.20852	−0.0874456	−0.0437228	+	0.999044i	$0.513922\pi$
$192$	−7.87214	−0.568123
$193$	22.0336	1.58601	0.793005	−	0.609215i	$-0.208515\pi$
$193$	22.0336	1.58601	0.793005	+	0.609215i	$0.208515\pi$
$194$	−29.8984	−2.14658
$195$	4.49933	0.322204
$196$	−8.37405	−0.598147
$197$	−13.1835	−0.939284	−0.469642	−	0.882857i	$-0.655617\pi$
$197$	−13.1835	−0.939284	−0.469642	+	0.882857i	$0.655617\pi$
$198$	−8.44174	−0.599928
$199$	−13.7041	−0.971456	−0.485728	−	0.874110i	$-0.661445\pi$
$199$	−13.7041	−0.971456	−0.485728	+	0.874110i	$0.661445\pi$
$200$	0.0665406	0.00470513
$201$	−9.60638	−0.677582
$202$	33.5317	2.35928
$203$	8.89677	0.624430
$204$	1.98408	0.138913
$205$	−18.8710	−1.31801
$206$	26.1168	1.81964
$207$	−2.12952	−0.148012
$208$	−6.81046	−0.472221
$209$	31.4587	2.17604
$210$	8.86309	0.611611
$211$	−19.8086	−1.36368	−0.681839	−	0.731502i	$-0.738820\pi$
$211$	−19.8086	−1.36368	−0.681839	+	0.731502i	$0.738820\pi$
$212$	13.7973	0.947605
$213$	−1.43635	−0.0984170
$214$	−1.50350	−0.102777
$215$	33.6908	2.29769
$216$	0.0317759	0.00216208
$217$	−8.10647	−0.550303
$218$	5.65058	0.382706
$219$	10.3575	0.699892
$220$	22.3499	1.50683
$221$	1.68928	0.113633
$222$	9.73058	0.653074
$223$	−3.70617	−0.248183	−0.124092	−	0.992271i	$-0.539602\pi$
$223$	−3.70617	−0.248183	−0.124092	+	0.992271i	$0.539602\pi$
$224$	−13.3098	−0.889296
$225$	2.09406	0.139604
$226$	−36.1462	−2.40441
$227$	3.73516	0.247911	0.123956	−	0.992288i	$-0.460442\pi$
$227$	3.73516	0.247911	0.123956	+	0.992288i	$0.460442\pi$
$228$	14.7582	0.977383
$229$	−6.76427	−0.446996	−0.223498	−	0.974704i	$-0.571748\pi$
$229$	−6.76427	−0.446996	−0.223498	+	0.974704i	$0.571748\pi$
$230$	11.3212	0.746498
$231$	−7.05086	−0.463912
$232$	−0.169573	−0.0111330
$233$	5.88216	0.385353	0.192676	−	0.981262i	$-0.438283\pi$
$233$	5.88216	0.385353	0.192676	+	0.981262i	$0.438283\pi$
$234$	−3.37182	−0.220423
$235$	−0.371892	−0.0242596
$236$	28.7906	1.87411
$237$	7.94830	0.516297
$238$	3.32765	0.215700
$239$	21.3934	1.38383	0.691913	−	0.721981i	$-0.256768\pi$
$239$	21.3934	1.38383	0.691913	+	0.721981i	$0.256768\pi$
$240$	−10.7380	−0.693135
$241$	11.9190	0.767768	0.383884	−	0.923381i	$-0.374586\pi$
$241$	11.9190	0.767768	0.383884	+	0.923381i	$0.374586\pi$
$242$	−13.7464	−0.883655
$243$	1.00000	0.0641500
$244$	0.127305	0.00814985
$245$	−11.2415	−0.718192
$246$	14.1420	0.901664
$247$	12.5653	0.799512
$248$	0.154510	0.00981139
$249$	−10.3132	−0.653573
$250$	15.4489	0.977076
$251$	1.41391	0.0892453	0.0446226	−	0.999004i	$-0.485791\pi$
$251$	1.41391	0.0892453	0.0446226	+	0.999004i	$0.485791\pi$
$252$	−3.30775	−0.208369
$253$	−9.00636	−0.566225
$254$	25.9677	1.62936
$255$	2.66347	0.166793
$256$	16.2517	1.01573
$257$	−23.6580	−1.47574	−0.737872	−	0.674940i	$-0.764169\pi$
$257$	−23.6580	−1.47574	−0.737872	+	0.674940i	$0.764169\pi$
$258$	−25.2480	−1.57187
$259$	8.12734	0.505008
$260$	8.92704	0.553631
$261$	−5.33652	−0.330322
$262$	18.9823	1.17273
$263$	25.8417	1.59347	0.796734	−	0.604330i	$-0.206559\pi$
$263$	25.8417	1.59347	0.796734	+	0.604330i	$0.206559\pi$
$264$	0.134390	0.00827112
$265$	18.5218	1.13779
$266$	24.7520	1.51764
$267$	13.2549	0.811185
$268$	−19.0598	−1.16426
$269$	−30.7226	−1.87319	−0.936594	−	0.350416i	$-0.886040\pi$
$269$	−30.7226	−1.87319	−0.936594	+	0.350416i	$0.886040\pi$
$270$	−5.31632	−0.323541
$271$	6.80945	0.413644	0.206822	−	0.978379i	$-0.433688\pi$
$271$	6.80945	0.413644	0.206822	+	0.978379i	$0.433688\pi$
$272$	−4.03159	−0.244451
$273$	−2.81627	−0.170449
$274$	−33.1674	−2.00371
$275$	8.85639	0.534060
$276$	−4.22513	−0.254323
$277$	−32.7136	−1.96557	−0.982784	−	0.184758i	$-0.940850\pi$
$277$	−32.7136	−1.96557	−0.982784	+	0.184758i	$0.940850\pi$
$278$	−27.6828	−1.66031
$279$	4.86248	0.291109
$280$	−0.141098	−0.00843219
$281$	3.27417	0.195321	0.0976604	−	0.995220i	$-0.468864\pi$
$281$	3.27417	0.195321	0.0976604	+	0.995220i	$0.468864\pi$
$282$	0.278698	0.0165962
$283$	26.9875	1.60424	0.802119	−	0.597164i	$-0.203706\pi$
$283$	26.9875	1.60424	0.802119	+	0.597164i	$0.203706\pi$
$284$	−2.84983	−0.169106
$285$	19.8116	1.17354
$286$	−14.2604	−0.843237
$287$	11.8120	0.697238
$288$	7.98356	0.470436
$289$	1.00000	0.0588235
$290$	28.3707	1.66598
$291$	14.9790	0.878087
$292$	20.5500	1.20260
$293$	16.1334	0.942524	0.471262	−	0.881993i	$-0.343799\pi$
$293$	16.1334	0.942524	0.471262	+	0.881993i	$0.343799\pi$
$294$	8.42443	0.491323
$295$	38.6490	2.25023
$296$	−0.154908	−0.00900383
$297$	4.22930	0.245409
$298$	35.4423	2.05312
$299$	−3.59734	−0.208040
$300$	4.15478	0.239876
$301$	−21.0881	−1.21550
$302$	−16.6494	−0.958067
$303$	−16.7993	−0.965095
$304$	−29.9881	−1.71993
$305$	0.170896	0.00978549
$306$	−1.99602	−0.114105
$307$	13.6503	0.779062	0.389531	−	0.921013i	$-0.372637\pi$
$307$	13.6503	0.779062	0.389531	+	0.921013i	$0.372637\pi$
$308$	−13.9895	−0.797124
$309$	−13.0844	−0.744348
$310$	−25.8505	−1.46821
$311$	−0.320409	−0.0181687	−0.00908435	−	0.999959i	$-0.502892\pi$
$311$	−0.320409	−0.0181687	−0.00908435	+	0.999959i	$0.502892\pi$
$312$	0.0536784	0.00303894
$313$	−21.1775	−1.19702	−0.598512	−	0.801114i	$-0.704241\pi$
$313$	−21.1775	−1.19702	−0.598512	+	0.801114i	$0.704241\pi$
$314$	−1.99602	−0.112642
$315$	−4.44039	−0.250188
$316$	15.7701	0.887135
$317$	6.91183	0.388207	0.194103	−	0.980981i	$-0.437820\pi$
$317$	6.91183	0.388207	0.194103	+	0.980981i	$0.437820\pi$
$318$	−13.8803	−0.778371
$319$	−22.5697	−1.26366
$320$	−20.9672	−1.17210
$321$	0.753252	0.0420424
$322$	−7.08629	−0.394904
$323$	7.43829	0.413877
$324$	1.98408	0.110227
$325$	3.53744	0.196222
$326$	9.95954	0.551608
$327$	−2.83093	−0.156551
$328$	−0.225137	−0.0124311
$329$	0.232779	0.0128335
$330$	−22.4843	−1.23772
$331$	−22.7265	−1.24916	−0.624581	−	0.780960i	$-0.714730\pi$
$331$	−22.7265	−1.24916	−0.624581	+	0.780960i	$0.714730\pi$
$332$	−20.4622	−1.12301
$333$	−4.87500	−0.267148
$334$	−25.4783	−1.39411
$335$	−25.5863	−1.39793
$336$	6.72125	0.366674
$337$	−4.39532	−0.239429	−0.119714	−	0.992808i	$-0.538198\pi$
$337$	−4.39532	−0.239429	−0.119714	+	0.992808i	$0.538198\pi$
$338$	20.2523	1.10158
$339$	18.1092	0.983555
$340$	5.28453	0.286594
$341$	20.5649	1.11365
$342$	−14.8469	−0.802830
$343$	18.7064	1.01005
$344$	0.401941	0.0216712
$345$	−5.67190	−0.305365
$346$	−30.3354	−1.63084
$347$	−24.7268	−1.32740	−0.663701	−	0.747998i	$-0.731015\pi$
$347$	−24.7268	−1.32740	−0.663701	+	0.747998i	$0.731015\pi$
$348$	−10.5881	−0.567581
$349$	−23.5574	−1.26100	−0.630500	−	0.776189i	$-0.717150\pi$
$349$	−23.5574	−1.26100	−0.630500	+	0.776189i	$0.717150\pi$
$350$	6.96829	0.372471
$351$	1.68928	0.0901669
$352$	33.7648	1.79967
$353$	6.38925	0.340066	0.170033	−	0.985438i	$-0.445613\pi$
$353$	6.38925	0.340066	0.170033	+	0.985438i	$0.445613\pi$
$354$	−28.9638	−1.53941
$355$	−3.82567	−0.203045
$356$	26.2987	1.39383
$357$	−1.66715	−0.0882348
$358$	−20.1705	−1.06604
$359$	19.0283	1.00428	0.502139	−	0.864787i	$-0.332547\pi$
$359$	19.0283	1.00428	0.502139	+	0.864787i	$0.332547\pi$
$360$	0.0846342	0.00446061
$361$	36.3281	1.91200
$362$	22.3520	1.17480
$363$	6.88694	0.361471
$364$	−5.58771	−0.292876
$365$	27.5867	1.44396
$366$	−0.128071	−0.00669435
$367$	−10.0855	−0.526458	−0.263229	−	0.964733i	$-0.584788\pi$
$367$	−10.0855	−0.526458	−0.263229	+	0.964733i	$0.584788\pi$
$368$	8.58533	0.447541
$369$	−7.08513	−0.368837
$370$	25.9171	1.34736
$371$	−11.5934	−0.601898
$372$	9.64755	0.500202
$373$	−1.44077	−0.0746002	−0.0373001	−	0.999304i	$-0.511876\pi$
$373$	−1.44077	−0.0746002	−0.0373001	+	0.999304i	$0.511876\pi$
$374$	−8.44174	−0.436512
$375$	−7.73988	−0.399686
$376$	−0.00443678	−0.000228810 0
$377$	−9.01486	−0.464289
$378$	3.32765	0.171156
$379$	−34.7656	−1.78579	−0.892895	−	0.450264i	$-0.851330\pi$
$379$	−34.7656	−1.78579	−0.892895	+	0.450264i	$0.851330\pi$
$380$	39.3079	2.01645
$381$	−13.0098	−0.666511
$382$	2.41223	0.123420
$383$	−1.16890	−0.0597279	−0.0298640	−	0.999554i	$-0.509507\pi$
$383$	−1.16890	−0.0597279	−0.0298640	+	0.999554i	$0.509507\pi$
$384$	−0.254200	−0.0129721
$385$	−18.7797	−0.957103
$386$	−43.9793	−2.23849
$387$	12.6492	0.642996
$388$	29.7196	1.50879
$389$	31.4845	1.59633	0.798163	−	0.602442i	$-0.205805\pi$
$389$	31.4845	1.59633	0.798163	+	0.602442i	$0.205805\pi$
$390$	−8.98074	−0.454758
$391$	−2.12952	−0.107694
$392$	−0.134114	−0.00677379
$393$	−9.51008	−0.479720
$394$	26.3144	1.32570
$395$	21.1700	1.06518
$396$	8.39126	0.421677
$397$	−1.07139	−0.0537717	−0.0268859	−	0.999639i	$-0.508559\pi$
$397$	−1.07139	−0.0537717	−0.0268859	+	0.999639i	$0.508559\pi$
$398$	27.3536	1.37111
$399$	−12.4007	−0.620812
$400$	−8.44237	−0.422119
$401$	31.3944	1.56776	0.783882	−	0.620910i	$-0.213237\pi$
$401$	31.3944	1.56776	0.783882	+	0.620910i	$0.213237\pi$
$402$	19.1745	0.956337
$403$	8.21408	0.409172
$404$	−33.3312	−1.65829
$405$	2.66347	0.132349
$406$	−17.7581	−0.881319
$407$	−20.6178	−1.02199
$408$	0.0317759	0.00157314
$409$	−18.1732	−0.898607	−0.449303	−	0.893379i	$-0.648328\pi$
$409$	−18.1732	−0.898607	−0.449303	+	0.893379i	$0.648328\pi$
$410$	37.6669	1.86023
$411$	16.6168	0.819646
$412$	−25.9606	−1.27899
$413$	−24.1916	−1.19039
$414$	4.25055	0.208903
$415$	−27.4689	−1.34840
$416$	13.4864	0.661227
$417$	13.8690	0.679170
$418$	−62.7921	−3.07126
$419$	3.46545	0.169298	0.0846492	−	0.996411i	$-0.473023\pi$
$419$	3.46545	0.169298	0.0846492	+	0.996411i	$0.473023\pi$
$420$	−8.81009	−0.429888
$421$	17.2884	0.842585	0.421292	−	0.906925i	$-0.361577\pi$
$421$	17.2884	0.842585	0.421292	+	0.906925i	$0.361577\pi$
$422$	39.5382	1.92469
$423$	−0.139627	−0.00678890
$424$	0.220971	0.0107313
$425$	2.09406	0.101577
$426$	2.86697	0.138905
$427$	−0.106969	−0.00517661
$428$	1.49451	0.0722399
$429$	7.14445	0.344937
$430$	−67.2473	−3.24295
$431$	−8.34896	−0.402155	−0.201078	−	0.979575i	$-0.564444\pi$
$431$	−8.34896	−0.402155	−0.201078	+	0.979575i	$0.564444\pi$
$432$	−4.03159	−0.193970
$433$	−27.4973	−1.32144	−0.660719	−	0.750633i	$-0.729748\pi$
$433$	−27.4973	−1.32144	−0.660719	+	0.750633i	$0.729748\pi$
$434$	16.1806	0.776696
$435$	−14.2137	−0.681492
$436$	−5.61679	−0.268995
$437$	−15.8400	−0.757728
$438$	−20.6736	−0.987825
$439$	−35.1387	−1.67708	−0.838539	−	0.544841i	$-0.816590\pi$
$439$	−35.1387	−1.67708	−0.838539	+	0.544841i	$0.816590\pi$
$440$	0.357943	0.0170643
$441$	−4.22062	−0.200982
$442$	−3.37182	−0.160381
$443$	−6.04430	−0.287173	−0.143587	−	0.989638i	$-0.545864\pi$
$443$	−6.04430	−0.287173	−0.143587	+	0.989638i	$0.545864\pi$
$444$	−9.67239	−0.459032
$445$	35.3039	1.67357
$446$	7.39757	0.350285
$447$	−17.7565	−0.839855
$448$	13.1240	0.620051
$449$	35.1279	1.65779	0.828894	−	0.559406i	$-0.188971\pi$
$449$	35.1279	1.65779	0.828894	+	0.559406i	$0.188971\pi$
$450$	−4.17977	−0.197036
$451$	−29.9651	−1.41100
$452$	35.9300	1.69001
$453$	8.34133	0.391910
$454$	−7.45544	−0.349901
$455$	−7.50105	−0.351655
$456$	0.236359	0.0110685
$457$	−20.8102	−0.973462	−0.486731	−	0.873552i	$-0.661811\pi$
$457$	−20.8102	−0.973462	−0.486731	+	0.873552i	$0.661811\pi$
$458$	13.5016	0.630888
$459$	1.00000	0.0466760
$460$	−11.2535	−0.524697
$461$	−15.5733	−0.725321	−0.362660	−	0.931921i	$-0.618132\pi$
$461$	−15.5733	−0.725321	−0.362660	+	0.931921i	$0.618132\pi$
$462$	14.0736	0.654764
$463$	12.1463	0.564484	0.282242	−	0.959343i	$-0.408922\pi$
$463$	12.1463	0.564484	0.282242	+	0.959343i	$0.408922\pi$
$464$	21.5146	0.998792
$465$	12.9511	0.600591
$466$	−11.7409	−0.543886
$467$	26.1873	1.21181	0.605903	−	0.795539i	$-0.292812\pi$
$467$	26.1873	1.21181	0.605903	+	0.795539i	$0.292812\pi$
$468$	3.35166	0.154931
$469$	16.0152	0.739516
$470$	0.742303	0.0342399
$471$	1.00000	0.0460776
$472$	0.461094	0.0212236
$473$	53.4973	2.45981
$474$	−15.8649	−0.728700
$475$	15.5762	0.714685
$476$	−3.30775	−0.151611
$477$	6.95402	0.318403
$478$	−42.7017	−1.95313
$479$	−20.7437	−0.947805	−0.473902	−	0.880577i	$-0.657155\pi$
$479$	−20.7437	−0.947805	−0.473902	+	0.880577i	$0.657155\pi$
$480$	21.2639	0.970562
$481$	−8.23523	−0.375494
$482$	−23.7905	−1.08363
$483$	3.55022	0.161540
$484$	13.6642	0.621102
$485$	39.8962	1.81159
$486$	−1.99602	−0.0905411
$487$	24.9536	1.13075	0.565377	−	0.824833i	$-0.308731\pi$
$487$	24.9536	1.13075	0.565377	+	0.824833i	$0.308731\pi$
$488$	0.00203884	9.22941e−5 0
$489$	−4.98971	−0.225642
$490$	22.4382	1.01365
$491$	−1.17597	−0.0530708	−0.0265354	−	0.999648i	$-0.508447\pi$
$491$	−1.17597	−0.0530708	−0.0265354	+	0.999648i	$0.508447\pi$
$492$	−14.0575	−0.633760
$493$	−5.33652	−0.240345
$494$	−25.0806	−1.12843
$495$	11.2646	0.506306
$496$	−19.6035	−0.880224
$497$	2.39460	0.107413
$498$	20.5853	0.922451
$499$	17.9074	0.801643	0.400822	−	0.916156i	$-0.368725\pi$
$499$	17.9074	0.801643	0.400822	+	0.916156i	$0.368725\pi$
$500$	−15.3566	−0.686766
$501$	12.7646	0.570280
$502$	−2.82219	−0.125960
$503$	−30.0178	−1.33843	−0.669213	−	0.743071i	$-0.733369\pi$
$503$	−30.0178	−1.33843	−0.669213	+	0.743071i	$0.733369\pi$
$504$	−0.0529752	−0.00235970
$505$	−44.7444	−1.99110
$506$	17.9768	0.799168
$507$	−10.1463	−0.450615
$508$	−25.8125	−1.14524
$509$	31.0378	1.37573	0.687863	−	0.725840i	$-0.258549\pi$
$509$	31.0378	1.37573	0.687863	+	0.725840i	$0.258549\pi$
$510$	−5.31632	−0.235411
$511$	−17.2674	−0.763865
$512$	−31.9302	−1.41113
$513$	7.43829	0.328408
$514$	47.2217	2.08286
$515$	−34.8500	−1.53567
$516$	25.0971	1.10484
$517$	−0.590524	−0.0259712
$518$	−16.2223	−0.712767
$519$	15.1980	0.667117
$520$	0.142971	0.00626967
$521$	26.8775	1.17752	0.588762	−	0.808306i	$-0.299615\pi$
$521$	26.8775	1.17752	0.588762	+	0.808306i	$0.299615\pi$
$522$	10.6518	0.466216
$523$	−11.3691	−0.497137	−0.248568	−	0.968614i	$-0.579960\pi$
$523$	−11.3691	−0.497137	−0.248568	+	0.968614i	$0.579960\pi$
$524$	−18.8688	−0.824286
$525$	−3.49110	−0.152364
$526$	−51.5805	−2.24902
$527$	4.86248	0.211813
$528$	−17.0508	−0.742039
$529$	−18.4652	−0.802833
$530$	−36.9698	−1.60587
$531$	14.5108	0.629715
$532$	−24.6040	−1.06672
$533$	−11.9688	−0.518424
$534$	−26.4569	−1.14490
$535$	2.00626	0.0867382
$536$	−0.305252	−0.0131849
$537$	10.1054	0.436079
$538$	61.3227	2.64381
$539$	−17.8503	−0.768865
$540$	5.28453	0.227410
$541$	−35.8543	−1.54150	−0.770749	−	0.637139i	$-0.780118\pi$
$541$	−35.8543	−1.54150	−0.770749	+	0.637139i	$0.780118\pi$
$542$	−13.5918	−0.583816
$543$	−11.1983	−0.480565
$544$	7.98356	0.342292
$545$	−7.54009	−0.322982
$546$	5.62132	0.240570
$547$	−13.6343	−0.582960	−0.291480	−	0.956577i	$-0.594148\pi$
$547$	−13.6343	−0.582960	−0.291480	+	0.956577i	$0.594148\pi$
$548$	32.9690	1.40837
$549$	0.0641631	0.00273841
$550$	−17.6775	−0.753771
$551$	−39.6946	−1.69105
$552$	−0.0676674	−0.00288012
$553$	−13.2510	−0.563489
$554$	65.2968	2.77420
$555$	−12.9844	−0.551157
$556$	27.5173	1.16699
$557$	3.97951	0.168617	0.0843087	−	0.996440i	$-0.473132\pi$
$557$	3.97951	0.168617	0.0843087	+	0.996440i	$0.473132\pi$
$558$	−9.70559	−0.410870
$559$	21.3680	0.903771
$560$	17.9018	0.756490
$561$	4.22930	0.178561
$562$	−6.53530	−0.275675
$563$	6.77992	0.285740	0.142870	−	0.989741i	$-0.454367\pi$
$563$	6.77992	0.285740	0.142870	+	0.989741i	$0.454367\pi$
$564$	−0.277031	−0.0116651
$565$	48.2332	2.02919
$566$	−53.8674	−2.26422
$567$	−1.66715	−0.0700136
$568$	−0.0456413	−0.00191507
$569$	−44.1615	−1.85135	−0.925673	−	0.378325i	$-0.876500\pi$
$569$	−44.1615	−1.85135	−0.925673	+	0.378325i	$0.876500\pi$
$570$	−39.5443	−1.65633
$571$	9.62064	0.402611	0.201306	−	0.979528i	$-0.435482\pi$
$571$	9.62064	0.402611	0.201306	+	0.979528i	$0.435482\pi$
$572$	14.1752	0.592693
$573$	−1.20852	−0.0504867
$574$	−23.5769	−0.984079
$575$	−4.45933	−0.185967
$576$	−7.87214	−0.328006
$577$	16.2857	0.677984	0.338992	−	0.940789i	$-0.389914\pi$
$577$	16.2857	0.677984	0.338992	+	0.940789i	$0.389914\pi$
$578$	−1.99602	−0.0830233
$579$	22.0336	0.915683
$580$	−28.2010	−1.17098
$581$	17.1936	0.713312
$582$	−29.8984	−1.23933
$583$	29.4106	1.21806
$584$	0.329118	0.0136190
$585$	4.49933	0.186025
$586$	−32.2025	−1.33027
$587$	−34.1763	−1.41061	−0.705304	−	0.708905i	$-0.749189\pi$
$587$	−34.1763	−1.41061	−0.705304	+	0.708905i	$0.749189\pi$
$588$	−8.37405	−0.345340
$589$	36.1685	1.49030
$590$	−77.1440	−3.17597
$591$	−13.1835	−0.542296
$592$	19.6540	0.807774
$593$	9.51952	0.390920	0.195460	−	0.980712i	$-0.437380\pi$
$593$	9.51952	0.390920	0.195460	+	0.980712i	$0.437380\pi$
$594$	−8.44174	−0.346369
$595$	−4.44039	−0.182038
$596$	−35.2304	−1.44309
$597$	−13.7041	−0.560870
$598$	7.18036	0.293627
$599$	−20.9887	−0.857576	−0.428788	−	0.903405i	$-0.641059\pi$
$599$	−20.9887	−0.857576	−0.428788	+	0.903405i	$0.641059\pi$
$600$	0.0665406	0.00271651
$601$	−30.6276	−1.24932	−0.624662	−	0.780895i	$-0.714763\pi$
$601$	−30.6276	−1.24932	−0.624662	+	0.780895i	$0.714763\pi$
$602$	42.0922	1.71555
$603$	−9.60638	−0.391202
$604$	16.5499	0.673404
$605$	18.3431	0.745755
$606$	33.5317	1.36213
$607$	45.4789	1.84593	0.922966	−	0.384883i	$-0.125758\pi$
$607$	45.4789	1.84593	0.922966	+	0.384883i	$0.125758\pi$
$608$	59.3840	2.40834
$609$	8.89677	0.360515
$610$	−0.341112	−0.0138112
$611$	−0.235869	−0.00954223
$612$	1.98408	0.0802017
$613$	13.3199	0.537985	0.268993	−	0.963142i	$-0.413309\pi$
$613$	13.3199	0.537985	0.268993	+	0.963142i	$0.413309\pi$
$614$	−27.2461	−1.09956
$615$	−18.8710	−0.760953
$616$	−0.224048	−0.00902714
$617$	20.2501	0.815237	0.407619	−	0.913152i	$-0.366359\pi$
$617$	20.2501	0.815237	0.407619	+	0.913152i	$0.366359\pi$
$618$	26.1168	1.05057
$619$	−3.93440	−0.158137	−0.0790684	−	0.996869i	$-0.525195\pi$
$619$	−3.93440	−0.158137	−0.0790684	+	0.996869i	$0.525195\pi$
$620$	25.6959	1.03197
$621$	−2.12952	−0.0854546
$622$	0.639541	0.0256433
$623$	−22.0978	−0.885330
$624$	−6.81046	−0.272637
$625$	−31.0852	−1.24341
$626$	42.2706	1.68947
$627$	31.4587	1.25634
$628$	1.98408	0.0791734
$629$	−4.87500	−0.194379
$630$	8.86309	0.353114
$631$	−6.81737	−0.271395	−0.135698	−	0.990750i	$-0.543328\pi$
$631$	−6.81737	−0.271395	−0.135698	+	0.990750i	$0.543328\pi$
$632$	0.252565	0.0100465
$633$	−19.8086	−0.787320
$634$	−13.7961	−0.547914
$635$	−34.6511	−1.37509
$636$	13.7973	0.547100
$637$	−7.12980	−0.282493
$638$	45.0495	1.78353
$639$	−1.43635	−0.0568211
$640$	−0.677052	−0.0267628
$641$	3.53387	0.139579	0.0697897	−	0.997562i	$-0.477767\pi$
$641$	3.53387	0.139579	0.0697897	+	0.997562i	$0.477767\pi$
$642$	−1.50350	−0.0593385
$643$	24.4725	0.965101	0.482550	−	0.875868i	$-0.339710\pi$
$643$	24.4725	0.965101	0.482550	+	0.875868i	$0.339710\pi$
$644$	7.04392	0.277569
$645$	33.6908	1.32657
$646$	−14.8469	−0.584145
$647$	14.3893	0.565703	0.282852	−	0.959164i	$-0.408720\pi$
$647$	14.3893	0.565703	0.282852	+	0.959164i	$0.408720\pi$
$648$	0.0317759	0.00124828
$649$	61.3704	2.40900
$650$	−7.06079	−0.276947
$651$	−8.10647	−0.317718
$652$	−9.89998	−0.387713
$653$	−39.9016	−1.56147	−0.780736	−	0.624861i	$-0.785156\pi$
$653$	−39.9016	−1.56147	−0.780736	+	0.624861i	$0.785156\pi$
$654$	5.65058	0.220955
$655$	−25.3298	−0.989717
$656$	28.5643	1.11525
$657$	10.3575	0.404083
$658$	−0.464630	−0.0181132
$659$	31.0804	1.21072	0.605361	−	0.795951i	$-0.293029\pi$
$659$	31.0804	1.21072	0.605361	+	0.795951i	$0.293029\pi$
$660$	22.3499	0.869967
$661$	−20.0636	−0.780384	−0.390192	−	0.920733i	$-0.627591\pi$
$661$	−20.0636	−0.780384	−0.390192	+	0.920733i	$0.627591\pi$
$662$	45.3625	1.76306
$663$	1.68928	0.0656061
$664$	−0.327712	−0.0127177
$665$	−33.0289	−1.28081
$666$	9.73058	0.377052
$667$	11.3642	0.440024
$668$	25.3260	0.979891
$669$	−3.70617	−0.143289
$670$	51.0706	1.97303
$671$	0.271365	0.0104759
$672$	−13.3098	−0.513435
$673$	8.06907	0.311040	0.155520	−	0.987833i	$-0.450295\pi$
$673$	8.06907	0.311040	0.155520	+	0.987833i	$0.450295\pi$
$674$	8.77314	0.337929
$675$	2.09406	0.0806003
$676$	−20.1312	−0.774275
$677$	−50.9131	−1.95675	−0.978375	−	0.206841i	$-0.933682\pi$
$677$	−50.9131	−1.95675	−0.978375	+	0.206841i	$0.933682\pi$
$678$	−36.1462	−1.38819
$679$	−24.9723	−0.958348
$680$	0.0846342	0.00324557
$681$	3.73516	0.143132
$682$	−41.0478	−1.57180
$683$	47.2871	1.80939	0.904695	−	0.426059i	$-0.140098\pi$
$683$	47.2871	1.80939	0.904695	+	0.426059i	$0.140098\pi$
$684$	14.7582	0.564292
$685$	44.2583	1.69102
$686$	−37.3383	−1.42558
$687$	−6.76427	−0.258073
$688$	−50.9964	−1.94422
$689$	11.7473	0.447535
$690$	11.3212	0.430991
$691$	−28.0249	−1.06612	−0.533058	−	0.846079i	$-0.678957\pi$
$691$	−28.0249	−1.06612	−0.533058	+	0.846079i	$0.678957\pi$
$692$	30.1540	1.14628
$693$	−7.05086	−0.267840
$694$	49.3550	1.87349
$695$	36.9397	1.40120
$696$	−0.169573	−0.00642765
$697$	−7.08513	−0.268369
$698$	47.0210	1.77977
$699$	5.88216	0.222484
$700$	−6.92662	−0.261802
$701$	−4.84423	−0.182964	−0.0914821	−	0.995807i	$-0.529160\pi$
$701$	−4.84423	−0.182964	−0.0914821	+	0.995807i	$0.529160\pi$
$702$	−3.37182	−0.127261
$703$	−36.2617	−1.36763
$704$	−33.2936	−1.25480
$705$	−0.371892	−0.0140063
$706$	−12.7531	−0.479968
$707$	28.0069	1.05331
$708$	28.7906	1.08202
$709$	27.5784	1.03573	0.517864	−	0.855463i	$-0.326727\pi$
$709$	27.5784	1.03573	0.517864	+	0.855463i	$0.326727\pi$
$710$	7.63609	0.286577
$711$	7.94830	0.298084
$712$	0.421186	0.0157846
$713$	−10.3547	−0.387788
$714$	3.32765	0.124534
$715$	19.0290	0.711645
$716$	20.0499	0.749299
$717$	21.3934	0.798953
$718$	−37.9809	−1.41743
$719$	−5.10424	−0.190356	−0.0951781	−	0.995460i	$-0.530342\pi$
$719$	−5.10424	−0.190356	−0.0951781	+	0.995460i	$0.530342\pi$
$720$	−10.7380	−0.400182
$721$	21.8137	0.812384
$722$	−72.5115	−2.69860
$723$	11.9190	0.443271
$724$	−22.2183	−0.825738
$725$	−11.1750	−0.415028
$726$	−13.7464	−0.510178
$727$	43.7869	1.62397	0.811983	−	0.583682i	$-0.198388\pi$
$727$	43.7869	1.62397	0.811983	+	0.583682i	$0.198388\pi$
$728$	−0.0894897	−0.00331671
$729$	1.00000	0.0370370
$730$	−55.0636	−2.03799
$731$	12.6492	0.467848
$732$	0.127305	0.00470532
$733$	1.22815	0.0453628	0.0226814	−	0.999743i	$-0.492780\pi$
$733$	1.22815	0.0453628	0.0226814	+	0.999743i	$0.492780\pi$
$734$	20.1308	0.743041
$735$	−11.2415	−0.414649
$736$	−17.0011	−0.626670
$737$	−40.6282	−1.49656
$738$	14.1420	0.520576
$739$	−44.2533	−1.62788	−0.813941	−	0.580947i	$-0.802682\pi$
$739$	−44.2533	−1.62788	−0.813941	+	0.580947i	$0.802682\pi$
$740$	−25.7621	−0.947034
$741$	12.5653	0.461599
$742$	23.1406	0.849517
$743$	10.6039	0.389020	0.194510	−	0.980901i	$-0.437688\pi$
$743$	10.6039	0.389020	0.194510	+	0.980901i	$0.437688\pi$
$744$	0.154510	0.00566461
$745$	−47.2939	−1.73272
$746$	2.87580	0.105290
$747$	−10.3132	−0.377341
$748$	8.39126	0.306815
$749$	−1.25578	−0.0458852
$750$	15.4489	0.564115
$751$	−28.7836	−1.05033	−0.525165	−	0.851001i	$-0.675996\pi$
$751$	−28.7836	−1.05033	−0.525165	+	0.851001i	$0.675996\pi$
$752$	0.562919	0.0205275
$753$	1.41391	0.0515258
$754$	17.9938	0.655296
$755$	22.2169	0.808554
$756$	−3.30775	−0.120302
$757$	38.4107	1.39606	0.698030	−	0.716069i	$-0.254060\pi$
$757$	38.4107	1.39606	0.698030	+	0.716069i	$0.254060\pi$
$758$	69.3928	2.52046
$759$	−9.00636	−0.326910
$760$	0.629533	0.0228356
$761$	28.0146	1.01553	0.507764	−	0.861496i	$-0.330472\pi$
$761$	28.0146	1.01553	0.507764	+	0.861496i	$0.330472\pi$
$762$	25.9677	0.940712
$763$	4.71957	0.170860
$764$	−2.39780	−0.0867495
$765$	2.66347	0.0962979
$766$	2.33314	0.0842998
$767$	24.5127	0.885104
$768$	16.2517	0.586431
$769$	53.4118	1.92608	0.963039	−	0.269361i	$-0.0868126\pi$
$769$	53.4118	1.92608	0.963039	+	0.269361i	$0.0868126\pi$
$770$	37.4846	1.35085
$771$	−23.6580	−0.852022
$772$	43.7163	1.57339
$773$	38.2595	1.37610	0.688049	−	0.725664i	$-0.258467\pi$
$773$	38.2595	1.37610	0.688049	+	0.725664i	$0.258467\pi$
$774$	−25.2480	−0.907522
$775$	10.1823	0.365759
$776$	0.475973	0.0170865
$777$	8.12734	0.291567
$778$	−62.8435	−2.25305
$779$	−52.7012	−1.88822
$780$	8.92704	0.319639
$781$	−6.07474	−0.217371
$782$	4.25055	0.151999
$783$	−5.33652	−0.190712
$784$	17.0158	0.607707
$785$	2.66347	0.0950632
$786$	18.9823	0.677075
$787$	−2.23783	−0.0797699	−0.0398850	−	0.999204i	$-0.512699\pi$
$787$	−2.23783	−0.0797699	−0.0398850	+	0.999204i	$0.512699\pi$
$788$	−26.1571	−0.931808
$789$	25.8417	0.919989
$790$	−42.2557	−1.50339
$791$	−30.1906	−1.07346
$792$	0.134390	0.00477534
$793$	0.108389	0.00384901
$794$	2.13852	0.0758932
$795$	18.5218	0.656901
$796$	−27.1900	−0.963723
$797$	15.2300	0.539474	0.269737	−	0.962934i	$-0.413063\pi$
$797$	15.2300	0.539474	0.269737	+	0.962934i	$0.413063\pi$
$798$	24.7520	0.876212
$799$	−0.139627	−0.00493965
$800$	16.7180	0.591072
$801$	13.2549	0.468338
$802$	−62.6638	−2.21274
$803$	43.8047	1.54584
$804$	−19.0598	−0.672189
$805$	9.45589	0.333276
$806$	−16.3954	−0.577504
$807$	−30.7226	−1.08149
$808$	−0.533814	−0.0187795
$809$	−10.1243	−0.355950	−0.177975	−	0.984035i	$-0.556955\pi$
$809$	−10.1243	−0.355950	−0.177975	+	0.984035i	$0.556955\pi$
$810$	−5.31632	−0.186797
$811$	39.5204	1.38775	0.693875	−	0.720095i	$-0.255902\pi$
$811$	39.5204	1.38775	0.693875	+	0.720095i	$0.255902\pi$
$812$	17.6519	0.619460
$813$	6.80945	0.238818
$814$	41.1535	1.44243
$815$	−13.2899	−0.465526
$816$	−4.03159	−0.141134
$817$	94.0885	3.29174
$818$	36.2740	1.26829
$819$	−2.81627	−0.0984085
$820$	−37.4416	−1.30752
$821$	46.6305	1.62741	0.813707	−	0.581275i	$-0.197446\pi$
$821$	46.6305	1.62741	0.813707	+	0.581275i	$0.197446\pi$
$822$	−33.1674	−1.15684
$823$	24.2775	0.846259	0.423130	−	0.906069i	$-0.360931\pi$
$823$	24.2775	0.846259	0.423130	+	0.906069i	$0.360931\pi$
$824$	−0.415771	−0.0144841
$825$	8.85639	0.308340
$826$	48.2868	1.68011
$827$	−41.5814	−1.44593	−0.722964	−	0.690886i	$-0.757221\pi$
$827$	−41.5814	−1.44593	−0.722964	+	0.690886i	$0.757221\pi$
$828$	−4.22513	−0.146834
$829$	−20.2797	−0.704344	−0.352172	−	0.935935i	$-0.614557\pi$
$829$	−20.2797	−0.704344	−0.352172	+	0.935935i	$0.614557\pi$
$830$	54.8284	1.90312
$831$	−32.7136	−1.13482
$832$	−13.2982	−0.461033
$833$	−4.22062	−0.146236
$834$	−27.6828	−0.958578
$835$	33.9981	1.17655
$836$	62.4166	2.15872
$837$	4.86248	0.168072
$838$	−6.91710	−0.238947
$839$	30.9020	1.06686	0.533428	−	0.845846i	$-0.320904\pi$
$839$	30.9020	1.06686	0.533428	+	0.845846i	$0.320904\pi$
$840$	−0.141098	−0.00486833
$841$	−0.521533	−0.0179839
$842$	−34.5079	−1.18922
$843$	3.27417	0.112769
$844$	−39.3018	−1.35282
$845$	−27.0245	−0.929669
$846$	0.278698	0.00958183
$847$	−11.4815	−0.394510
$848$	−28.0357	−0.962751
$849$	26.9875	0.926208
$850$	−4.17977	−0.143365
$851$	10.3814	0.355870
$852$	−2.84983	−0.0976336
$853$	20.4521	0.700267	0.350133	−	0.936700i	$-0.386136\pi$
$853$	20.4521	0.700267	0.350133	+	0.936700i	$0.386136\pi$
$854$	0.213512	0.00730624
$855$	19.8116	0.677543
$856$	0.0239353	0.000818091 0
$857$	49.8881	1.70415	0.852073	−	0.523423i	$-0.175345\pi$
$857$	49.8881	1.70415	0.852073	+	0.523423i	$0.175345\pi$
$858$	−14.2604	−0.486843
$859$	42.7949	1.46014	0.730071	−	0.683371i	$-0.239487\pi$
$859$	42.7949	1.46014	0.730071	+	0.683371i	$0.239487\pi$
$860$	66.8452	2.27940
$861$	11.8120	0.402550
$862$	16.6647	0.567600
$863$	−2.35788	−0.0802631	−0.0401316	−	0.999194i	$-0.512778\pi$
$863$	−2.35788	−0.0802631	−0.0401316	+	0.999194i	$0.512778\pi$
$864$	7.98356	0.271606
$865$	40.4793	1.37634
$866$	54.8851	1.86507
$867$	1.00000	0.0339618
$868$	−16.0839	−0.545923
$869$	33.6157	1.14033
$870$	28.3707	0.961856
$871$	−16.2278	−0.549859
$872$	−0.0899555	−0.00304628
$873$	14.9790	0.506964
$874$	31.6168	1.06945
$875$	12.9035	0.436219
$876$	20.5500	0.694321
$877$	9.49477	0.320616	0.160308	−	0.987067i	$-0.448751\pi$
$877$	9.49477	0.320616	0.160308	+	0.987067i	$0.448751\pi$
$878$	70.1374	2.36702
$879$	16.1334	0.544166
$880$	−45.4142	−1.53091
$881$	−20.1240	−0.677993	−0.338997	−	0.940788i	$-0.610088\pi$
$881$	−20.1240	−0.677993	−0.338997	+	0.940788i	$0.610088\pi$
$882$	8.42443	0.283665
$883$	4.15911	0.139965	0.0699826	−	0.997548i	$-0.477706\pi$
$883$	4.15911	0.139965	0.0699826	+	0.997548i	$0.477706\pi$
$884$	3.35166	0.112729
$885$	38.6490	1.29917
$886$	12.0645	0.405315
$887$	41.2229	1.38413	0.692065	−	0.721835i	$-0.256701\pi$
$887$	41.2229	1.38413	0.692065	+	0.721835i	$0.256701\pi$
$888$	−0.154908	−0.00519836
$889$	21.6892	0.727433
$890$	−70.4672	−2.36206
$891$	4.22930	0.141687
$892$	−7.35334	−0.246208
$893$	−1.03859	−0.0347550
$894$	35.4423	1.18537
$895$	26.9153	0.899681
$896$	0.423788	0.0141578
$897$	−3.59734	−0.120112
$898$	−70.1158	−2.33980
$899$	−25.9487	−0.865439
$900$	4.15478	0.138493
$901$	6.95402	0.231672
$902$	59.8109	1.99148
$903$	−21.0881	−0.701768
$904$	0.575436	0.0191387
$905$	−29.8263	−0.991461
$906$	−16.6494	−0.553140
$907$	31.3897	1.04228	0.521139	−	0.853472i	$-0.325507\pi$
$907$	31.3897	1.04228	0.521139	+	0.853472i	$0.325507\pi$
$908$	7.41086	0.245938
$909$	−16.7993	−0.557198
$910$	14.9722	0.496324
$911$	−35.7098	−1.18312	−0.591559	−	0.806262i	$-0.701487\pi$
$911$	−35.7098	−1.18312	−0.591559	+	0.806262i	$0.701487\pi$
$912$	−29.9881	−0.993005
$913$	−43.6176	−1.44353
$914$	41.5376	1.37394
$915$	0.170896	0.00564966
$916$	−13.4209	−0.443438
$917$	15.8547	0.523568
$918$	−1.99602	−0.0658783
$919$	−26.2396	−0.865566	−0.432783	−	0.901498i	$-0.642468\pi$
$919$	−26.2396	−0.865566	−0.432783	+	0.901498i	$0.642468\pi$
$920$	−0.180230	−0.00594200
$921$	13.6503	0.449791
$922$	31.0846	1.02372
$923$	−2.42639	−0.0798656
$924$	−13.9895	−0.460220
$925$	−10.2085	−0.335654
$926$	−24.2441	−0.796711
$927$	−13.0844	−0.429749
$928$	−42.6044	−1.39856
$929$	6.69586	0.219684	0.109842	−	0.993949i	$-0.464965\pi$
$929$	6.69586	0.219684	0.109842	+	0.993949i	$0.464965\pi$
$930$	−25.8505	−0.847672
$931$	−31.3942	−1.02890
$932$	11.6707	0.382286
$933$	−0.320409	−0.0104897
$934$	−52.2704	−1.71034
$935$	11.2646	0.368391
$936$	0.0536784	0.00175453
$937$	35.2317	1.15097	0.575485	−	0.817813i	$-0.304813\pi$
$937$	35.2317	1.15097	0.575485	+	0.817813i	$0.304813\pi$
$938$	−31.9667	−1.04375
$939$	−21.1775	−0.691102
$940$	−0.737864	−0.0240665
$941$	−19.8776	−0.647993	−0.323996	−	0.946058i	$-0.605027\pi$
$941$	−19.8776	−0.647993	−0.323996	+	0.946058i	$0.605027\pi$
$942$	−1.99602	−0.0650337
$943$	15.0879	0.491330
$944$	−58.5015	−1.90406
$945$	−4.44039	−0.144446
$946$	−106.781	−3.47176
$947$	−4.59456	−0.149303	−0.0746515	−	0.997210i	$-0.523784\pi$
$947$	−4.59456	−0.149303	−0.0746515	+	0.997210i	$0.523784\pi$
$948$	15.7701	0.512188
$949$	17.4966	0.567964
$950$	−31.0903	−1.00870
$951$	6.91183	0.224131
$952$	−0.0529752	−0.00171693
$953$	5.69670	0.184534	0.0922671	−	0.995734i	$-0.470589\pi$
$953$	5.69670	0.184534	0.0922671	+	0.995734i	$0.470589\pi$
$954$	−13.8803	−0.449393
$955$	−3.21886	−0.104160
$956$	42.4463	1.37281
$957$	−22.5697	−0.729576
$958$	41.4048	1.33773
$959$	−27.7026	−0.894564
$960$	−20.9672	−0.676713
$961$	−7.35628	−0.237299
$962$	16.4376	0.529971
$963$	0.753252	0.0242732
$964$	23.6482	0.761657
$965$	58.6856	1.88916
$966$	−7.08629	−0.227998
$967$	−11.8785	−0.381987	−0.190994	−	0.981591i	$-0.561171\pi$
$967$	−11.8785	−0.381987	−0.190994	+	0.981591i	$0.561171\pi$
$968$	0.218839	0.00703375
$969$	7.43829	0.238952
$970$	−79.6335	−2.55688
$971$	5.61436	0.180173	0.0900867	−	0.995934i	$-0.471286\pi$
$971$	5.61436	0.180173	0.0900867	+	0.995934i	$0.471286\pi$
$972$	1.98408	0.0636394
$973$	−23.1217	−0.741248
$974$	−49.8077	−1.59594
$975$	3.53744	0.113289
$976$	−0.258679	−0.00828011
$977$	−24.0109	−0.768175	−0.384088	−	0.923297i	$-0.625484\pi$
$977$	−24.0109	−0.768175	−0.384088	+	0.923297i	$0.625484\pi$
$978$	9.95954	0.318471
$979$	56.0588	1.79165
$980$	−22.3040	−0.712476
$981$	−2.83093	−0.0903846
$982$	2.34726	0.0749040
$983$	−30.4793	−0.972140	−0.486070	−	0.873920i	$-0.661570\pi$
$983$	−30.4793	−0.972140	−0.486070	+	0.873920i	$0.661570\pi$
$984$	−0.225137	−0.00717710
$985$	−35.1138	−1.11882
$986$	10.6518	0.339222
$987$	0.232779	0.00740943
$988$	24.9306	0.793148
$989$	−26.9367	−0.856538
$990$	−22.4843	−0.714598
$991$	23.2017	0.737026	0.368513	−	0.929623i	$-0.379867\pi$
$991$	23.2017	0.737026	0.368513	+	0.929623i	$0.379867\pi$
$992$	38.8199	1.23253
$993$	−22.7265	−0.721204
$994$	−4.77967	−0.151602
$995$	−36.5003	−1.15714
$996$	−20.4622	−0.648371
$997$	−32.5263	−1.03012	−0.515058	−	0.857155i	$-0.672230\pi$
$997$	−32.5263	−1.03012	−0.515058	+	0.857155i	$0.672230\pi$
$998$	−35.7434	−1.13144
$999$	−4.87500	−0.154238

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.i.1.12	✓	63

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.i.1.12	✓	63	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.99602 q^{2} +1.00000 q^{3} +1.98408 q^{4} +2.66347 q^{5} -1.99602 q^{6} -1.66715 q^{7} +0.0317759 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.99602 q^{2} +1.00000 q^{3} +1.98408 q^{4} +2.66347 q^{5} -1.99602 q^{6} -1.66715 q^{7} +0.0317759 q^{8} +1.00000 q^{9} -5.31632 q^{10} +4.22930 q^{11} +1.98408 q^{12} +1.68928 q^{13} +3.32765 q^{14} +2.66347 q^{15} -4.03159 q^{16} +1.00000 q^{17} -1.99602 q^{18} +7.43829 q^{19} +5.28453 q^{20} -1.66715 q^{21} -8.44174 q^{22} -2.12952 q^{23} +0.0317759 q^{24} +2.09406 q^{25} -3.37182 q^{26} +1.00000 q^{27} -3.30775 q^{28} -5.33652 q^{29} -5.31632 q^{30} +4.86248 q^{31} +7.98356 q^{32} +4.22930 q^{33} -1.99602 q^{34} -4.44039 q^{35} +1.98408 q^{36} -4.87500 q^{37} -14.8469 q^{38} +1.68928 q^{39} +0.0846342 q^{40} -7.08513 q^{41} +3.32765 q^{42} +12.6492 q^{43} +8.39126 q^{44} +2.66347 q^{45} +4.25055 q^{46} -0.139627 q^{47} -4.03159 q^{48} -4.22062 q^{49} -4.17977 q^{50} +1.00000 q^{51} +3.35166 q^{52} +6.95402 q^{53} -1.99602 q^{54} +11.2646 q^{55} -0.0529752 q^{56} +7.43829 q^{57} +10.6518 q^{58} +14.5108 q^{59} +5.28453 q^{60} +0.0641631 q^{61} -9.70559 q^{62} -1.66715 q^{63} -7.87214 q^{64} +4.49933 q^{65} -8.44174 q^{66} -9.60638 q^{67} +1.98408 q^{68} -2.12952 q^{69} +8.86309 q^{70} -1.43635 q^{71} +0.0317759 q^{72} +10.3575 q^{73} +9.73058 q^{74} +2.09406 q^{75} +14.7582 q^{76} -7.05086 q^{77} -3.37182 q^{78} +7.94830 q^{79} -10.7380 q^{80} +1.00000 q^{81} +14.1420 q^{82} -10.3132 q^{83} -3.30775 q^{84} +2.66347 q^{85} -25.2480 q^{86} -5.33652 q^{87} +0.134390 q^{88} +13.2549 q^{89} -5.31632 q^{90} -2.81627 q^{91} -4.22513 q^{92} +4.86248 q^{93} +0.278698 q^{94} +19.8116 q^{95} +7.98356 q^{96} +14.9790 q^{97} +8.42443 q^{98} +4.22930 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * q^99

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